Minkowski Spacetime A Hundred Years Later
Petkov, Vesselin
2009-01-01
This volume is dedicated to the one hundredth anniversary of the publication of Hermann Minkowski's paper "Space and Time" in 1909. His work on the spacetime representation of special relativity had a huge impact on the twentieth century physics to the extent that modern physics would be impossible without the notion of spacetime. While there is consensus on the mathematical significance of spacetime in theoretical physics, for a hundred years there has been no consensus on the nature of spacetime itself. We owe Minkowski a clear answer to the question of the nature of spacetime -- whether it is only a mathematical space or represents a real four-dimensional world. A century after its publication the original Minkowski paper still represents an enrichment to the physicists, especially the relativists, who read it with the intent to fully investigate the depth of Minkowski's ideas on space and time and the physical meaning of special relativity. The volume begins with an excellent retranslation of Minkowski's ...
Dynamics of quantum entanglement in de Sitter spacetime and thermal Minkowski spacetime
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Zhiming Huang
2017-10-01
Full Text Available We investigate the dynamics of entanglement between two atoms in de Sitter spacetime and in thermal Minkowski spacetime. We treat the two-atom system as an open quantum system which is coupled to a conformally coupled massless scalar field in the de Sitter invariant vacuum or to a thermal bath in the Minkowski spacetime, and derive the master equation that governs its evolution. We compare the phenomena of entanglement creation, degradation, revival and enhancement for the de Sitter spacetime case with that for the thermal Minkowski spacetime case. We find that the entanglement dynamics of two atoms for these two spacetime cases behave quite differently. In particular, the two atoms interacting with the field in the thermal Minkowski spacetime (with the field in the de Sitter-invariant vacuum, under certain conditions, could be entangled, while they would not become entangled in the corresponding de Sitter case (in the corresponding thermal Minkowski case. Thus, although a single static atom in the de Sitter-invariant vacuum responds as if it were bathed in thermal radiation in a Minkowski universe, with the help of the different dynamic evolution behaviors of entanglement for two atoms one can in principle distinguish these two universes.
Minkowski space-time is locally extendible
International Nuclear Information System (INIS)
Beem, J.K.
1980-01-01
An example of a real analytic local extension of Minkowski space-time is given in this note. This local extension is not across points of the b-boundary since Minkowski space-time has an empty b-boundary. Furthermore, this local extension is not across points of the causal boundary. The example indicates that the concept of local inextendibility may be less useful than originally envisioned. (orig.)
We live in the quantum 4-dimensional Minkowski space-time
Hwang, W-Y. Pauchy
2015-01-01
We try to define "our world" by stating that "we live in the quantum 4-dimensional Minkowski space-time with the force-fields gauge group $SU_c(3) \\times SU_L(2) \\times U(1) \\times SU_f(3)$ built-in from the outset". We begin by explaining what "space" and "time" are meaning for us - the 4-dimensional Minkowski space-time, then proceeding to the quantum 4-dimensional Minkowski space-time. In our world, there are fields, or, point-like particles. Particle physics is described by the so-called ...
Explicit Minkowski invariance and differential calculus in the quantum space-time
International Nuclear Information System (INIS)
Xu Zhan.
1991-11-01
In terms of the R-circumflex matrix of the quantum group SL q (2), the explicit Minkowski coordinate commutation relations in the four-dimensional quantum space-time are given, and the invariance of the Minkowski metric is shown. The differential calculus in this quantum space-time is discussed and the corresponding commutation relations are proposed. (author). 17 refs
Poincare covariance and κ-Minkowski spacetime
International Nuclear Information System (INIS)
Dabrowski, Ludwik; Piacitelli, Gherardo
2011-01-01
A fully Poincare covariant model is constructed as an extension of the κ-Minkowski spacetime. Covariance is implemented by a unitary representation of the Poincare group, and thus complies with the original Wigner approach to quantum symmetries. This provides yet another example (besides the DFR model), where Poincare covariance is realised a la Wigner in the presence of two characteristic dimensionful parameters: the light speed and the Planck length. In other words, a Doubly Special Relativity (DSR) framework may well be realised without deforming the meaning of 'Poincare covariance'. -- Highlights: → We construct a 4d model of noncommuting coordinates (quantum spacetime). → The coordinates are fully covariant under the undeformed Poincare group. → Covariance a la Wigner holds in presence of two dimensionful parameters. → Hence we are not forced to deform covariance (e.g. as quantum groups). → The underlying κ-Minkowski model is unphysical; covariantisation does not cure this.
Petkov, Vesselin
2010-01-01
This volume is dedicated to the centennial anniversary of Minkowski's discovery of spacetime. It contains selected papers by physicists and philosophers on the Nature and Ontology of Spacetime. The first six papers, comprising Part I of the book, provide examples of the impact of Minkowski's spacetime representation of special relativity on the twentieth century physics. Part II also contains six papers which deal with implications of Minkowski's ideas for the philosophy of space and time. The last part is represented by two papers which explore the influence of Minkowski's ideas beyond the philosophy of space and time.
On de Sitter-like and Minkowski-like spacetimes
International Nuclear Information System (INIS)
Luebbe, Christian; Kroon, Juan Antonio Valiente
2009-01-01
Friedrich's proofs for the global existence results of de Sitter-like spacetimes and of semi-global existence of Minkowski-like spacetimes (Friedrich 1986 Commun. Math. Phys. 107 587) are re-examined and discussed, making use of the extended conformal field equations and a gauge based on conformal geodesics. In this gauge, the location of the conformal boundary of the spacetimes is known a priori once the initial data have been prescribed. Thus, it provides an analysis which is conceptually and calculationally simpler.
Revisiting Special Relativity: A Natural Algebraic Alternative to Minkowski Spacetime
Chappell, James M.; Iqbal, Azhar; Iannella, Nicolangelo; Abbott, Derek
2012-01-01
Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension , with the unit imaginary producing the correct spacetime distance , and the results of Einstein’s then recently developed theory of special relativity, thus providing an explanation for Einstein’s theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary , with the Clifford bivector for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis and . We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton’s scattering formula, and a simple formulation of Dirac’s and Maxwell’s equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane. PMID:23300566
Constant scalar curvature hypersurfaces in (3 + 1) -dimensional GHMC Minkowski spacetimes
Smith, Graham
2018-06-01
We prove that every (3 + 1) -dimensional flat GHMC Minkowski spacetime which is not a translation spacetime or a Misner spacetime carries a unique foliation by spacelike hypersurfaces of constant scalar curvature. In other words, we prove that every such spacetime carries a unique time function with isochrones of constant scalar curvature. Furthermore, this time function is a smooth submersion.
Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
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James M Chappell
Full Text Available Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.
Revisiting special relativity: a natural algebraic alternative to Minkowski spacetime.
Chappell, James M; Iqbal, Azhar; Iannella, Nicolangelo; Abbott, Derek
2012-01-01
Minkowski famously introduced the concept of a space-time continuum in 1908, merging the three dimensions of space with an imaginary time dimension [Formula: see text], with the unit imaginary producing the correct spacetime distance [Formula: see text], and the results of Einstein's then recently developed theory of special relativity, thus providing an explanation for Einstein's theory in terms of the structure of space and time. As an alternative to a planar Minkowski space-time of two space dimensions and one time dimension, we replace the unit imaginary [Formula: see text], with the Clifford bivector [Formula: see text] for the plane that also squares to minus one, but which can be included without the addition of an extra dimension, as it is an integral part of the real Cartesian plane with the orthonormal basis [Formula: see text] and [Formula: see text]. We find that with this model of planar spacetime, using a two-dimensional Clifford multivector, the spacetime metric and the Lorentz transformations follow immediately as properties of the algebra. This also leads to momentum and energy being represented as components of a multivector and we give a new efficient derivation of Compton's scattering formula, and a simple formulation of Dirac's and Maxwell's equations. Based on the mathematical structure of the multivector, we produce a semi-classical model of massive particles, which can then be viewed as the origin of the Minkowski spacetime structure and thus a deeper explanation for relativistic effects. We also find a new perspective on the nature of time, which is now given a precise mathematical definition as the bivector of the plane.
From Discrete Space-Time to Minkowski Space: Basic Mechanisms, Methods and Perspectives
Finster, Felix
This survey article reviews recent results on fermion systems in discrete space-time and corresponding systems in Minkowski space. After a basic introduction to the discrete setting, we explain a mechanism of spontaneous symmetry breaking which leads to the emergence of a discrete causal structure. As methods to study the transition between discrete space-time and Minkowski space, we describe a lattice model for a static and isotropic space-time, outline the analysis of regularization tails of vacuum Dirac sea configurations, and introduce a Lorentz invariant action for the masses of the Dirac seas. We mention the method of the continuum limit, which allows to analyze interacting systems. Open problems are discussed.
Racing a quantum computer through Minkowski spacetime
International Nuclear Information System (INIS)
Biamonte, Jacob D
2010-01-01
The Lorentzian length of a timelike curve connecting both endpoints of a computation in Minkowski spacetime is smaller than the Lorentzian length of the corresponding geodesic. In this talk, I will point out some properties of spacetime that allow an inertial classical computer to outperform a quantum one, at the completion of a long journey. We will focus on a comparison between the optimal quadratic Grover speed up from quantum computing and an n=2 speedup using classical computers and relativistic effects. These results are not practical as a new model of computation, but allow us to probe the ultimate limits physics places on computers.
κ-Minkowski Spacetimes and DSR Algebras: Fresh Look and Old Problems
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Andrzej Borowiec
2010-10-01
Full Text Available Some classes of Deformed Special Relativity (DSR theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates with Poincaré generators, can be obtained by nonlinear change of generators from undeformed one. Its various realizations in terms of the standard (undeformed Weyl-Heisenberg algebra opens the way for quantum mechanical interpretation of DSR theories in terms of relativistic (Stückelberg version Quantum Mechanics. On this basis we review some recent results concerning twist realization of κ-Minkowski spacetime described as a quantum covariant algebra determining a deformation quantization of the corresponding linear Poisson structure. Formal and conceptual issues concerning quantum κ-Poincaré and κ-Minkowski algebras as well as DSR theories are discussed. Particularly, the so-called ''q-analog'' version of DSR algebra is introduced. Is deformed special relativity quantization of doubly special relativity remains an open question. Finally, possible physical applications of DSR algebra to description of some aspects of Planck scale physics are shortly recalled.
κ-Minkowski spacetime as the result of Jordanian twist deformation
International Nuclear Information System (INIS)
Borowiec, A.; Pachol, A.
2009-01-01
Two one-parameter families of twists providing κ-Minkowski * product deformed spacetime are considered: Abelian and Jordanian. We compare the derivation of quantum Minkowski space from two perspectives. The first one is the Hopf module algebra point of view, which is strictly related with Drinfeld's twisting tensor technique. The other one relies on an appropriate extension of ''deformed realizations'' of nondeformed Lorentz algebra by the quantum Minkowski algebra. This extension turns out to be de Sitter Lie algebra. We show the way both approaches are related. The second path allows us to calculate deformed dispersion relations for toy models ensuing from different twist parameters. In the Abelian case, one recovers κ-Poincare dispersion relations having numerous applications in doubly special relativity. Jordanian twists provide a new type of dispersion relations which in the minimal case (related to Weyl-Poincare algebra) takes an energy-dependent linear mass deformation form.
Minkowski spacetime and Lorentz invariance: The cart and the horse or two sides of a single coin?
Acuña, Pablo
2016-08-01
Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties-that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a constructive interpretation of special relativity-are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invariance, a misconception that in turn sheds more shadows than light on our understanding of the explanatory nature and power of Einstein's theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and unidirectional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers.
Minkowski spacetime does not apply to a homogeneously accelerating medium
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Brian Coleman
Full Text Available Home and comoving inertial frame parameters of an individual point of an idealized medium of launch length L uniformly co-accelerating between identical fixed-thrust rockets, are well known. This is not the case with the varying inter-rocket radar periods and related implications regarding a changing ‘noninertial own-length’ Λ which differs from a front rocket’s retrospective separation L from the simultaneously relatively moving rear rocket. On the other hand, the nonhomogeneous acceleration case involving every comoving frame’s unchanging perception of a contrived ‘rigor mortis’ medium (so-called ‘rigid motion’ traditionally associated with ‘Rindler coordinates’ whereby Λ=L=L, constitutes the sole extended accelerating medium scenario where the entrenched Minkowski metric is actually applicable. Paraphrasing Wolfgang Pauli, not only is Minkowski spacetime not correct [in the general sense], it is not even wrong [in the restricted sense]. Keywords: Homogeneous acceleration, Radar intervals, Minkowski metric, Rigor mortis acceleration, Medium-timed photon crossing rate, Retrospective separation
Relativistic helicity and link in Minkowski space-time
International Nuclear Information System (INIS)
Yoshida, Z.; Kawazura, Y.; Yokoyama, T.
2014-01-01
A relativistic helicity has been formulated in the four-dimensional Minkowski space-time. Whereas the relativistic distortion of space-time violates the conservation of the conventional helicity, the newly defined relativistic helicity conserves in a barotropic fluid or plasma, dictating a fundamental topological constraint. The relation between the helicity and the vortex-line topology has been delineated by analyzing the linking number of vortex filaments which are singular differential forms representing the pure states of Banach algebra. While the dimension of space-time is four, vortex filaments link, because vorticities are primarily 2-forms and the corresponding 2-chains link in four dimension; the relativistic helicity measures the linking number of vortex filaments that are proper-time cross-sections of the vorticity 2-chains. A thermodynamic force yields an additional term in the vorticity, by which the vortex filaments on a reference-time plane are no longer pure states. However, the vortex filaments on a proper-time plane remain to be pure states, if the thermodynamic force is exact (barotropic), thus, the linking number of vortex filaments conserves
On the Penrose inequality for dust null shells in the Minkowski spacetime of arbitrary dimension
International Nuclear Information System (INIS)
Mars, Marc; Soria, Alberto
2012-01-01
A particular, yet relevant, case of the Penrose inequality involves null shells propagating in the Minkowski spacetime. Despite previous claims in the literature, the validity of this inequality remains open. In this paper, we rewrite this inequality in terms of the geometry of the surface obtained by intersecting the past null cone of the original surface S with a constant time hyperplane and the 'time height' function of S over this hyperplane. We also specialize to the case when S lies in the past null cone of a point and show the validity of the corresponding inequality in any dimension (in four dimensions this inequality was proved by Tod (1985 Class. Quantum Grav. 2 L65-8). Exploiting properties of convex hypersurfaces in the Euclidean space, we write down the Penrose inequality in the Minkowski spacetime of an arbitrary dimension n + 2 as an inequality for two smooth functions on the sphere S n . We finally obtain a sufficient condition for the validity of the Penrose inequality in the four-dimensional Minkowski spacetime and show that this condition is satisfied by a large class of surfaces. (paper)
Observables and dispersion relations in κ-Minkowski spacetime
Aschieri, Paolo; Borowiec, Andrzej; Pachoł, Anna
2017-10-01
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in the case of κ-Minkowski spacetime. The corresponding quantum Poincaré-Weyl Lie algebra of in-finitesimal translations, rotations and dilatations is obtained. The d'Alembert wave operator coincides with the quadratic Casimir of quantum translations and it is deformed as in Deformed Special Relativity theories. Also momenta (infinitesimal quantum translations) are deformed, and correspondingly the Einstein-Planck relation and the de Broglie one. The energy-momentum relations (dispersion relations) are consequently deduced. These results complement those of the phenomenological literature on the subject.
Minkowski spacetime does not apply to a homogeneously accelerating medium
Coleman, Brian
Home and comoving inertial frame parameters of an individual point of an idealized medium of launch length L uniformly co-accelerating between identical fixed-thrust rockets, are well known. This is not the case with the varying inter-rocket radar periods and related implications regarding a changing 'noninertial own-length' Λ which differs from a front rocket's retrospective separation L from the simultaneously relatively moving rear rocket. On the other hand, the nonhomogeneous acceleration case involving every comoving frame's unchanging perception of a contrived 'rigor mortis' medium (so-called 'rigid motion' traditionally associated with 'Rindler coordinates') whereby Λ = L = L , constitutes the sole extended accelerating medium scenario where the entrenched Minkowski metric is actually applicable. Paraphrasing Wolfgang Pauli, not only is Minkowski spacetime not correct [in the general sense], it is not even wrong [in the restricted sense].
Coordinates system adapted to non-inertial frames in Minkowski spacetime
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Felix, Patricio; Dahia, F. [Universidade Federal de Campo Grande (UFCG), PB (Brazil)
2011-07-01
Full text: Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitation Field (in the Newtonian sense). Based on this interpretation and the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. This work has motivated the fact that according to the principle of equivalence, it is expected that some physical features of gravity cam be mimicked by accelerated frames in Minkowski spacetime. The Rindler frame, which is adapted to a family of uniformly accelerated observers, is a famous example of a non-inertial system that simulates some characteristics of a black hole's geometry. This frame has been widely investigated in the literature and here we are going to start our discussion pointing out a peculiar aspect of the Rindler frame. It is related to the remarkable characteristic that the proper acceleration 'a' of Rindler observers, which is constant along their world lines, varies according to the law a = 1/ρ in relation to the observers, where ρ corresponds to the initial distance of the observers with respect to the origin of an inertial frame. This particular dependence of a ρ is connected to the behavior of static observers in Schwarzschild geometry in the vicinity of the horizon. Indeed, if ρ denotes the radial distance of an observer to the horizon, then, the proper acceleration the observers need in order to stay at rest in their position close to the horizon is proportional to 1/ρ. Therefore the Rindler congruence and the static Schwarzschild observers have the same acceleration field
Coordinates system adapted to non-inertial frames in Minkowski spacetime
International Nuclear Information System (INIS)
Felix, Patricio; Dahia, F.
2011-01-01
Full text: Static observers in curved spacetimes may interpret their proper acceleration as the opposite of a local gravitation Field (in the Newtonian sense). Based on this interpretation and the equivalence principle, we are led to investigate congruences of timelike curves in Minkowski spacetime whose acceleration field coincides with the acceleration field of static observers of curved spaces. The congruences give rise to non-inertial frames that are examined. Specifically we find, based on the locality principle, the embedding of simultaneity hypersurfaces adapted to the non-inertial frame in an explicit form for arbitrary acceleration fields. This work has motivated the fact that according to the principle of equivalence, it is expected that some physical features of gravity cam be mimicked by accelerated frames in Minkowski spacetime. The Rindler frame, which is adapted to a family of uniformly accelerated observers, is a famous example of a non-inertial system that simulates some characteristics of a black hole's geometry. This frame has been widely investigated in the literature and here we are going to start our discussion pointing out a peculiar aspect of the Rindler frame. It is related to the remarkable characteristic that the proper acceleration 'a' of Rindler observers, which is constant along their world lines, varies according to the law a = 1/ρ in relation to the observers, where ρ corresponds to the initial distance of the observers with respect to the origin of an inertial frame. This particular dependence of a ρ is connected to the behavior of static observers in Schwarzschild geometry in the vicinity of the horizon. Indeed, if ρ denotes the radial distance of an observer to the horizon, then, the proper acceleration the observers need in order to stay at rest in their position close to the horizon is proportional to 1/ρ. Therefore the Rindler congruence and the static Schwarzschild observers have the same acceleration field a(ρ). However
Dirac spinors for doubly special relativity and κ-Minkowski noncommutative spacetime
International Nuclear Information System (INIS)
Agostini, Alessandra; Amelino-Camelia, Giovanni; Arzano, Michele
2004-01-01
We construct a Dirac equation that is consistent with one of the recently-proposed schemes for a 'doubly special relativity', a relativity with both an observer-independent velocity scale (still naturally identified with the speed-of-light constant) and an observer-independent length/momentum scale (possibly given by the Planck length/momentum). We find that the introduction of the second observer-independent scale only induces a mild deformation of the structure of Dirac spinors. We also show that our modified Dirac equation naturally arises in constructing a Dirac equation in the κ-Minkowski noncommutative spacetime. Previous, more heuristic studies had already argued for a possible role of doubly special relativity in κ-Minkowski, but remained vague on the nature of the consistency requirements that should be implemented in order to assure the observer-independence of the two scales. We find that a key role is played by the choice of a differential calculus in κ-Minkowski. A much-studied choice of the differential calculus does lead to our doubly special relativity Dirac equation, but a different scenario is encountered for another popular choice of differential calculus
κ-Minkowski representations on Hilbert spaces
International Nuclear Information System (INIS)
Agostini, Alessandra
2007-01-01
The algebra of functions on κ-Minkowski noncommutative space-time is studied as algebra of operators on Hilbert spaces. The representations of this algebra are constructed and classified. This new approach leads to a natural construction of integration in κ-Minkowski space-time in terms of the usual trace of operators
Flat slices in Minkowski space
Murchadha, Niall Ó.; Xie, Naqing
2015-03-01
Minkowski space, flat spacetime, with a distance measure in natural units of d{{s}2}=-d{{t}2}+d{{x}2}+d{{y}2}+d{{z}2}, or equivalently, with spacetime metric diag(-1, +1, +1, +1), is recognized as a fundamental arena for physics. The Poincaré group, the set of all rigid spacetime rotations and translations, is the symmetry group of Minkowski space. The action of this group preserves the form of the spacetime metric. Each t = constant slice of each preferred coordinate system is flat. We show that there are also nontrivial non-singular representations of Minkowski space with complete flat slices. If the embedding of the flat slices decays appropriately at infinity, the only flat slices are the standard ones. However, if we remove the decay condition, we find non-trivial flat slices with non-vanishing extrinsic curvature. We write out explicitly the coordinate transformation to a frame with such slices.
International Nuclear Information System (INIS)
Chu, Yi-Zen
2014-01-01
Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes – particularly around black holes – we show how, for certain classes of geometries, one might obtain its retarded or advanced minimally coupled massless scalar Green's function by using the corresponding Green's functions in the higher dimensional Minkowski spacetime where it is embedded. Analogous statements hold for certain classes of curved Riemannian spaces, with positive definite metrics, which may be embedded in higher dimensional Euclidean spaces. The general formula is applied to (d ≥ 2)-dimensional de Sitter spacetime, and the scalar Green's function is demonstrated to be sourced by a line emanating infinitesimally close to the origin of the ambient (d + 1)-dimensional Minkowski spacetime and piercing orthogonally through the de Sitter hyperboloids of all finite sizes. This method does not require solving the de Sitter wave equation directly. Only the zero mode solution to an ordinary differential equation, the “wave equation” perpendicular to the hyperboloid – followed by a one-dimensional integral – needs to be evaluated. A topological obstruction to the general construction is also discussed by utilizing it to derive a generalized Green's function of the Laplacian on the (d ≥ 2)-dimensional sphere
Extensions of the stability theorem of the Minkowski space in general relativity
Bieri, Lydia
2009-01-01
A famous result of Christodoulou and Klainerman is the global nonlinear stability of Minkowski spacetime. In this book, Bieri and Zipser provide two extensions to this result. In the first part, Bieri solves the Cauchy problem for the Einstein vacuum equations with more general, asymptotically flat initial data, and describes precisely the asymptotic behavior. In particular, she assumes less decay in the power of r and one less derivative than in the Christodoulou-Klainerman result. She proves that in this case, too, the initial data, being globally close to the trivial data, yields a solution which is a complete spacetime, tending to the Minkowski spacetime at infinity along any geodesic. In contrast to the original situation, certain estimates in this proof are borderline in view of decay, indicating that the conditions in the main theorem on the decay at infinity on the initial data are sharp. In the second part, Zipser proves the existence of smooth, global solutions to the Einstein-Maxwell equations. A n...
The Historical Origins of Spacetime
Walter, Scott
The idea of spacetime investigated in this chapter, with a view toward understanding its immediate sources and development, is the one formulated and proposed by Hermann Minkowski in 1908. Until recently, the principle source used to form historical narratives of Minkowski's discovery of spacetime has been Minkowski's own discovery account, outlined in the lecture he delivered in Cologne, entitled Space and time [1]. Minkowski's lecture is usually considered as a bona fide first-person narrative of lived events. According to this received view, spacetime was a natural outgrowth of Felix Klein's successful project to promote the study of geometries via their characteristic groups of transformations. Or as Minkowski expressed the same basic thought himself, the theory of relativity discovered by physicists in 1905 could just as well have been proposed by some late-nineteenth-century mathematician, by simply reflecting upon the groups of transformations that left invariant the form of the equation of a propagating light wave. Minkowski's publications and research notes provide a contrasting picture of the discovery of spacetime, in which group theory plays no direct part. In order to relate the steps of Minkowski's discovery, we begin with an account of Poincaré's theory of gravitation, where Minkowski found some of the germs of spacetime. Poincaré's geometric interpretation of the Lorentz transformation is examined, along with his reasons for not pursuing a four-dimensional vector calculus. In the second section, Minkowski's discovery and presentation of the notion of a world line in spacetime is presented. In the third and final section, Poincaré's and Minkowski's diagrammatic interpretations of the Lorentz transformation are compared.
Fermion fields in η-ξ spacetime
International Nuclear Information System (INIS)
Gui, Y.
1992-01-01
Fermion fields in η-ζ spacetime are discussed. By the path-integral formulation of quantum field theory, we show that the (zero-temperature) Green's functions for Dirac fields on the Euclidean section in η-ζ spacetime are equal to the imaginary-time thermal Green's functions in Minkowski spacetime, and that the (zero-temperature) Green's functions on the Lorentzian section in η-ζ spacetime correspond to the real-time thermal Green's functions in Minkowski spacetime. The antiperiodicity of fermion fields in η-ζ spacetime originates from Lorentz transformation properties of the fields
Antigravity from a spacetime defect
Klinkhamer, F. R.; Queiruga, J. M.
2018-01-01
We argue that there may exist spacetime defects embedded in Minkowski spacetime, which have negative active gravitational mass. One such spacetime defect then repels a test particle, corresponding to what may be called "antigravity."
Inconsistency of Minkowski higher-derivative theories
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Aglietti, Ugo G. [Universita di Roma ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); Anselmi, Damiano [Universita di Pisa, Dipartimento di Fisica ' ' Enrico Fermi' ' , Pisa (Italy); INFN, Sezione di Pisa, Pisa (Italy)
2017-02-15
We show that Minkowski higher-derivative quantum field theories are generically inconsistent, because they generate nonlocal, non-hermitian ultraviolet divergences, which cannot be removed by means of standard renormalization procedures. By ''Minkowski theories'' we mean theories that are defined directly in Minkowski spacetime. The problems occur when the propagators have complex poles, so that the correlation functions cannot be obtained as the analytic continuations of their Euclidean versions. The usual power counting rules fail and are replaced by much weaker ones. Self-energies generate complex divergences proportional to inverse powers of D'Alembertians. Three-point functions give more involved nonlocal divergences, which couple to infrared effects. We illustrate the violations of the locality and hermiticity of counterterms in scalar models and higher-derivative gravity. (orig.)
Constraints on spacetime anisotropy and Lorentz violation from the GRAAL experiment
Energy Technology Data Exchange (ETDEWEB)
Chang, Zhe [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China); Chinese Academy of Sciences, Theoretical Physics Center for Science Facilities, Beijing (China); Wang, Sai [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)
2013-02-15
The GRAAL experiment could constrain the variations of the speed of light. The anisotropy of the speed of light may imply that the spacetime is anisotropic. Finsler geometry is a reasonable candidate to deal with the spacetime anisotropy. In this paper, the Lorentz invariance violation (LIV) of the photon sector is investigated in the locally Minkowski spacetime. The locally Minkowski spacetime is a class of flat Finsler spacetime and refers a metric with the anisotropic departure from the Minkowski one. The LIV matrices used to fit the experimental data are represented in terms of these metric deviations. The GRAAL experiment constrains the spacetime anisotropy to be less than 10{sup -14}. In addition, we find that the simplest Finslerian photon sector could be viewed as a geometric representation of the photon sector in the minimal standard model extension (SME). (orig.)
Quantum field in η-ξ spacetime
International Nuclear Information System (INIS)
Gui, Y.
1990-01-01
A new spacetime, η-ξ spacetime, is constructed. The quantum field in η-ξ spacetime is discussed. It is shown that the vacuum state of quantum field in η-ξ spacetime is a thermal state for an inertial observer in Minkowski spacetime, and the vacuum Green's functions in η-ξ spacetime are just the thermal Green's functions in usual statistical mechanics
Nonextreme and ultraextreme domain walls and their global space-times
International Nuclear Information System (INIS)
Cvetic, M.; Griffies, S.; Soleng, H.H.
1993-01-01
Nonextreme walls (bubbles with two insides) and ultraextreme walls (bubbles of false vacuum decay) are discussed. Their respective energy densities are higher and lower than that of the corresponding extreme (supersymmetric), planar domain wall. These singularity free space-times exhibit nontrivial causal structure analogous to certain nonextreme black holes. We focus on anti--de Sitter--Minkowski walls and comment on Minkowski-Minkowski walls with trivial extreme limit, as well as walls adjacent to de Sitter space-times with no extreme limit
Scalar field propagation in the phi^4 kappa-Minkowski model
Meljanac, S.; Samsarov, A.; Trampetic, J.; Wohlgenannt, M.
2011-01-01
In this article we use the noncommutative (NC) kappa-Minkowski phi^4 model based on the kappa-deformed star product, ({*}_h). The action is modified by expanding up to linear order in the kappa-deformation parameter a, producing an effective model on commutative spacetime. For the computation of the tadpole diagram contributions to the scalar field propagation/self-energy, we anticipate that statistics on the kappa-Minkowski is specifically kappa-deformed. Thus our prescription in fact repres...
Spacetime and Euclidean geometry
Brill, Dieter; Jacobson, Ted
2006-04-01
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem.
Hyperbolic statics in space-time
Pavlov, Dmitry; Kokarev, Sergey
2014-01-01
Based on the concept of material event as an elementary material source that is concentrated on metric sphere of zero radius --- light-cone of Minkowski space-time, we deduce the analog of Coulomb's law for hyperbolic space-time field universally acting between the events of space-time. Collective field that enables interaction of world lines of a pair of particles at rest contains a standard 3-dimensional Coulomb's part and logarithmic addendum. We've found that the Coulomb's part depends on...
Scalar field propagation in the ϕ 4 κ-Minkowski model
Meljanac, S.; Samsarov, A.; Trampetić, J.; Wohlgenannt, M.
2011-12-01
In this article we use the noncommutative (NC) κ-Minkowski ϕ 4 model based on the κ-deformed star product, (★ h ). The action is modified by expanding up to linear order in the κ-deformation parameter a, producing an effective model on commutative spacetime. For the computation of the tadpole diagram contributions to the scalar field propagation/self-energy, we anticipate that statistics on the κ-Minkowski is specifically κ-deformed. Thus our prescription in fact represents hybrid approach between standard quantum field theory (QFT) and NCQFT on the κ-deformed Minkowski spacetime, resulting in a κ-effective model. The propagation is analyzed in the framework of the two-point Green's function for low, intermediate, and for the Planckian propagation energies, respectively. Semiclassical/hybrid behavior of the first order quantum correction do show up due to the κ-deformed momentum conservation law. For low energies, the dependence of the tadpole contribution on the deformation parameter a drops out completely, while for Planckian energies, it tends to a fixed finite value. The mass term of the scalar field is shifted and these shifts are very different at different propagation energies. At the Planck-ian energies we obtain the direction dependent κ-modified dispersion relations. Thus our κ-effective model for the massive scalar field shows a birefringence effect.
Relativistic positioning in Schwarzschild space-time
International Nuclear Information System (INIS)
Puchades, Neus; Sáez, Diego
2015-01-01
In the Schwarzschild space-time created by an idealized static spherically symmetric Earth, two approaches -based on relativistic positioning- may be used to estimate the user position from the proper times broadcast by four satellites. In the first approach, satellites move in the Schwarzschild space-time and the photons emitted by the satellites follow null geodesics of the Minkowski space-time asymptotic to the Schwarzschild geometry. This assumption leads to positioning errors since the photon world lines are not geodesics of any Minkowski geometry. In the second approach -the most coherent one- satellites and photons move in the Schwarzschild space-time. This approach is a first order one in the dimensionless parameter GM/R (with the speed of light c=1). The two approaches give different inertial coordinates for a given user. The differences are estimated and appropriately represented for users located inside a great region surrounding Earth. The resulting values (errors) are small enough to justify the use of the first approach, which is the simplest and the most manageable one. The satellite evolution mimics that of the GALILEO global navigation satellite system. (paper)
q-conformally covariant q-Minkowski space-time and invariant equations
International Nuclear Information System (INIS)
Dobrev, V.K.
1997-09-01
We present explicitly the covariant action of the q-conformal algebra on the q-Minkowski space we proposed earlier. We also present some q-conformally invariant equations, namely a hierarchy of q-Maxwell equations, and also a q-d'Alembert equation, proposed earlier by us, in a form different from the original . (author). 19 refs
International Nuclear Information System (INIS)
Loran, Farhang
2004-01-01
We solve Klein-Gordon equation for massless scalars on (d+1)-dimensional Minkowski (Euclidean) space in terms of the Cauchy data on the hypersurface t=0. By inserting the solution into the action of massless scalars in Minkowski (Euclidean) space we obtain the action of dual theory on the boundary t=0 which is exactly the holographic dual of conformally coupled scalars on (d+1)-dimensional (Euclidean anti) de Sitter space obtained in (A)dS/CFT correspondence. The observed equivalence of dual theories is explained using the one-to-one map between conformally coupled scalar fields on Minkowski (Euclidean) space and (Euclidean anti) de Sitter space which is an isomorphism between the hypersurface t=0 of Minkowski (Euclidean) space and the boundary of (A)dS space
Fermi Coordinates of an Observer Moving in a Circle in Minkowski Space: Apparent Behavior of Clocks
National Research Council Canada - National Science Library
Bahder, Thomas
2000-01-01
Space-time coordinate transformations valid for arbitrarily long coordinate time are derived from global Minkowski coordinates to the Fermi coordinates of an observer moving in a circle in three-dimensional space...
Coproduct and star product in field theories on Lie-algebra noncommutative space-times
International Nuclear Information System (INIS)
Amelino-Camelia, Giovanni; Arzano, Michele
2002-01-01
We propose a new approach to field theory on κ-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the κ-Poincare coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in κ-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in κ-Minkowski field theories it is convenient to introduce the concepts of 'planar' and 'nonplanar' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times
Quantum corrections in thermal states of fermions on anti-de Sitter space-time
Ambruş, Victor E.; Winstanley, Elizabeth
2017-12-01
We study the energy density and pressure of a relativistic thermal gas of massless fermions on four-dimensional Minkowski and anti-de Sitter space-times using relativistic kinetic theory. The corresponding quantum field theory quantities are given by components of the renormalized expectation value of the stress-energy tensor operator acting on a thermal state. On Minkowski space-time, the renormalized vacuum expectation value of the stress-energy tensor is by definition zero, while on anti-de Sitter space-time the vacuum contribution to this expectation value is in general nonzero. We compare the properties of the vacuum and thermal expectation values of the energy density and pressure for massless fermions and discuss the circumstances in which the thermal contribution dominates over the vacuum one.
Radiative processes of two entangled atoms in cosmic string spacetime
Cai, Huabing; Ren, Zhongzhou
2018-01-01
We investigate the radiative processes of two static two-level atoms in a maximally entangled state coupled to vacuum electromagnetic field in the cosmic string spacetime. We find that the decay rate from the entangled state to the ground state crucially depends on the atomic separation, the polarization directions of the individual atoms, the atom-string distance and the deficit angle induced by the string. As the atom-string distance increases, the decay rate oscillates around the result in Minkowski spacetime and the amplitude gradually decreases. The oscillation is more severe for larger planar angle deficit. We analyze the decay rate in different circumstances such as near zone and specific polarization cases. Some comparisons between symmetric and antisymmetric states are performed. By contrast with the case in Minkowski spacetime, we can reveal the effects of the cosmic string on the radiative properties of the entangled atoms.
A flat space-time relativistic explanation for the perihelion advance of Mercury
Behera, Harihar; Naik, P. C.
2003-01-01
Starting with the flat space-time relativistic versions of Maxwell-Heaviside's toy model vector theory of gravity and introducing the gravitational analogues for the electromagnetic Lienard-Wiechert potentials together with the notion of a gravitational Thomas Precession; the observed anomalous perihelion advance of Mercury's orbit is here explained as a relativistic effect in flat (Minkowski) space-time, unlike Einstein's curved space-time relativistic explanation. In this new explanation fo...
International Nuclear Information System (INIS)
Goncharov, Yu.P.
1982-01-01
In a spacetime having a nontrivial topology QCD may have properties which are absent for QCD in Minkowski spacetime. Two new possibilities for QCD are discussed by the example of spacetime with topology R x (S 1 ) 3 and flat metric: the topological origin of flavours and topological gluon mass generation. (orig.)
On classical de Sitter and Minkowski solutions with intersecting branes
Andriot, David
2018-03-01
Motivated by the connection of string theory to cosmology or particle physics, we study solutions of type II supergravities having a four-dimensional de Sitter or Minkowski space-time, with intersecting D p -branes and orientifold O p -planes. Only few such solutions are known, and we aim at a better characterisation. Modulo a few restrictions, we prove that there exists no classical de Sitter solution for any combination of D 3/ O 3 and D 7/ O 7, while we derive interesting constraints for intersecting D 5/ O 5 or D 6/ O 6, or combinations of D 4/ O 4 and D 8/ O 8. Concerning classical Minkowski solutions, we understand some typical features, and propose a solution ansatz. Overall, a central information appears to be the way intersecting D p / O p overlap each other, a point we focus on.
Some aspects of quantum field theory in non-Minkowskian space-times
International Nuclear Information System (INIS)
Toms, D.J.
1980-01-01
Several aspects of quantum field theory in space-times which are different from Minkowski space-time, either because of the presence of a non-zero curvature or as a consequence of the topology of the manifold, are discussed. The Casimir effect is a quantum field theory in a space-time which has a different topology. A short review of some of its popular derivations is presented with comments. Renormalization of interacting scalar field theories in a flat space-time with a non-Minkowskian topology is considered. The presence of a non-trivial topology can lead to additional non-local divergent terms in the Schwinger-Dyson equations for a general scalar field theory; however, the theory may be renormalized with the same choice of counterterms as in Minkowski space-time. Propagators can develop poles corresponding to the generation of a topological mass. Zeta-function regularization is shown to fit naturally into the functional approach to the effective potential. This formalism is used to calculate the effective potential for some scalar field theories in non-Minkowskian space-times. Topological mass generation is discussed, and it is shown how radiative corrections can lead to spontaneous symmetry breaking. One- and two-loop contributions to the vacuum energy density are obtained for both massless and massive fields. In the massive case the role of renormalization in removing non-local divergences is discussed
Special relativity derived from spacetime magma.
Greensite, Fred
2014-01-01
We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid) existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.
Special relativity derived from spacetime magma.
Directory of Open Access Journals (Sweden)
Fred Greensite
Full Text Available We present a derivation of relativistic spacetime largely untethered from specific physical considerations, in constrast to the many physically-based derivations that have appeared in the last few decades. The argument proceeds from the inherent magma (groupoid existing on the union of spacetime frame components [Formula: see text] and Euclidean [Formula: see text] which is consistent with an "inversion symmetry" constraint from which the Minkowski norm results. In this context, the latter is also characterized as one member of a class of "inverse norms" which play major roles with respect to various unital [Formula: see text]-algebras more generally.
Some New Algebraic and Topological Properties of the Minkowski Inverse in the Minkowski Space
Directory of Open Access Journals (Sweden)
Hanifa Zekraoui
2013-01-01
Full Text Available We introduce some new algebraic and topological properties of the Minkowski inverse A⊕ of an arbitrary matrix A∈Mm,n (including singular and rectangular in a Minkowski space μ. Furthermore, we show that the Minkowski inverse A⊕ in a Minkowski space and the Moore-Penrose inverse A+ in a Hilbert space are different in many properties such as the existence, continuity, norm, and SVD. New conditions of the Minkowski inverse are also given. These conditions are related to the existence, continuity, and reverse order law. Finally, a new representation of the Minkowski inverse A⊕ is also derived.
Extended Rindler spacetime and a new multiverse structure
Araya, Ignacio J.; Bars, Itzhak
2018-04-01
This is the first of a series of papers in which we use analyticity properties of quantum fields propagating on a spacetime to uncover a new multiverse geometry when the classical geometry has horizons and/or singularities. The nature and origin of the "multiverse" idea presented in this paper, that is shared by the fields in the standard model coupled to gravity, are different from other notions of a multiverse. Via analyticity we are able to establish definite relations among the universes. In this paper we illustrate these properties for the extended Rindler space, while black hole spacetime and the cosmological geometry of mini-superspace (see Appendix B) will appear in later papers. In classical general relativity, extended Rindler space is equivalent to flat Minkowski space; it consists of the union of the four wedges in (u ,v ) light-cone coordinates as in Fig. 1. In quantum mechanics, the wavefunction is an analytic function of (u ,v ) that is sensitive to branch points at the horizons u =0 or v =0 , with branch cuts attached to them. The wave function is uniquely defined by analyticity on an infinite number of sheets in the cut analytic (u ,v ) spacetime. This structure is naturally interpreted as an infinite stack of identical Minkowski geometries, or "universes", connected to each other by analyticity across branch cuts, such that each sheet represents a different Minkowski universe when (u ,v ) are analytically continued to the real axis on any sheet. We show in this paper that, in the absence of interactions, information does not flow from one Rindler sheet to another. By contrast, for an eternal black hole spacetime, which may be viewed as a modification of Rindler that includes gravitational interactions, analyticity shows how information is "lost" due to a flow to other universes, enabled by an additional branch point and cut due to the black hole singularity.
The Adolescence of Relativity: Einstein, Minkowski, and the Philosophy of Space and Time
Dieks, Dennis
An often repeated account of the genesis of special relativity tells us that relativity theory was to a considerable extent the fruit of an operationalist philosophy of science. Indeed, Einstein's 1905 paper stresses the importance of rods and clocks for giving concrete physical content to spatial and temporal notions. I argue, however, that it would be a mistake to read too much into this. Einstein's operationalist remarks should be seen as serving rhetoric purposes rather than as attempts to promulgate a particular philosophical position - in fact, Einstein never came close to operationalism in any of his philosophical writings. By focussing on what could actually be measured with rods and clocks Einstein shed doubt on the empirical status of a number of pre-relativistic concepts, with the intention to persuade his readers that the applicability of these concepts was not obvious. This rhetoric manoeuvre has not always been rightly appreciated in the philosophy of physics. Thus, the influence of operationalist misinterpretations, according to which associated operations strictly define what a concept means, can still be felt in present-day discussions about the conventionality of simultaneity.The standard story continues by pointing out that Minkowski in 1908 supplanted Einstein's approach with a realist spacetime account that has no room for a foundational role of rods and clocks: relativity theory became a description of a four-dimensional "absolute world." As it turns out, however, it is not at all clear that Minkowski was proposing a substantivalist position with respect to spacetime. On the contrary, it seems that from a philosophical point of view Minkowski's general position was not very unlike the one in the back of Einstein's mind. However, in Minkowski's formulation of special relativity it becomes more explicit that the content of spatiotemporal concepts relates to considerations about the form of physical laws. If accepted, this position has important
Cosgrove, Joseph K
2018-01-01
In 1908, three years after Einstein first published his special theory of relativity, the mathematician Hermann Minkowski introduced his four-dimensional “spacetime” interpretation of the theory. Einstein initially dismissed Minkowski’s theory, remarking that “since the mathematicians have invaded the theory of relativity I do not understand it myself anymore.” Yet Minkowski’s theory soon found wide acceptance among physicists, including eventually Einstein himself, whose conversion to Minkowski’s way of thinking was engendered by the realization that he could profitably employ it for the formulation of his new theory of gravity. The validity of Minkowski’s mathematical “merging” of space and time has rarely been questioned by either physicists or philosophers since Einstein incorporated it into his theory of gravity. Physicists often employ Minkowski spacetime with little regard to the whether it provides a true account of the physical world as opposed to a useful mathematical tool in th...
arXiv On classical de Sitter and Minkowski solutions with intersecting branes
Andriot, David
2018-03-09
Motivated by the connection of string theory to cosmology or particle physics, we study solutions of type II supergravities having a four-dimensional de Sitter or Minkowski space-time, with intersecting D$_{p}$ -branes and orientifold O$_{p}$ -planes. Only few such solutions are known, and we aim at a better characterisation. Modulo a few restrictions, we prove that there exists no classical de Sitter solution for any combination of D$_{3}$/O$_{3}$ and D$_{7}$/O$_{7}$, while we derive interesting constraints for intersecting D$_{5}$/O$_{5}$ or D$_{6}$/O$_{6}$, or combinations of D$_{4}$/O$_{4}$ and D$_{8}$/O$_{8}$. Concerning classical Minkowski solutions, we understand some typical features, and propose a solution ansatz. Overall, a central information appears to be the way intersecting D$_{p}$ /O$_{p}$ overlap each other, a point we focus on.
Space-Time, Phenomenology, and the Picture Theory of Language
Grelland, Hans Herlof
To estimate Minkowski's introduction of space-time in relativity, the case is made for the view that abstract language and mathematics carries meaning not only by its connections with observation but as pictures of facts. This view is contrasted to the more traditional intuitionism of Hume, Mach, and Husserl. Einstein's attempt at a conceptual reconstruction of space and time as well as Husserl's analysis of the loss of meaning in science through increasing abstraction is analysed. Wittgenstein's picture theory of language is used to explain how meaning is conveyed by abstract expressions, with the Minkowski space as a case.
Radar orthogonality and radar length in Finsler and metric spacetime geometry
Pfeifer, Christian
2014-09-01
The radar experiment connects the geometry of spacetime with an observers measurement of spatial length. We investigate the radar experiment on Finsler spacetimes which leads to a general definition of radar orthogonality and radar length. The directions radar orthogonal to an observer form the spatial equal time surface an observer experiences and the radar length is the physical length the observer associates to spatial objects. We demonstrate these concepts on a forth order polynomial Finsler spacetime geometry which may emerge from area metric or premetric linear electrodynamics or in quantum gravity phenomenology. In an explicit generalization of Minkowski spacetime geometry we derive the deviation from the Euclidean spatial length measure in an observers rest frame explicitly.
Quantum Space-Time Deformed Symmetries Versus Broken Symmetries
Amelino-Camelia, G
2002-01-01
Several recent studies have concerned the faith of classical symmetries in quantum space-time. In particular, it appears likely that quantum (discretized, noncommutative,...) versions of Minkowski space-time would not enjoy the classical Lorentz symmetries. I compare two interesting cases: the case in which the classical symmetries are "broken", i.e. at the quantum level some classical symmetries are lost, and the case in which the classical symmetries are "deformed", i.e. the quantum space-time has as many symmetries as its classical counterpart but the nature of these symmetries is affected by the space-time quantization procedure. While some general features, such as the emergence of deformed dispersion relations, characterize both the symmetry-breaking case and the symmetry-deformation case, the two scenarios are also characterized by sharp differences, even concerning the nature of the new effects predicted. I illustrate this point within an illustrative calculation concerning the role of space-time symm...
Quantization of a scalar field in the Kerr spacetime
International Nuclear Information System (INIS)
Ford, L.H.
1974-01-01
A discussion of field quantization in a curved background spacetime is presented, with emphasis on the quantization of a scalar field in the Kerr spacetime. The ambiguity in the choice of a Fock space is discussed. The example of quantized fields in a rotating frame of reference in Minkowski space is analyzed, and it is shown that there is a preferred choice of states which makes particle number an invariant under transformation to the rotating frame. This choice allows the existence of negative energy quanta of the field
Cosmological applications of algebraic quantum field theory in curved spacetimes
Hack, Thomas-Paul
2016-01-01
This book provides a largely self-contained and broadly accessible exposition on two cosmological applications of algebraic quantum field theory (QFT) in curved spacetime: a fundamental analysis of the cosmological evolution according to the Standard Model of Cosmology; and a fundamental study of the perturbations in inflation. The two central sections of the book dealing with these applications are preceded by sections providing a pedagogical introduction to the subject. Introductory material on the construction of linear QFTs on general curved spacetimes with and without gauge symmetry in the algebraic approach, physically meaningful quantum states on general curved spacetimes, and the backreaction of quantum fields in curved spacetimes via the semiclassical Einstein equation is also given. The reader should have a basic understanding of General Relativity and QFT on Minkowski spacetime, but no background in QFT on curved spacetimes or the algebraic approach to QFT is required.
Electromagnetic vacuum fluctuations around a cosmic string in de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Saharian, A.A.; Saharyan, N.A. [Yerevan State University, Department of Physics, Yerevan (Armenia); Manukyan, V.F. [Gyumri State Pedagogical Institute, Department of Physics and Mathematics, Gyumri (Armenia)
2017-07-15
The electromagnetic field correlators are evaluated around a cosmic string in background of (D + 1)-dimensional dS spacetime assuming that the field is prepared in the Bunch-Davies vacuum state. The correlators are presented in the decomposed form where the string-induced topological parts are explicitly extracted. With this decomposition, the renormalization of the local vacuum expectation values (VEVs) in the coincidence limit is reduced to the one for dS spacetime in the absence of the cosmic string. The VEVs of the squared electric and magnetic fields, and of the vacuum energy density are investigated. Near the string they are dominated by the topological contributions and the effects induced by the background gravitational field are small. In this region, the leading terms in the topological contributions are obtained from the corresponding VEVs for a string on the Minkowski bulk multiplying by the conformal factor. At distances from the string larger than the curvature radius of the background geometry, the pure dS parts in the VEVs dominate. In this region, for spatial dimensions D > 3, the influence of the gravitational field on the topological contributions is crucial and the corresponding behavior is essentially different from that for a cosmic string on the Minkowski bulk. There are well-motivated inflationary models which produce cosmic strings. We argue that, as a consequence of the quantum-to-classical transition of super-Hubble electromagnetic fluctuations during inflation, in the post-inflationary era these strings will be surrounded by large-scale stochastic magnetic fields. These fields could be among the distinctive features of the cosmic strings produced during the inflation and also of the corresponding inflationary models. (orig.)
Renormalization and scaling behavior of non-Abelian gauge fields in curved spacetime
International Nuclear Information System (INIS)
Leen, T.K.
1983-01-01
In this article we discuss the one loop renormalization and scaling behavior of non-Abelian gauge field theories in a general curved spacetime. A generating functional is constructed which forms the basis for both the perturbation expansion and the Ward identifies. Local momentum space representations for the vector and ghost particles are developed and used to extract the divergent parts of Feynman integrals. The one loop diagram for the ghost propagator and the vector-ghost vertex are shown to have no divergences not present in Minkowski space. The Ward identities insure that this is true for the vector propagator as well. It is shown that the above renormalizations render the three- and four-vector vertices finite. Finally, a renormalization group equation valid in curved spacetimes is derived. Its solution is given and the theory is shown to be asymptotically free as in Minkowski space
Quantum relativity theory and quantum space-time
International Nuclear Information System (INIS)
Banai, M.
1984-01-01
A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is shown that the quantum space-time models of Banai introduced in another paper is formulated in terms of Davis's quantum relativity. The recently proposed classical relativistic quantum theory of Prugovecki and his corresponding classical relativistic quantum model of space-time open the way to introduce, in a consistent way, the quantum space-time model (the quantum substitute of Minkowski space) of Banai proposed in the paper mentioned. The goal of quantum mechanics of quantum relativistic particles living in this model of space-time is to predict the rest mass system properties of classically relativistic (massive) quantum particles (''elementary particles''). The main new aspect of this quantum mechanics is that it provides a true mass eigenvalue problem, and that the excited mass states of quantum relativistic particles can be interpreted as elementary particles. The question of field theory over quantum relativistic model of space-time is also discussed. Finally it is suggested that ''quarks'' should be considered as quantum relativistic particles. (author)
International Nuclear Information System (INIS)
Hawking, S.W.; King, A.R.; McCarthy, P.J.
1976-01-01
A new topology is proposed for strongly causal space--times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal, differential, and conformal structures of space--time. The topology is more appealing, physical, and manageable than the topology previously proposed by Zeeman for Minkowski space. It thus seems that many calculations involving the above structures may be made purely topological
Spontaneous symmetry breaking in curved space-time
International Nuclear Information System (INIS)
Toms, D.J.
1982-01-01
An approach dealing with some of the complications which arise when studying spontaneous symmetry breaking beyond the tree-graph level in situations where the effective potential may not be used is discussed. These situations include quantum field theory on general curved backgrounds or in flat space-times with non-trivial topologies. Examples discussed are a twisted scalar field in S 1 xR 3 and instabilities in an expanding universe. From these it is seen that the topology and curvature of a space-time may affect the stability of the vacuum state. There can be critical length scales or times beyond which symmetries may be broken or restored in certain cases. These features are not present in Minkowski space-time and so would not show up in the usual types of early universe calculations. (U.K.)
Particle Detectors in the Theory of Quantum Fields on Curved Spacetimes
Cant, John Fraser
This work discusses aspects of a fundamental problem in the theory of quantum fields on curved spacetimes--that of giving physical meaning to the particle representations of the theory. In particular, the response of model particle detectors is analysed in detail. Unruh (1976) first introduced the idea of a model particle detector in order to give an operational definition to particles. He found that even in flat spacetime, the excitation of a particle detector does not necessarily correspond to the presence of an energy carrier--an accelerating detector will excite in response to the zero-energy state of the Minkowski vacuum. The central question I consider in this work is --where does the energy for the excitation of the accelerating detector come from? The accepted response has been that the accelerating force provides the energy. Evaluating the energy carried by the (conformally-invariant massless scalar) field after the interaction with the detector, however, I find that the detector excitation is compensated by an equal but opposite emission of negative energy. This result suggests that there may be states of lesser energy than that of the Minkowski vacuum. To resolve this paradox, I argue that the emission of a detector following a more realistic trajectory than that of constant acceleration--one that starts and finishes in inertial motion--will in total be positive, although during periods of constant acceleration the detector will still emit negative energy. The Minkowski vacuum retains its status as the field state of lowest energy. The second question I consider is the response of Unruh's detector in curved spacetime--is it possible to use such a detector to measure the energy carried by the field? In the particular case of a detector following a Killing trajectory, I find that there is a response to the energy of the field, but that there is also an inherent 'noise'. In a two dimensional model spacetime, I show that this 'noise' depends on the detector
The Green functions in curved spacetime
International Nuclear Information System (INIS)
Buchbinder, I.L.; Kirillova, E.N.; Odinstov, S.D.
1987-01-01
The theory of a free scalar field with conformal coupling in curved spacetime with some special metrics is considered. The integral representations for the green function G-tilde in the form of integrals with Schwinger-De Witt kernel over contours in the complex plane of proper time are obtained. It is shown how the transitions from a unique Green function in Euclidean space to different Green functions in Minkowski space and vice versa can be carried out. (author)
International Nuclear Information System (INIS)
Silva O, G.; Garcia G, P.
2004-01-01
In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three dimensional Minkowski metric. (Author)
Green's functions in Bianchi type-I spaces. Relation between Minkowski and Euclidean approaches
International Nuclear Information System (INIS)
Bukhbinder, I.L.; Kirillova, E.N.
1988-01-01
A theory is considered for a free scalar field with a conformal connection in a curved space-time with a Bianchi type-I metric. A representation is obtained for the Green's function G∼ in in in the form of an integral of a Schwinger-DeWitt kernel along a contour in a plane of complex-valued proper time. It is shown how as transition may be accomplished from Green's functions in space with the Euclidean signature to Green's functions in space with Minkowski signature and vice versa
Supersymmetry on a euclidean spacetime lattice 1. A target theory with four supercharges
International Nuclear Information System (INIS)
Cohen, Andrew G.; Kaplan, David B.; Katz, Emanuel; Uensal, Mithat
2003-01-01
We formulate a euclidean spacetime lattice whose continuum limit is (2,2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction described previously for spatial lattices in Minkowski space, and can be generalized to more complicated theories with additional supersymmetry and more spacetime dimensions. (author)
Quantum mechanics, stochasticity and space-time
International Nuclear Information System (INIS)
Ramanathan, R.
1986-04-01
An extended and more rigorous version of a recent proposal for an objective stochastic formulation of quantum mechanics along with its extension to the relativistic case without spin is presented. The relativistic Klein-Gordon equation is shown to be a particular form of the relativistic Kolmogorov-Fokker-Planck equation which is derived from a covariant formulation of the Chapman-Kolmogorov condition. Complexification of probability amplitudes is again achieved only through a conformal rotation of Minkowski space-time M 4 . (author)
How to use retarded Green's functions in de Sitter spacetime
International Nuclear Information System (INIS)
Higuchi, Atsushi; Cheong, Lee Yen
2008-01-01
We demonstrate in examples that the covariant retarded Green's functions in electromagnetism and linearized gravity work as expected in de Sitter spacetime. We first clarify how retarded Green's functions should be used in spacetimes with spacelike past infinity such as de Sitter spacetime. In particular, we remind the reader of a general formula which gives the field for given initial data on a Cauchy surface and a given source (a charge or stress-energy tensor distribution) in its future. We then apply this formula to three examples: (i) electromagnetism in the future of a Cauchy surface in Minkowski spacetime, (ii) electromagnetism in de Sitter spacetime, and (iii) linearized gravity in de Sitter spacetime. In each example the field is reproduced correctly as predicted by the general argument. In the third example we construct a linearized gravitational field from two equal point masses located at the 'North and South Poles' which is nonsingular on the cosmological horizon and satisfies a covariant gauge condition and show that this field is reproduced by the retarded Green's function with corresponding gauge parameters.
International Nuclear Information System (INIS)
Ogievetsky, O.; Pillin, M.; Schmidke, W.B.; Wess, J.; Zumino, B.
1993-01-01
In this lecture I discuss the algebraic structure of a q-deformed four-vector space. It serves as a good example of quantizing Minkowski space. To give a physical interpretation of such a quantized Minkowski space we construct the Hilbert space representation and find that the relevant time and space operators have a discrete spectrum. Thus the q-deformed Minkowski space has a lattice structure. Nevertheless this lattice structure is compatible with the operation of q-deformed Lorentz transformations. The generators of the q-deformed Lorentz group can be represented as linear operators in the same Hilbert space. (orig.)
The Dual Orlicz-Brunn-Minkowski Theory
Gardner, Richard J.; Hug, Daniel; Weil, Wolfgang; Ye, Deping
2014-01-01
This paper introduces the dual Orlicz-Brunn-Minkowski theory for star sets. A radial Orlicz addition of two or more star sets is proposed and a corresponding dual Orlicz-Brunn-Minkowski inequality is established. Based on a radial Orlicz linear combination of two star sets, a formula for the dual Orlicz mixed volume is derived and a corresponding dual Orlicz-Minkowski inequality proved. The inequalities proved yield as special cases the precise duals of the conjectured log-Brunn-Minkowski and...
Vacuum polarization in curved spacetime
International Nuclear Information System (INIS)
Guy, R.W.
1979-01-01
A necessary step in the process of understanding the quantum theory of gravity is the calculation of the stress-energy tensor of quantized fields in curved space-times. The determination of the stress tensor, a formally divergent object, is made possible in this dissertation by utilizing the zeta-function method of regularization and renormalization. By employing this scheme's representation of the renormalized effective action functional, an expression of the stress tensor for a massless, conformally invariant scalar field, first given by DeWitt, is derived. The form of the renormalized stress tensor is first tested in various examples of flat space-times. It is shown to vanish in Minkowski space and to yield the accepted value of the energy density in the Casimir effect. Next, the stress tensor is calculated in two space-times of constant curvature, the Einstein universe and the deSitter universe, and the results are shown to agree with those given by an expression of the stress tensor that is valid in conformally flat space-times. This work culminates in the determination of the stress tensor on the horizon of a Schwarzschild black hole. This is accomplished by approximating the radial part of the eigen-functions and the metric in the vicinity of the horizon. The stress tensor at this level approximation is found to be pure trace. The approximated forms of the Schwarzschild metric describes a conformally flat space-time that possesses horizons
Yang-Feldman formalism on noncommutative Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Doescher, C.
2006-12-15
We examine quantum field theory on noncummutative spacetime. For this we choose an approach which lives explicitly on the noncommutative Minkowski space, namely the Yang-Feldman formalism. Here the ansatz is to try to solve the field equation of the quantum fields. In this setting we first take a look at an additional mass term, and use this to discuss possible IR cutoffs. We find classes of IR cutoffs which indeed yield the expected limit. Furthermore, we look at interacting models, namely the {phi}{sup 3} model in four and six dimensions, the {phi}{sup 4} model and the Wess-Zumino model. For these we calculate dispersion relations. We see that there exist huge differences in the orders of magnitude between logarithmically and quadratically divergent models. Integrals which are made finite by twisting factors are calculated rigorously in the sense of the theory of oscillatory integrals. (orig.)
Analysis of interacting quantum field theory in curved spacetime
International Nuclear Information System (INIS)
Birrell, N.D.; Taylor, J.G.
1980-01-01
A detailed analysis of interacting quantized fields propagating in a curved background spacetime is given. Reduction formulas for S-matrix elements in terms of vacuum Green's functions are derived, special attention being paid to the possibility that the ''in'' and ''out'' vacuum states may not be equivalent. Green's functions equations are obtained and a diagrammatic representation for them given, allowing a formal, diagrammatic renormalization to be effected. Coordinate space techniques for showing renormalizability are developed in Minkowski space, for lambdaphi 3 /sub() 4,6/ field theories. The extension of these techniques to curved spacetimes is considered. It is shown that the possibility of field theories becoming nonrenormalizable there cannot be ruled out, although, allowing certain modifications to the theory, phi 3 /sub( 4 ) is proven renormalizable in a large class of spacetimes. Finally particle production from the vacuum by the gravitational field is discussed with particular reference to Schwarzschild spacetime. We shed some light on the nonlocalizability of the production process and on the definition of the S matrix for such processes
Volume sums of polar Blaschke–Minkowski homomorphisms
Indian Academy of Sciences (India)
In this article, we establish Minkowski and Aleksandrov–Fenchel type inequalities for the volume sum of polars of Blaschke–Minkowski homomorphisms. Keywords. Blaschke–Minkowski homomorphism; volume differences; volume sum; projection body operator. 2010 Mathematics Subject Classification. 52A40, 52A30. 1.
Iorio, Alfredo; Lambiase, Gaetano
2014-07-01
The solutions of many issues, of the ongoing efforts to make deformed graphene a tabletop quantum field theory in curved spacetimes, are presented. A detailed explanation of the special features of curved spacetimes, originating from embedding portions of the Lobachevsky plane into R3, is given, and the special role of coordinates for the physical realizations in graphene is explicitly shown, in general, and for various examples. The Rindler spacetime is reobtained, with new important differences with respect to earlier results. The de Sitter spacetime naturally emerges, for the first time, paving the way to future applications in cosmology. The role of the Bañados, Teitelboim, and Zanelli (BTZ) black hole is also briefly addressed. The singular boundary of the pseudospheres, "Hilbert horizon," is seen to be closely related to the event horizon of the Rindler, de Sitter, and BTZ kind. This gives new, and stronger, arguments for the Hawking phenomenon to take place. An important geometric parameter, c, overlooked in earlier work, takes here its place for physical applications, and it is shown to be related to graphene's lattice spacing, ℓ. It is shown that all surfaces of constant negative curvature, K =-r-2, are unified, in the limit c/r→0, where they are locally applicable to the Beltrami pseudosphere. This, and c=ℓ, allow us (a) to have a phenomenological control on the reaching of the horizon; (b) to use spacetimes different from the Rindler spacetime for the Hawking phenomenon; and (c) to approach the generic surface of the family. An improved expression for the thermal LDOS is obtained. A nonthermal term for the total LDOS is found. It takes into account (i) the peculiarities of the graphene-based Rindler spacetime; (ii) the finiteness of a laboratory surface; and (iii) the optimal use of the Minkowski quantum vacuum, through the choice of this Minkowski-static boundary.
Quantization of spacetime and the corresponding quantum mechanics
International Nuclear Information System (INIS)
Banai, M.
1983-11-01
An axiomatic framework for describing general space-time models is outlined. Space-time models to which irreducible propositional systems belong as causal logics are quantum(q) theoretically interpretable and their event spaces are Hilbert spaces. As a basic assumption, the time t and the radial coordinate r of a q particle satisfy the CCR (t, r)=+-i(h/2π). The two cases will be considered simultaneously. In that case the even space is the Hilbert space L 2 (IR 3 ). Unitary symmetries consist of Poincare-like symmetries: translations, rotations and inversion, and of gauge-like symmetries. Space inversion implies the time inversion. This q space-time reveals a confinement phenomenon: the q particle is 'confined' in a (h/2π) size region of Minkowski space IM 4 at any time. One particle mechanics over q space-time provides mass eigenvalue equations for elementary particles. Prugovecki's stochastic q mechanics and q space-time offer a natural way for introducing and interpreting consistently such a q space-time and q particles living in it. The mass eigenstates of q particles generate Prugovecki's extended elementary particles. When (h/2π) → 0, these particles shrink to point particles and IM 4 is recovered as the classical (c) limit of q space-time. Conceptual considerations prefer the case (t, r)=+i(h/2π) and applications in hadron physics give the fit (h/2π) approx.2/5 fermi/GeV. (author)
Log-Concavity Properties of Minkowski Valuations
Berg, Astrid; Parapatits, Lukas; Schuster, Franz E.; Weberndorfer, Manuel
2014-01-01
New Orlicz Brunn-Minkowski inequalities are established for rigid motion compatible Minkowski valuations of arbitrary degree. These extend classical log-concavity properties of intrinsic volumes and generalize seminal results of Lutwak and others. Two different approaches which refine previously employed techniques are explored. It is shown that both lead to the same class of Minkowski valuations for which these inequalities hold. An appendix by Semyon Alesker contains the proof of a new clas...
The extensions of space-time. Physics in the 8-dimensional homogeneous space D = SU(2,2)/K
International Nuclear Information System (INIS)
Barut, A.O.
1993-07-01
The Minkowski space-time is only a boundary of a bigger homogeneous space of the conformal group. The conformal group is the symmetry group of our most fundamental massless wave equations. These extended groups and spaces have many remarkable properties and physical implications. (author). 36 refs
Properties of states of low energy on cosmological spacetimes
International Nuclear Information System (INIS)
Degner, Andreas
2013-01-01
The present thesis investigates properties of a class of physical states of the quantised scalar field in FRW spacetimes, namely the states of low energy (SLE's). These states are characterised by minimising the time-smeared energy density measured by an isotropic observer, where the smearing is performed with respect to a test function f of compact support. Furthermore, they share all spatial symmetries of the spacetime. Since SLE's are Hadamard states, expectations values of observables like the energy density can be rigorously defined via the so called point-splitting method. In a first step, this procedure is applied to the explicit calculation of the energy density in SLE's for the case of de Sitter space with flat spatial sections. In particular, the e ect of the choice of the mass m and the test function f is discussed. The obtained results motivate the question whether SLE's converge to a distinguished state (namely the Bunch Davies state) when the support of f is shifted to the infinite past. It is shown that this is indeed the case, even in the more general class of asymptotic de Sitter spacetimes, where an analogon of the Bunch Davies state can be defined. This result enables the interpretation of such distinguished states to be SLE's in the infinite past, independently of the form of the smearing function f. Finally, the role of SLE's for the semiclassical backreaction problem is discussed. We derive the semiclassical Friedmann equation in a perturbative approach over Minkowski space. This equation allows for a stability analysis of Minkowski space by the investigation of asymptotic properties of solutions. We also treat this problem using a numerical method.
Lorentz violations in multifractal spacetimes
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2017-05-15
Using the recent observation of gravitational waves (GW) produced by a black-hole merger, we place a lower bound on the energy above which a multifractal spacetime would display an anomalous geometry and, in particular, violations of Lorentz invariance. In the so-called multifractional theory with q-derivatives, we show that the deformation of dispersion relations is much stronger than in generic quantum-gravity approaches (including loop quantum gravity) and, contrary to the latter, present observations on GWs can place very strong bounds on the characteristic scales at which spacetime deviates from standard Minkowski. The energy at which multifractal effects should become apparent is E{sub *} > 10{sup 14} GeV (thus improving previous bounds by 12 orders of magnitude) when the exponents in the measure are fixed to their central value 1 / 2. We also estimate, for the first time, the effect of logarithmic oscillations in the measure (corresponding to a discrete spacetime structure) and find that they do not change much the bounds obtained in their absence, unless the amplitude of the oscillations is fine tuned. This feature, unavailable in known quantum-gravity scenarios, may help the theory to avoid being ruled out by gamma-ray burst (GRB) observations, for which E{sub *} > 10{sup 17} GeV or greater. (orig.)
An anthology of non-local QFT and QFT on non-commutative spacetime
Schroer, Bert
2005-09-01
Ever since the appearance of renormalization theory, there have been several differently motivated attempts at non-localized (in the sense of not generated by pointlike fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review in the light of previous results on this subject.
An anthology of non-local QFT and QFT on non-commutative spacetime
International Nuclear Information System (INIS)
Schroer, Bert
2005-01-01
Ever since the appearance of renormalization theory, there have been several differently motivated attempts at non-localized (in the sense of not generated by pointlike fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review in the light of previous results on this subject
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail
2010-01-01
In this paper we classify cylindrically symmetric static space-times according to their teleparallel homothetic vector fields using direct integration technique. It turns out that the dimensions of the teleparallel homothetic vector fields are 4, 5, 7 or 11, which are the same in numbers as in general relativity. In case of 4, 5 or 7 proper teleparallel homothetic vector fields exist for the special choice to the space-times. In the case of 11 teleparallel homothetic vector fields the space-time becomes Minkowski with all the zero torsion components. Teleparallel homothetic vector fields in this case are exactly the same as in general relativity. It is important to note that this classification also covers the plane symmetric static space-times. (general)
Thermal ambience of expanding event horizon in Minkowski space-time
International Nuclear Information System (INIS)
Gerlach, U.H.
1983-01-01
It is shown that in flat space-time the thermal ambience of accelerated observers is not associated exclusively with flat event horizons, but arises also with (observer-dependent) event horizons that are light cones. The quanta of this ambience are characterized by a generalized frequency which identifies the representation of the Lorentz group. Global and local model detectors capable of responding to quanta of any given generalized frequency are exhibited. The discussion of the thermal ambience is implemented in terms of a partial-wave analysis using a set of harmonics on the hyperboloid x 2 +y 2 +z 2 -t 2 = 1
Global spacetime symmetries in the functional Schroedinger picture
International Nuclear Information System (INIS)
Halliwell, J.J.
1991-01-01
In the conventional functional Schroedinger quantization of field theory, the background spacetime manifold is foliated into a set of three-surfaces and the quantum state of the field is represented by a wave functional of the field configurations on each three-surface. Although this procedure may be covariantly described, the wave functionals generally fail to carry a representation of the complete spacetime symmetry group of the background, such as the Poincare group in Minkowski spacetime, because spacetime symmetries generally involve distortions or motions of the three-surfaces themselves within that spacetime. In this paper, we show that global spacetime symmetries in the functional Schroedinger picture may be represented by parametrizing the field theory---raising to the status of dynamical variables the embedding variables describing the spacetime location of each three-surface. In particular, we show that the embedding variables provide a connection between the purely geometrical operation of an isometry group on the spacetime and the operation of the usual global symmetry generators (constructed from the energy-momentum tensor) on the wave functionals of the theory. We study the path-integral representation of the wave functionals of the parametrized field theory. We show how to construct, from the path integral, wave functionals that are annihilated by the global symmetry generators, i.e., that are invariant under global spacetime symmetry groups. The invariance of the class of histories summed over in the path integral is identified as the source of the invariance of the wave functionals. We apply this understanding to a study of vacuum states in the de Sitter spacetime. We make mathematically precise a previously given heuristic argument for the de Sitter invariance of the matter wave functionals defined by the no-boundary proposal of Hartle and Hawking
Quantum field theory on curved spacetimes: Axiomatic framework and examples
International Nuclear Information System (INIS)
Fredenhagen, Klaus; Rejzner, Kasia
2016-01-01
In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.
Quantum field theory on curved spacetimes: Axiomatic framework and examples
Energy Technology Data Exchange (ETDEWEB)
Fredenhagen, Klaus [II Institut fur Theoretische Physik, Universitat Hamburg, Hamburg 22761 (Germany); Rejzner, Kasia [Department of Mathematics, University of York, York YO10 5DD (United Kingdom)
2016-03-15
In this review article, we want to expose a systematic development of quantum field theory on curved spacetimes. The leading principle is the emphasis on local properties. It turns out that this requires a reformulation of the QFT framework which also yields a new perspective for the theories on Minkowski space. The aim of the present work is to provide an almost self-contained introduction into the framework, which should be accessible for both mathematical physicists and mathematicians.
An anthology of non-local QFT and QFT on noncommutative spacetime
International Nuclear Information System (INIS)
Schroer, Bert; E-mail schroer@cbpf.br
2004-05-01
Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review of contemporary ideas in the light of previous results on this subject. (author)
Twistor Cosmology and Quantum Space-Time
International Nuclear Information System (INIS)
Brody, D.C.; Hughston, L.P.
2005-01-01
The purpose of this paper is to present a model of a 'quantum space-time' in which the global symmetries of space-time are unified in a coherent manner with the internal symmetries associated with the state space of quantum-mechanics. If we take into account the fact that these distinct families of symmetries should in some sense merge and become essentially indistinguishable in the unified regime, our framework may provide an approximate description of or elementary model for the structure of the universe at early times. The quantum elements employed in our characterisation of the geometry of space-time imply that the pseudo-Riemannian structure commonly regarded as an essential feature in relativistic theories must be dispensed with. Nevertheless, the causal structure and the physical kinematics of quantum space-time are shown to persist in a manner that remains highly analogous to the corresponding features of the classical theory. In the case of the simplest conformally flat cosmological models arising in this framework, the twistorial description of quantum space-time is shown to be effective in characterising the various physical and geometrical properties of the theory. As an example, a sixteen-dimensional analogue of the Friedmann-Robertson-Walker cosmologies is constructed, and its chronological development is analysed in some detail. More generally, whenever the dimension of a quantum space-time is an even perfect square, there exists a canonical way of breaking the global quantum space-time symmetry so that a generic point of quantum space-time can be consistently interpreted as a quantum operator taking values in Minkowski space. In this scenario, the breakdown of the fundamental symmetry of the theory is due to a loss of quantum entanglement between space-time and internal quantum degrees of freedom. It is thus possible to show in a certain specific sense that the classical space-time description is an emergent feature arising as a consequence of a
Divergence, spacetime dimension and fractal structure
International Nuclear Information System (INIS)
Nakamura, Hiroshi
2000-01-01
With a Cantor spacetime in mind, we assume the dimension of spacetime to be slightly smaller than four. Within the framework of QED, this dimension can be determined by calculating Feynman diagrams. We infer that the dimension of spacetime may be influenced by holes in space. (author)
Dai, Guowei; Romero, Alfonso; Torres, Pedro J.
2018-06-01
We study the existence of spacelike graphs for the prescribed mean curvature equation in the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime. By using a conformal change of variable, this problem is translated into an equivalent problem in the Lorentz-Minkowski spacetime. Then, by using Rabinowitz's global bifurcation method, we obtain the existence and multiplicity of positive solutions for this equation with 0-Dirichlet boundary condition on a ball. Moreover, the global structure of the positive solution set is studied.
Properties of states of low energy on cosmological spacetimes
Energy Technology Data Exchange (ETDEWEB)
Degner, Andreas
2013-01-15
The present thesis investigates properties of a class of physical states of the quantised scalar field in FRW spacetimes, namely the states of low energy (SLE's). These states are characterised by minimising the time-smeared energy density measured by an isotropic observer, where the smearing is performed with respect to a test function f of compact support. Furthermore, they share all spatial symmetries of the spacetime. Since SLE's are Hadamard states, expectations values of observables like the energy density can be rigorously defined via the so called point-splitting method. In a first step, this procedure is applied to the explicit calculation of the energy density in SLE's for the case of de Sitter space with flat spatial sections. In particular, the e ect of the choice of the mass m and the test function f is discussed. The obtained results motivate the question whether SLE's converge to a distinguished state (namely the Bunch Davies state) when the support of f is shifted to the infinite past. It is shown that this is indeed the case, even in the more general class of asymptotic de Sitter spacetimes, where an analogon of the Bunch Davies state can be defined. This result enables the interpretation of such distinguished states to be SLE's in the infinite past, independently of the form of the smearing function f. Finally, the role of SLE's for the semiclassical backreaction problem is discussed. We derive the semiclassical Friedmann equation in a perturbative approach over Minkowski space. This equation allows for a stability analysis of Minkowski space by the investigation of asymptotic properties of solutions. We also treat this problem using a numerical method.
On the differentiability of space-time
International Nuclear Information System (INIS)
Clarke, C.J.S.
1977-01-01
It is shown that the differentiability of a space-time is implied by that of its Riemann tensor, assuming a priori only boundedness of the first derivations of the metric. Consequently all the results on space-time singularities proved in earlier papers by the author hold true in C 2- space-times. (author)
Energy Technology Data Exchange (ETDEWEB)
Silva O, G.; Garcia G, P. [Facultad de Ciencias Fisico Matematicas de la Universidad Autonoma de Puebla, A.P. 1152, 72001 Puebla (Mexico)
2004-07-01
In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three dimensional Minkowski metric. (Author)
Causal fermion systems: A quantum space-time emerging from an action principle
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix [Mathematics Department, University of Regensburg (Germany)
2013-07-01
Causal fermion systems provide a general framework for the formulation of relativistic quantum theory. A particular feature is that space-time is a secondary object which emerges by minimizing an action. The aim of the talk is to give a simple introduction, with an emphasis on conceptual issues. We begin with Dirac spinors in Minkowski space and explain how to formulate the system as a causal fermion system. As an example in curved space-time, we then consider spinors on a globally hyperbolic space-time. An example on a space-time lattice illustrates that causal fermion systems also allow for the description of discrete space-times. These examples lead us to the general definition of causal fermion systems. The causal action principle is introduced. We outline how for a given minimizer, one has notions of causality, connection and curvature, which generalize the classical notions and give rise to a proposal for a ''quantum geometry''. In the last part of the talk, we outline how quantum field theory can be described in this framework and discuss the relation to other approaches.
Lorentz invariance violation and electromagnetic field in an intrinsically anisotropic spacetime
Energy Technology Data Exchange (ETDEWEB)
Chang, Zhe [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China); Chinese Academy of Sciences, Theoretical Physics Center for Science Facilities, Beijing (China); Wang, Sai [Chinese Academy of Sciences, Institute of High Energy Physics, Beijing (China)
2012-09-15
Recently, Kostelecky [V.A. Kostelecky, Phys. Lett. B 701, 137 (2011)] proposed that the spontaneous Lorentz invariance violation (sLIV) is related to Finsler geometry. Finsler spacetime is intrinsically anisotropic and naturally induces Lorentz invariance violation (LIV). In this paper, the electromagnetic field is investigated in locally Minkowski spacetime. The Lagrangian is presented explicitly for the electromagnetic field. It is compatible with the one in the standard model extension (SME). We show the Lorentz-violating Maxwell equations as well as the electromagnetic wave equation. The formal plane wave solution is obtained for the electromagnetic wave. The speed of light may depend on the direction of light and the lightcone may be enlarged or narrowed. The LIV effects could be viewed as influence from an anisotropic media on the electromagnetic wave. In addition, birefringence of light will not emerge at the leading order in this model. A constraint on the spacetime anisotropy is obtained from observations on gamma-ray bursts (GRBs). (orig.)
The real meaning of complex Minkowski-space world-lines
Energy Technology Data Exchange (ETDEWEB)
Adamo, T M [University of Oxford, Mathematical Institute, 24-29 St Giles, Oxford, OX1 3LB (United Kingdom); Newman, E T, E-mail: newman@pitt.ed [University of Pittsburgh, Department of Physics and Astronomy, Pittsburgh, PA 15213 (United States)
2010-04-07
In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.
The real meaning of complex Minkowski-space world-lines
International Nuclear Information System (INIS)
Adamo, T M; Newman, E T
2010-01-01
In connection with the study of shear-free null geodesics in Minkowski space, we investigate the real geometric effects in real Minkowski space that are induced by and associated with complex world-lines in complex Minkowski space. It was already known, in a formal manner, that complex analytic curves in complex Minkowski space induce shear-free null geodesic congruences. Here we look at the direct geometric connections of the complex line and the real structures. Among other items, we show, in particular, how a complex world-line projects into the real Minkowski space in the form of a real shear-free null geodesic congruence.
Spacetime algebra as a powerful tool for electromagnetism
Energy Technology Data Exchange (ETDEWEB)
Dressel, Justin, E-mail: prof.justin.dressel@gmail.com [Department of Electrical and Computer Engineering, University of California, Riverside, CA 92521 (United States); Center for Emergent Matter Science (CEMS), RIKEN, Wako-shi, Saitama, 351-0198 (Japan); Bliokh, Konstantin Y. [Center for Emergent Matter Science (CEMS), RIKEN, Wako-shi, Saitama, 351-0198 (Japan); Interdisciplinary Theoretical Science Research Group (iTHES), RIKEN, Wako-shi, Saitama, 351-0198 (Japan); Nori, Franco [Center for Emergent Matter Science (CEMS), RIKEN, Wako-shi, Saitama, 351-0198 (Japan); Physics Department, University of Michigan, Ann Arbor, MI 48109-1040 (United States)
2015-08-08
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann–Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric–magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.
Spacetime algebra as a powerful tool for electromagnetism
Dressel, Justin; Bliokh, Konstantin Y.; Nori, Franco
2015-08-01
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry, with a particular focus on its intrinsic (and often overlooked) complex structure. Notably, the scalar imaginary that appears throughout the electromagnetic theory properly corresponds to the unit 4-volume of spacetime itself, and thus has physical meaning. The electric and magnetic fields are combined into a single complex and frame-independent bivector field, which generalizes the Riemann-Silberstein complex vector that has recently resurfaced in studies of the single photon wavefunction. The complex structure of spacetime also underpins the emergence of electromagnetic waves, circular polarizations, the normal variables for canonical quantization, the distinction between electric and magnetic charge, complex spinor representations of Lorentz transformations, and the dual (electric-magnetic field exchange) symmetry that produces helicity conservation in vacuum fields. This latter symmetry manifests as an arbitrary global phase of the complex field, motivating the use of a complex vector potential, along with an associated transverse and gauge-invariant bivector potential, as well as complex (bivector and scalar) Hertz potentials. Our detailed treatment aims to encourage the use of spacetime algebra as a readily available and mature extension to existing vector calculus and tensor methods that can greatly simplify the analysis of fundamentally relativistic objects like the electromagnetic field.
On the instability of Minkowski space
International Nuclear Information System (INIS)
Castagnino, M.A.; Paz, J.P.
1985-01-01
We study the stability of Minkowski space under global conformal fluctuations in the framework of QFT in curved space. We obtain that when a scalar massive free field is present, Minkowski space is an unstable solution of the semiclassical cosmological problem. We also study the consequences of considering a nonlinear gravitational action. (orig.)
Blaschke- and Minkowski-endomorphisms of convex bodies
DEFF Research Database (Denmark)
Kiderlen, Markus
2006-01-01
We consider maps of the family of convex bodies in Euclidean d-dimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d>2, a representation theorem for such maps......-endomorphisms, where additivity is now understood with respect to Blaschke-addition. Using a special mixed volume, an adjoining operator can be introduced. This operator allows one to identify the class of Blaschke-endomorphisms with the class of weakly monotonic, non-degenerate and translation-covariant Minkowski...
Newtonian gravity on quantum spacetime
Directory of Open Access Journals (Sweden)
Majid Shahn
2014-04-01
Full Text Available The bicrossproduct model λ-Minkowski (or ‘κ-Minkowski’ quantum space-time has an anomaly for the action of the Poincaré quantum group which was resolved by an extra cotangent direction θ’ not visible classically. We show that gauging a coefficient of θ′ introduces gravity into the model. We solve and analyse the model nonrelativisticaly in a 1/r potential, finding an induced constant term in the effective potential energy and a weakening and separation of the effective gravitational and inertial masses as the test particle Klein-Gordon mass increases. The present work is intended as a proof of concept but the approach could be relevant to an understanding of dark energy and possibly to macroscopic quantum systems.
Optical Properties of Quantum Vacuum. Space-Time Engineering
International Nuclear Information System (INIS)
Gevorkyan, A. S.; Gevorkyan, A. A.
2011-01-01
The propagation of electromagnetic waves in the vacuum is considered taking into account quantum fluctuations in the limits of Maxwell-Langevin (ML) type stochastic differential equations. For a model of fluctuations, type of 'white noise', using ML equations a partial differential equation of second order is obtained which describes the quantum distribution of virtual particles in vacuum. It is proved that in order to satisfy observed facts, the Lamb Shift etc, the virtual particles should be quantized in unperturbed vacuum. It is shown that the quantized virtual particles in toto (approximately 86 percent) are condensed on the 'ground state' energy level. It is proved that the extension of Maxwell electrodynamics with inclusion of quantum vacuum fluctuations may be constructed on a 6D space-time continuum, where 4D is Minkowski space-time and 2D is a compactified subspace. In detail is studied of vacuum's refraction indexes under the influence of external electromagnetic fields.
Deformed Spacetime Geometrizing Interactions in Four and Five Dimensions
Cardone, Fabio
2007-01-01
This volume provides a detailed discussion of the mathematical aspects and the physical applications of a new geometrical structure of space-time, based on a generalization ("deformation") of the usual Minkowski space, as supposed to be endowed with a metric whose coefficients depend on the energy. Such a formalism (Deformed Special Relativity, DSR) allows one to account for breakdown of local Lorentz invariance in the usual, special-relativistic meaning (however, Lorentz invariance is recovered in a generalized sense) to provide an effective geometrical description of the four fundamental interactions (electromagnetic, weak, strong and gravitational) Moreover, the four-dimensional energy-dependent space-time is just a manifestation of a larger, five-dimensional space in which energy plays the role of a fifth (non-compactified) dimension. This new five-dimensional scheme (Deformed Relativity in Five Dimensions, DR5) represents a true generalization of the usual Kaluza-Klein (KK) formalism. The mathematical pr...
On extracting physical content from asymptotically flat spacetime metrics
International Nuclear Information System (INIS)
Kozameh, C; Newman, E T; Silva-Ortigoza, G
2008-01-01
A major issue in general relativity, from its earliest days to the present, is how to extract physical information from any solution or class of solutions to the Einstein equations. Though certain information can be obtained for arbitrary solutions, e.g., via geodesic deviation, in general, because of the coordinate freedom, it is often hard or impossible to do. Most of the time information is found from special conditions, e.g. degenerate principle null vectors, weak fields close to Minkowski space (using coordinates close to Minkowski coordinates), or from solutions that have symmetries or approximate symmetries. In the present work, we will be concerned with asymptotically flat spacetimes where the approximate symmetry is the Bondi-Metzner-Sachs group. For these spaces the Bondi 4-momentum vector and its evolution, found from the Weyl tensor at infinity, describes the total energy-momentum of the interior source and the energy-momentum radiated. By generalizing the structures (shear-free null geodesic congruences) associated with the algebraically special metrics to asymptotically shear-free null geodesic congruences, which are available in all asymptotically flat spacetimes, we give kinematic meaning to the Bondi 4-momentum. In other words, we describe the Bondi vector and its evolution in terms of a center of mass position vector, its velocity and a spin vector, all having clear geometric meaning. Among other items, from dynamic arguments, we define a unique (at our level of approximation) total angular momentum and extract its evolution equation in the form of a conservation law with an angular momentum flux
Zeta-function regularization approach to finite temperature effects in Kaluza-Klein space-times
International Nuclear Information System (INIS)
Bytsenko, A.A.; Vanzo, L.; Zerbini, S.
1992-01-01
In the framework of heat-kernel approach to zeta-function regularization, in this paper the one-loop effective potential at finite temperature for scalar and spinor fields on Kaluza-Klein space-time of the form M p x M c n , where M p is p-dimensional Minkowski space-time is evaluated. In particular, when the compact manifold is M c n = H n /Γ, the Selberg tracer formula associated with discrete torsion-free group Γ of the n-dimensional Lobachevsky space H n is used. An explicit representation for the thermodynamic potential valid for arbitrary temperature is found. As a result a complete high temperature expansion is presented and the roles of zero modes and topological contributions is discussed
Local field theory on κ-Minkowski space, star products and noncommutative translations
International Nuclear Information System (INIS)
Kosinski, P.; Maslanka, P.; Lukierski, J.
2000-01-01
We consider local field theory on κ-deformed Minkowski space which is an example of solvable Lie-algebraic noncommutative structure. Using integration formula over κ-Minkowski space and κ-deformed Fourier transform, we consider for deformed local fields the reality conditions as well as deformation of action functionals in standard Minkowski space. We present explicit formulas for two equivalent star products describing CBH quantization of field theory on κ-Minkowski space. We express also via star product technique the noncommutative translations in κ-Minkowski space by commutative translations in standard Minkowski space. (author)
Noether analysis of the twisted Hopf symmetries of canonical noncommutative spacetimes
International Nuclear Information System (INIS)
Amelino-Camelia, Giovanni; Gubitosi, Giulia; Marciano, Antonino; Martinetti, Pierre; Mercati, Flavio; Briscese, Fabio
2008-01-01
We study the twisted Hopf-algebra symmetries of observer-independent canonical spacetime noncommutativity, for which the commutators of the spacetime coordinates take the form [x^ μ ,x^ ν ]=iθ μν with observer-independent (and coordinate-independent) θ μν . We find that it is necessary to introduce nontrivial commutators between transformation parameters and spacetime coordinates, and that the form of these commutators implies that all symmetry transformations must include a translation component. We show that with our noncommutative transformation parameters the Noether analysis of the symmetries is straightforward, and we compare our canonical-noncommutativity results with the structure of the conserved charges and the ''no-pure-boost'' requirement derived in a previous study of κ-Minkowski noncommutativity. We also verify that, while at intermediate stages of the analysis we do find terms that depend on the ordering convention adopted in setting up the Weyl map, the final result for the conserved charges is reassuringly independent of the choice of Weyl map and (the corresponding choice of) star product.
A local-to-global singularity theorem for quantum field theory on curved space-time
International Nuclear Information System (INIS)
Radzikowski, M.J.; York Univ.
1996-01-01
We prove that if a reference two-point distribution of positive type on a time orientable curved space-time (CST) satisfies a certain condition on its wave front set (the ''class P M,g condition'') and if any other two-point distribution (i) is of positive type, (ii) has the same antisymmetric part as the reference modulo smooth function and (iii) has the same local singularity structure, then it has the same global singularity structure. In the proof we use a smoothing, positivity-preserving pseudo-differential operator the support of whose symbol is restricted to a certain conic region which depends on the wave front set of the reference state. This local-to-global theorem, together with results published elsewhere, leads to a verification of a conjecture by Kay that for quasi-free states of the Klein-Gordon quantum field on a globally hyperbolic CST, the local Hadamard condition implies the global Hadamard condition. A counterexample to the local-to-global theorem on a strip in Minkowski space is given when the class P M,g condition is not assumed. (orig.)
International Nuclear Information System (INIS)
Shabbir, Ghulam; Khan, Suhail; Ali, Amjad
2011-01-01
In this paper we classify spatially homogeneous rotating space-times according to their teleparallel Killing vector fields using direct integration technique. It turns out that the dimension of the teleparallel Killing vector fields is 5 or 10. In the case of 10 teleparallel Killing vector fields the space-time becomes Minkowski and all the torsion components are zero. Teleparallel Killing vector fields in this case are exactly the same as in general relativity. In the cases of 5 teleparallel Killing vector fields we get two more conservation laws in the teleparallel theory of gravitation. Here we also discuss some well-known examples of spatially homogeneous rotating space-times according to their teleparallel Killing vector fields. (general)
Field theories on conformally related space-times: Some global considerations
International Nuclear Information System (INIS)
Candelas, P.; Dowker, J.S.
1979-01-01
The nature of the vacua appearing in the relation between the vacuum expectation value of stress tensors in conformally flat spaces is clarified. The simple but essential point is that the relevant spaces should have conformally related global Cauchy surfaces. Some commonly occurring conformally flat space-times are divided into two families according to whether they are conformally equivalent to Minkowski space or to the Rindler wedge. Expressions, some new, are obtained for the vacuum expectation value of the stress tensor for a number of illustrative cases. It is noted that thermalization relates the Green's functions of these two families
Fermionic vacuum polarization by a cylindrical boundary in the cosmic string spacetime
International Nuclear Information System (INIS)
Bezerra de Mello, E. R.; Bezerra, V. B.; Saharian, A. A.; Tarloyan, A. S.
2008-01-01
The vacuum expectation values of the energy-momentum tensor and the fermionic condensate are analyzed for a massive spinor field obeying the MIT bag boundary condition on a cylindrical shell in the cosmic string spacetime. Both regions inside and outside the shell are considered. By applying to the corresponding mode sums a variant of the generalized Abel-Plana formula, we explicitly extract the parts in the expectation values corresponding to the cosmic string geometry without boundaries. In this way the renormalization procedure is reduced to that for the boundary-free cosmic string spacetime. The parts induced by the cylindrical shell are presented in terms of integrals rapidly convergent for points away from the boundary. The behavior of the vacuum densities is investigated in various asymptotic regions of the parameters. In the limit of large values of the planar angle deficit, the boundary-induced expectation values are exponentially suppressed. As a special case, we discuss the fermionic vacuum densities for the cylindrical shell on the background of the Minkowski spacetime.
Physics in space-time with scale-dependent metrics
Balankin, Alexander S.
2013-10-01
We construct three-dimensional space Rγ3 with the scale-dependent metric and the corresponding Minkowski space-time Mγ,β4 with the scale-dependent fractal (DH) and spectral (DS) dimensions. The local derivatives based on scale-dependent metrics are defined and differential vector calculus in Rγ3 is developed. We state that Mγ,β4 provides a unified phenomenological framework for dimensional flow observed in quite different models of quantum gravity. Nevertheless, the main attention is focused on the special case of flat space-time M1/3,14 with the scale-dependent Cantor-dust-like distribution of admissible states, such that DH increases from DH=2 on the scale ≪ℓ0 to DH=4 in the infrared limit ≫ℓ0, where ℓ0 is the characteristic length (e.g. the Planck length, or characteristic size of multi-fractal features in heterogeneous medium), whereas DS≡4 in all scales. Possible applications of approach based on the scale-dependent metric to systems of different nature are briefly discussed.
Infinite-parametric extension of the conformal algebra in D>2 space-time dimension
International Nuclear Information System (INIS)
Fradkin, E.S.; Linetsky, V.Ya.
1990-09-01
On the basis of the analytic continuations of semisimple Lie algebras discovered recently by us we construct manifestly quasiconformal infinite-dimensional algebras AC(so(4,1)) and PAC(so(3,2)) extending the conformal algebras in three-dimensional Euclidean and Minkowski space-time like the Virasoro algebra extends so(2,1). Their higher spin generalizations are also constructed. A counterpart of the central extension for D>2 and possible applications in exactly solvable conformal quantum field models in D>2 are discussed. (author). 31 refs, 2 figs
Two-transitive MInkowski planes
Wilbrink, H.A.
1982-01-01
In this paper we determine all finite Minkowski planes with an automorphism group which satisfies the following transitivity property: any ordered pair of nonparallel points can be mapped onto any other ordered pair of nonparallel points.
The stress energy tensor of a locally supersymmetric quantum field on a curved spacetime
International Nuclear Information System (INIS)
Koehler, M.
1995-04-01
For an analogon of the free Wess-Zumino model on Ricci flat spacetimes, the relation between a conserved 'supercurrent' and the point-separated improved energy momentum tensor is investigated and a similar relation as on Minkowski space is established. The expectation value of the latter in any globally Hadamard product state is found to be a priori finite in the coincidence limit if the theory is massive. On arbitrary globally hyperbolic spacetimes the 'supercurrent' is shown to be a well defined operator valued distribution on the GNS Hilbertspace of any globally Hadamard product state. Viewed as a new field, all n-point distributions exist, giving a new example for a Wightman field on that manifold. Moreover, it is shown that this field satisfies a new wave front set spectrum condition in a nontrivial way. (orig.)
Relativity and the dimensionality of the world
2007-01-01
All physicists would agree that one of the most fundamental problems of the 21st century physics is the dimensionality of the world. In the four-dimensional world of Minkowski (or Minkowski spacetime) the most challenging problem is the nature of the temporal dimension. In Minkowski spacetime it is merely one of the four dimensions, which means that it is entirely given like the other three spacial dimensions. If the temporal dimension were not given in its entirety and only one constantly changing moment of it existed, Minkowski spacetime would be reduced to the ordinary three-dimensional space. But if the physical world, represented by Minkowski spacetime, is indeed four-dimensional with time being the fourth dimension, then such a world is drastically different from its image based on our perceptions. Minkowski four-dimensional world is a block Universe, a frozen world in which nothing happens since all moments of time are given ‘at once', which means that physical bodies are four-dimensional worldtubes ...
Ob the Froissart-Martin bound in spaces with compact dimensions
Petrov, V A
2002-01-01
It is shown by the example of the 5-dimensional space-time, that by availability of the additional compact (space-time-like) measurements to the general Minkowski space all the conditions for proving the Froissart-Martin bound retain their force. Thus, by the circumference R -> 0 the theory smoothly transfers to the theory of the neutral scalar field in the 4-dimensional Minkowski space-time. It was assumed in this work, that the masses are bound from below by the non-zero value. The bounds for elastic scattering by absence of the mass gap are trivial, however in this case it is obviously possible to obtain also nontrivial bounds for complete inelastic cross sections. It takes place in the Regge-eikonal approach though there exist no strong proof for it
Positioning with stationary emitters in a two-dimensional space-time
International Nuclear Information System (INIS)
Coll, Bartolome; Ferrando, Joan Josep; Morales, Juan Antonio
2006-01-01
The basic elements of the relativistic positioning systems in a two-dimensional space-time have been introduced in a previous work [Phys. Rev. D 73, 084017 (2006)] where geodesic positioning systems, constituted by two geodesic emitters, have been considered in a flat space-time. Here, we want to show in what precise senses positioning systems allow to make relativistic gravimetry. For this purpose, we consider stationary positioning systems, constituted by two uniformly accelerated emitters separated by a constant distance, in two different situations: absence of gravitational field (Minkowski plane) and presence of a gravitational mass (Schwarzschild plane). The physical coordinate system constituted by the electromagnetic signals broadcasting the proper time of the emitters are the so called emission coordinates, and we show that, in such emission coordinates, the trajectories of the emitters in both situations, the absence and presence of a gravitational field, are identical. The interesting point is that, in spite of this fact, particular additional information on the system or on the user allows us not only to distinguish both space-times, but also to complete the dynamical description of emitters and user and even to measure the mass of the gravitational field. The precise information under which these dynamical and gravimetric results may be obtained is carefully pointed out
DUAL TIMELIKE NORMAL AND DUAL TIMELIKE SPHERICAL CURVES IN DUAL MINKOWSKI SPACE
ÖNDER, Mehmet
2009-01-01
Abstract: In this paper, we give characterizations of dual timelike normal and dual timelike spherical curves in the dual Minkowski 3-space and we show that every dual timelike normal curve is also a dual timelike spherical curve. Keywords: Normal curves, Dual Minkowski 3-Space, Dual Timelike curves. Mathematics Subject Classifications (2000): 53C50, 53C40. DUAL MINKOWSKI UZAYINDA DUAL TIMELIKE NORMAL VE DUAL TIMELIKE KÜRESEL EĞRİLER Özet: Bu çalışmada, dual Minkowski 3-...
Comparison of two global digital algorithms for Minkowski tensor estimation
DEFF Research Database (Denmark)
The geometry of real world objects can be described by Minkowski tensors. Algorithms have been suggested to approximate Minkowski tensors if only a binary image of the object is available. This paper presents implementations of two such algorithms. The theoretical convergence properties...... are confirmed by simulations on test sets, and recommendations for input arguments of the algorithms are given. For increasing resolutions, we obtain more accurate estimators for the Minkowski tensors. Digitisations of more complicated objects are shown to require higher resolutions....
Towards an improved duality between tensor network states and AdS spacetime
Energy Technology Data Exchange (ETDEWEB)
Papadopoulos, Charalampos; Orus, Roman [Institute of Physics, Johannes Gutenberg University, 55099 Mainz (Germany)
2016-07-01
The conjectured AdS/CFT Correspondence, which states that a Conformal Field Theory (CFT) in Minkowski spacetime has a gravity dual in an asymptotically Anti-de Sitter space (AdS), is one of the best understood examples of the holographic principle, and has important applications in condensed matter physics. Tensor Networks (TNs) are a efficient way to calculate low-energy properties for strongly-correlated quantum many-body systems. The Multi-scale Entanglement Renormalization Ansatz (MERA) is a specific TN for a efficient description of critical quantum systems (CFTs). It was recently suggested that the MERA provides naturally a discretization of AdS spacetime on a lattice. It is however known that a conventional MERA can not reproduce the so-called ''Bousso Bound'', also called holographic entropy bound, which is a bound on the bulk entropy in spacetime. In this context, our aim is to generalize the proposed AdS/MERA correspondence to a more general AdS/TN duality, where the Bousso bound is satisfied. Progress in this direction as well as connections to strongly correlated systems will be discussed.
On conjectures of Minkowski and Woods for n = 9
Indian Academy of Sciences (India)
Here we shall prove Conjecture II for n = 9, thereby proving Minkowski's Conjecture for n = 9. Woods [20 ... result that if hypothesis of Conjecture III holds, then any closed sphere in R9 of radius. √ ...... tures of Minkowski and Watson, Number Theory, Trends in Mathematics (2000) (Basel: ... Journal of the Indian Math. Soc.
Partially massless graviton on beyond Einstein spacetimes
Bernard, Laura; Deffayet, Cédric; Hinterbichler, Kurt; von Strauss, Mikael
2017-06-01
We show that a partially massless graviton can propagate on a large set of spacetimes which are not Einstein spacetimes. Starting from a recently constructed theory for a massive graviton that propagates the correct number of degrees of freedom on an arbitrary spacetime, we first give the full explicit form of the scalar constraint responsible for the absence of a sixth degree of freedom. We then spell out generic conditions for the constraint to be identically satisfied, so that there is a scalar gauge symmetry which makes the graviton partially massless. These simplify if one assumes that spacetime is Ricci symmetric. Under this assumption, we find explicit non-Einstein spacetimes (some, but not all, with vanishing Bach tensors) allowing for the propagation of a partially massless graviton. These include in particular the Einstein static Universe.
Böbel, A.; Knapek, C. A.; Räth, C.
2018-05-01
Experiments of the recrystallization processes in two-dimensional complex plasmas are analyzed to rigorously test a recently developed scale-free phase transition theory. The "fractal-domain-structure" (FDS) theory is based on the kinetic theory of Frenkel. It assumes the formation of homogeneous domains, separated by defect lines, during crystallization and a fractal relationship between domain area and boundary length. For the defect number fraction and system energy a scale-free power-law relation is predicted. The long-range scaling behavior of the bond-order correlation function shows clearly that the complex plasma phase transitions are not of the Kosterlitz, Thouless, Halperin, Nelson, and Young type. Previous preliminary results obtained by counting the number of dislocations and applying a bond-order metric for structural analysis are reproduced. These findings are supplemented by extending the use of the bond-order metric to measure the defect number fraction and furthermore applying state-of-the-art analysis methods, allowing a systematic testing of the FDS theory with unprecedented scrutiny: A morphological analysis of lattice structure is performed via Minkowski tensor methods. Minkowski tensors form a complete family of additive, motion covariant and continuous morphological measures that are sensitive to nonlinear properties. The FDS theory is rigorously confirmed and predictions of the theory are reproduced extremely well. The predicted scale-free power-law relation between defect fraction number and system energy is verified for one more order of magnitude at high energies compared to the inherently discontinuous bond-order metric. It is found that the fractal relation between crystalline domain area and circumference is independent of the experiment, the particular Minkowski tensor method, and the particular choice of parameters. Thus, the fractal relationship seems to be inherent to two-dimensional phase transitions in complex plasmas. Minkowski
What does the Euclidean pseudoparticle do in Minkowski space
International Nuclear Information System (INIS)
Ju, I.
1978-08-01
Self dual pseudoparticle solutions for the classical Yang--Mills field equation with finite action have been constructed in Minkowski space. It is shown that the topological structures apparent in Euclidean space are no longer present in Minkowski space. Topological charges become fractional leading to the unquantized axial charge violation in the process involving fermions. 17 references
Electrodynamics and Spacetime Geometry: Foundations
Cabral, Francisco; Lobo, Francisco S. N.
2017-02-01
We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.
Memory effect for particle scattering in odd spacetime dimensions
Satishchandran, Gautam; Wald, Robert M.
2018-01-01
We investigate the gravitational memory effect for linearized perturbations off of Minkowski space in odd spacetime dimensions d by examining the effects of gravitational radiation from classical point particle scattering. We also investigate analogous memory effects for electromagnetic and scalar radiation. We find that there is no gravitational memory effect in all odd dimensions. For scalar and electromagnetic fields, there is no memory effect for d ≥7 ; for d =3 there is an infinite momentum memory effect, whereas for d =5 there is no momentum memory effect but the displacement of a test particle will grow unboundedly with time. Our results are further elucidated by analyzing the memory effect for any slowly moving source of compact spatial support in odd dimensions.
Energy Technology Data Exchange (ETDEWEB)
Hack, Thomas-Paul; Makedonski, Mathias [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik
2011-06-15
We first introduce a set of conditions which assure that a free spin (3)/(2) field with m{>=}0 can be consistently ('unitarily') quantized on all four-dimensional curved spacetimes, i.e. also on spacetimes which are not assumed to be solutions of the Einstein equations. We discuss a large - and, as we argue, exhaustive - class of spin (3)/(2) field equations obtained from the Rarita-Schwinger equation by the addition of non-minimal couplings and prove that no equation in this class fulfils all sufficient conditions. Afterwards, we investigate the situation in supergravity, where the curved background is usually assumed to satisfy the Einstein equations and, hence, detailed knowledge on the spacetime curvature is available. We provide a necessary condition for the unitary quantization of a spin (3)/(2) Majorana field and prove that this condition is not met by supergravity models in four-dimensional Robertson-Walker spacetimes if local supersymmetry is broken. Our proof is model-independent as we merely assume that the gravitino has the standard kinetic term. (orig.)
The Thermal Entropy Density of Spacetime
Directory of Open Access Journals (Sweden)
Rongjia Yang
2013-01-01
Full Text Available Introducing the notion of thermal entropy density via the first law of thermodynamics and assuming the Einstein equation as an equation of thermal state, we obtain the thermal entropy density of any arbitrary spacetime without assuming a temperature or a horizon. The results confirm that there is a profound connection between gravity and thermodynamics.
Three-dimensional gravity and Drinfel'd doubles: Spacetimes and symmetries from quantum deformations
International Nuclear Information System (INIS)
Ballesteros, Angel; Herranz, Francisco J.; Meusburger, Catherine
2010-01-01
We show how the constant curvature spacetimes of 3d gravity and the associated symmetry algebras can be derived from a single quantum deformation of the 3d Lorentz algebra sl(2,R). We investigate the classical Drinfel'd double of a 'hybrid' deformation of sl(2,R) that depends on two parameters (η,z). With an appropriate choice of basis and real structure, this Drinfel'd double agrees with the 3d anti-de Sitter algebra. The deformation parameter η is related to the cosmological constant, while z is identified with the inverse of the speed of light and defines the signature of the metric. We generalise this result to de Sitter space, the three-sphere and 3d hyperbolic space through analytic continuation in η and z; we also investigate the limits of vanishing η and z, which yield the flat spacetimes (Minkowski and Euclidean spaces) and Newtonian models, respectively.
Spinor Casimir densities for a spherical shell in the global monopole spacetime
International Nuclear Information System (INIS)
Saharian, A A; Mello, E R Bezerra de
2004-01-01
We investigate the vacuum expectation values of the energy-momentum tensor and the fermionic condensate associated with a massive spinor field obeying the MIT bag boundary condition on a spherical shell in the global monopole spacetime. In order to do that, we use the generalized Abel-Plana summation formula. As we shall see, this procedure allows us to extract from the vacuum expectation values the contribution coming from the unbounded spacetime and to explicitly present the boundary induced parts. As regards the boundary induced contribution, two distinct situations are examined: the vacuum average effects inside and outside the spherical shell. The asymptotic behaviour of the vacuum densities is investigated near the sphere centre and near the surface, and at large distances from the sphere. In the limit of strong gravitational field corresponding to small values of the parameter describing the solid angle deficit in the global monopole geometry, the sphere induced expectation values are exponentially suppressed. We discuss, as a special case, the fermionic vacuum densities for the spherical shell on the background of the Minkowski spacetime. Previous approaches to this problem within the framework of the QCD bag models have been global and our calculation is a local extension of these contributions
An Efficient Algorithm to Calculate the Minkowski Sum of Convex 3D Polyhedra
Bekker, Henk; Roerdink, Jos B.T.M.
2001-01-01
A new method is presented to calculate the Minkowski sum of two convex polyhedra A and B in 3D. These graphs are given edge attributes. From these attributed graphs the attributed graph of the Minkowski sum is constructed. This graph is then transformed into the Minkowski sum of A and B. The running
The zero mass limit of Kerr and Kerr-(anti-)de-Sitter space-times: exact solutions and wormholes
Birkandan, T.; Hortaçsu, M.
2018-03-01
Heun-type exact solutions emerge for both the radial and the angular equations for the case of a scalar particle coupled to the zero mass limit of both the Kerr and Kerr-(anti)de-Sitter spacetime. Since any type D metric has Heun-type solutions, it is interesting that this property is retained in the zero mass case. This work further refutes the claims that M going to zero limit of the Kerr metric is both locally and globally the same as the Minkowski metric.
The stochastic versus the Euclidean approach to quantum fields on a static space-time
International Nuclear Information System (INIS)
De Angelis, G.F.; de Falco, D.
1986-01-01
Equations are presented which modify the definition of the Gaussian field in the Rindler chart in order to make contact with the Wightman state, the Hartle-Hawking state, and the Euclidean field. By taking Ornstein-Uhlenbeck processes the authors have chosen, in the sense of stochastic mechanics, to place precisely the Fulling modes in their harmonic oscillator ground state. In this respect, together with the periodicity of Minkowski space-time, the authors observe that the covariance of the Ornstein-Uhlenbeck process can be obtained by analytical continuation of the Wightman function of the harmonic oscillator at zero temperature
Lie-deformed quantum Minkowski spaces from twists: Hopf-algebraic versus Hopf-algebroid approach
Lukierski, Jerzy; Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel; Woronowicz, Mariusz
2018-02-01
We consider new Abelian twists of Poincare algebra describing nonsymmetric generalization of the ones given in [1], which lead to the class of Lie-deformed quantum Minkowski spaces. We apply corresponding twist quantization in two ways: as generating quantum Poincare-Hopf algebra providing quantum Poincare symmetries, and by considering the quantization which provides Hopf algebroid describing class of quantum relativistic phase spaces with built-in quantum Poincare covariance. If we assume that Lorentz generators are orbital i.e. do not describe spin degrees of freedom, one can embed the considered generalized phase spaces into the ones describing the quantum-deformed Heisenberg algebras.
Directory of Open Access Journals (Sweden)
Virginia E. Suassuna Martins Costa
2009-06-01
Full Text Available Este artigo tem como objetivo abordar as concepções de tempo assimilado ao espaço e de tempo vivido, especificando seus elementos estruturais e os fenômenos a eles relacionados, com base na perspectiva de Eugène Minkowski. Para tal, evidencia algumas conceituações a respeito do tempo em Santo Agostinho e em Henry Bergson", assim com em alguns aspectos biográficos de Minkowski, que contribuíram para a compreensão a respeito do fenômeno tempo. Como meta, pretende oferecer subsídios para a reflexão dos profissionais de saúde no encontro clínico.Este artículo tiene el objetivo de tratar sobre los conceptos del tiempo asimilados al espacio y del tiempo vivido, especificando sus elementos estructurales y fenómenos relacionados, embasados en la perspectiva de Eugène Minkowski. Para esto, se evidencia algunos conceptos relacionados con el tiempo en Santo Agostinho y en Henry Bergson, así como los aspectos biográficos de Minkowski que han contribuido para entenderse sobre el fenómeno del tiempo. Como meta, este artículo se propone a ofrecer subsidios a la reflexión por los profesionales de salud en el encuentro clínico.This article has the objective to deal about the conceptions of time assimilated with the space and the lived time, specifying its structural elements and related phenomena, based on Eugène Minkowski's perspective. For this, it is evidenced some concepts related to time in Saint Augustin and in Henry Bergson, as well as some Minkowski's biographic aspects that have contributed for understanding about time's phenomenon. As a goal, this paper intends to offer subsidies for the reflection by health professionals on clinic meeting.
Relation of a unified quantum field theory of spinors to the structure of general relativity
International Nuclear Information System (INIS)
Kober, Martin
2009-01-01
Based on a unified quantum field theory of spinors assumed to describe all matter fields and their interactions we construct the space-time structure of general relativity according to a general connection within the corresponding spinor space. The tetrad field and the corresponding metric field are composed from a space-time dependent basis of spinors within the internal space of the fundamental matter field. Similar to twistor theory the Minkowski signature of the space-time metric is related to this spinor nature of elementary matter, if we assume the spinor space to be endowed with a symplectic structure. The equivalence principle and the property of background independence arise from the fact that all elementary fields are composed from the fundamental spinor field. This means that the structure of space-time according to general relativity seems to be a consequence of a fundamental theory of matter fields and not a presupposition as in the usual setting of relativistic quantum field theories.
A model of spontaneous symmetry breakdown in spatially flat cosmological spacetimes
International Nuclear Information System (INIS)
Kundu, P.
1984-01-01
This paper is an elaboration of a previous short exposition of a theory of spontaneous symmetry breaking in a conformally coupled, massless lambdaphi 4 model in a spatially flat Robertson-Walker spacetime. Under the weakened global boundary condition allowing the physical spacetime to be conformal to only a portion of the Minkowski spacetime, the model admits a pair of degenerate vacua in which the phi->phi symmetry is spontaneously broken. The model is formulated as a euclidean field theory in a space with a positive-definite metric obtained by analytically continuing the conformal time coordinate. An appropriate time-dependent zero energy solution of the euclidean equation of motion representing the field configuration in the asymmetric vacuum is considered and the corresponding quantum trace anomaly is computed in the one-loop approximation. The nontrivial infrared behavior of the model due to the singular nature of the classical background field forces a modification of the boundary conditions on the propagator. A general form for an 'improved' one-loop trace anomaly is found by a simple argument based on renormalization group invariance. Via the Einstein equation, the trace anomaly leads to a self-consistent dynamical equation for the cosmic expansion scale factor. Some physical aspects of the back-reaction problem based on a simple power law model of the expansion scale factor are discussed. (orig.)
Reexamination of the Abraham-Minkowski dilemma
Silveirinha, Mário G.
2017-09-01
Here the Abraham-Minkowski controversy on the correct definition of the light momentum in a macroscopic medium is revisited with the purpose to highlight that an effective medium formalism necessarily restricts the available information on the internal state of a system, and that this is ultimately the reason why the dilemma has no universal solution. Despite these difficulties, it is demonstrated that in the limit of no material absorption and under steady-state conditions, the time-averaged light (kinetic) momentum may be unambiguously determined by the Abraham result, both for bodies at rest and for circulatory flows of matter. The implications of these findings are discussed in the context of quantum optics of moving media, and we examine in detail the fundamental role of the Minkowski momentum in such a context.
Quantum mechanics in curved space-time and its consequences for the theory on the flat space-time
International Nuclear Information System (INIS)
Tagirov, E.A.
1997-01-01
Thus, the structure is extracted from the initial general-relativistic setting of the quantum theory of the scalar field φ that can be considered as quantum mechanics in V 1,3 in the Schroedinger picture, which includes relativistic corrections not only in the Hamiltonian of the Schroedinger equation but also in the operators of primary observables. In the terms pertaining to these corrections the operators differ from their counterparts resulting from quantization of a classical spinless particle. In general, they do not commute at all and thus the quantum phase space loses the feature that half its coordinates retain a manifold structure, which Biedenharn called 'a miracle of quantization'. This non-commutativity expands up to the exact (in the sense 'non-asymptotic in c -2 ') quantum mechanics of a free motion in the Minkowski space-time if curvilinear coordinates are taken as observables, which are necessary if non-inertial frames of references are considered
Toward a holographic theory for general spacetimes
Nomura, Yasunori; Salzetta, Nico; Sanches, Fabio; Weinberg, Sean J.
2017-04-01
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct-sum and "spacetime-equals-entanglement" structure. The former preserves a naive relationship between linear operators and observable quantities, while the latter respects a more direct connection between holographic entanglement and spacetime. We also discuss the issue of selecting a state in quantum gravity, in particular how the state of the multiverse may be selected in the landscape.
Homothetic and conformal symmetries of solutions to Einstein's equations
International Nuclear Information System (INIS)
Eardley, D.; Isenberg, J.; Marsden, J.; Moncrief, V.; Yale Univ., New Haven, CT
1986-01-01
We present several results about the nonexistence of solutions of Einstein's equations with homoethetic or conformal symmetry. We show that the only spatially compact, globally hyperbolic spacetimes admitting a hypersurface of constant mean extrinsic curvature, and also admitting an infinitesimal proper homothetic symmetry, are everywhere locally flat; this assumes that the matter fields either obey certain energy conditions, or are the Yang-Mills or massless Klein-Gordon fields. We find that the only vacuum solutions admitting an infinitesimal proper conformal symmetry are everywhere locally flat spacetimes and certain plane wave solutions. We show that if the dominant energy condition is assumed, then Minkowski spacetime is the only asymptotically flat solution which has an infinitesimal conformal symmetry that is asymptotic to a dilation. In other words, with the exceptions cited, homothetic or conformal Killing fields are in fact Killing in spatially compact or asymptotically flat spacetimes. In the conformal procedure for solving the initial value problem, we show that data with infinitesimal conformal symmetry evolves to a spacetime with full isometry. (orig.)
A heuristic derivation of Minkowski distance and Lorentz transformation
International Nuclear Information System (INIS)
Hassani, Sadri
2008-01-01
Students learn new abstract concepts best when these concepts are connected through a well-designed analogy, to familiar ideas. Since the concept of the relativistic spacetime distance is highly abstract, it would be desirable to connect it to the familiar Euclidean distance, but present the latter in such a way that it makes a transparent contact with the former. Starting with some intuitive and 'obvious' assumptions concerning distance in one dimension, we 'derive' the two-dimensional Euclidean distance between two points in terms of their coordinates. Then, assuming the invariance of this distance, we deduce the (familiar) two-dimensional orthogonal coordinate transformation. We present the derivation in such a way that the transition to spacetime becomes 'self-evident.' Thus, following exactly the same procedure, we derive the Minkowskian distance and the corresponding transformation that respects the invariance of that distance, i.e., the Lorentz transformation
Singular lensing from the scattering on special space-time defects
Energy Technology Data Exchange (ETDEWEB)
Mavromatos, Nick E. [University of Valencia - CSIC, Department of Theoretical Physics and IFIC, Valencia (Spain); King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Papavassiliou, Joannis [University of Valencia - CSIC, Department of Theoretical Physics and IFIC, Valencia (Spain)
2018-01-15
It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent (''singular lensing''). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals. (orig.)
Singular lensing from the scattering on special space-time defects
International Nuclear Information System (INIS)
Mavromatos, Nick E.; Papavassiliou, Joannis
2018-01-01
It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent (''singular lensing''). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals. (orig.)
Singular lensing from the scattering on special space-time defects
Mavromatos, Nick E.; Papavassiliou, Joannis
2018-01-01
It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent ("singular lensing"). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.
International Nuclear Information System (INIS)
Lusanna, Luca
2006-01-01
This is a review of the chrono-geometrical structure of special and general relativity with a special emphasis on the role of non-inertial frames and of the conventions for the synchronization of distant clocks. ADM canonical metric and tetrad gravity are analyzed in a class of space-times suitable to incorporate particle physics by using Dirac theory of constraints, which allows to arrive at a separation of the genuine degrees of freedom of the gravitational field, the Dirac observables describing generalized tidal effects, from its gauge variables, describing generalized inertial effects. A background-independent formulation (the rest-frame instant form of tetrad gravity) emerges, since the chosen boundary conditions at spatial infinity imply the existence of an asymptotic flat metric. By switching off the Newton constant in presence of matter this description deparametrizes to the rest-frame instant form for such matter in the framework of parametrized Minkowski theories. The problem of the objectivity of the spacetime point-events, implied by Einstein's Hole Argument, is analyzed
A definition of distance and method of making space-time measurements
International Nuclear Information System (INIS)
Brisson, D.W.
1980-01-01
The paper explores an extended definition of the absolute value of a complex number and thus a new definition of distance. This new definition, called the nabsolute value of a complex number, is (Z) where Z = (a or ia) + (b or ib), so that (Z) is equivalent to [α 2 + β 2 ]sup(1/2), and α = a or ia, β = b or ib. This is shown on a superimposed X,Y plot and iX,iY plot so that four dimensions are represented in a plane. The application of this scheme to space-time measurement is then identified with the Minkowski Plane which has identical properties with the complex plane, with this new interpretation of the absolute value of a complex number. (Auth.)
The physical spacetime as a chronostat defining time. (Prolegomena to a future chronodynamics)
International Nuclear Information System (INIS)
Krolikowski, W.
1993-01-01
The familiar analogy, appearing in the quantum theory, between the time evolution of an isolated system and the thermal equilibrium of a system with a thermostat, is taken at its face value. This leads us to the phenomenological conjecture that, in reality, the so called isolated system may remain in a ''temporal equilibrium'' with the physical spacetime which plays than the role of a ''chronostat'' defining time equal at all space points (in a Minkowski frame of reference). Such a conjecture suggest virtual deviations from this equilibrium and so seems to imply an extension of the first law of thermodynamics as well as of the state equation in the quantum theory. (author). 5 refs
Chiral-symmetry breaking and confinement in Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Biernat, Elmer P. [Unibersidade de Lisboa, 104-001, Lisboa, Portugal; Pena, M. T. [Universidade de Lisboa, 1049-001, Lisboa, Portugal; Ribiero, J. E. [Universidade de Lisboa, 1049-001 Lisboa, Portugal; Stadler, Alfred [Universidade de Ãvora, 7000-671 Ãvora, Portugal; Universidade de Lisboa, 1049-001 Lisboa, Portugal; Gross, Franz [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-01-01
We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab.
Chiral-symmetry breaking and confinement in Minkowski space
International Nuclear Information System (INIS)
Biernat, Elmar P.; Peña, M. T.; Ribeiro, J. E.; Stadler, Alfred; Gross, Franz
2016-01-01
We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab
Chiral-symmetry breaking and confinement in Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Biernat, Elmar P. [Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Peña, M. T. [Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Departamento de Física, Instituto Superior Técnico (IST), Universidadede Lisboa, 1049-001 Lisboa (Portugal); Ribeiro, J. E. [Centro de Física das Interações Fundamentais (CFIF), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Stadler, Alfred [Departamento de Física, Universidade de Évora, 7000-671 Évora (Portugal); Centro de Física Teórica de Partículas (CFTP), Instituto Superior Técnico (IST), Universidade de Lisboa, 1049-001 Lisboa (Portugal); Gross, Franz [Thomas Jefferson National Accelerator Facility (JLab), Newport News, Virginia 23606 (United States)
2016-01-22
We present a model for the quark-antiquark interaction formulated in Minkowski space using the Covariant Spectator Theory. The quark propagators are dressed with the same kernel that describes the interaction between different quarks. By applying the axial-vector Ward-Takahashi identity we show that our model satisfies the Adler-zero constraint imposed by chiral symmetry. For this model, our Minkowski-space results of the dressed quark mass function are compared to lattice QCD data obtained in Euclidean space. The mass function is then used in the calculation of the electromagnetic pion form factor in relativistic impulse approximation, and the results are presented and compared with the experimental data from JLab.
International Nuclear Information System (INIS)
Ishibashi, Nobuyuki; Onogi, Tetsuya
1989-01-01
Consistency conditions of open string theories, which can be a powerful tool in open string model building, are proposed. By making use of these conditions and assuming a simple prescription for the Chan-Paton factors, open string theories in several backgrounds are studied. We show that 1. there exist a large number of consistent bosonic open string theories on Z 2 orbifolds, 2. SO(32) type I superstring is the unique consistent model among fermionic string theories on the ten-dimensional flat Minkowski space, and 3. with our prescription for the Chan-Paton factors, there exist no consistent open superstring theories on (six-dimensional Minkowski space-time) x (Z 2 orbifold). (orig.)
Local differential geometry of null curves in conformally flat space-time
International Nuclear Information System (INIS)
Urbantke, H.
1989-01-01
The conformally invariant differential geometry of null curves in conformally flat space-times is given, using the six-vector formalism which has generalizations to higher dimensions. This is then paralleled by a twistor description, with a twofold merit: firstly, sometimes the description is easier in twistor terms, sometimes in six-vector terms, which leads to a mutual enlightenment of both; and secondly, the case of null curves in timelike pseudospheres or 2+1 Minkowski space we were only able to treat twistorially, making use of an invariant differential found by Fubini and Cech. The result is the expected one: apart from stated exceptional cases there is a conformally invariant parameter and two conformally invariant curvatures which, when specified in terms of this parameter, serve to characterize the curve up to conformal transformations. 12 refs. (Author)
Collision-free gases in spatially homogeneous space-times
International Nuclear Information System (INIS)
Maartens, R.; Maharaj, S.D.
1985-01-01
The kinematical and dynamical properties of one-component collision-free gases in spatially homogeneous, locally rotationally symmetric (LRS) space-times are analyzed. Following Ray and Zimmerman [Nuovo Cimento B 42, 183 (1977)], it is assumed that the distribution function f of the gas inherits the symmetry of space-time, in order to construct solutions of Liouville's equation. The redundancy of their further assumption that f be based on Killing vector constants of the motion is shown. The Ray and Zimmerman results for Kantowski--Sachs space-time are extended to all spatially homogeneous LRS space-times. It is shown that in all these space-times the kinematic average four-velocity u/sup i/ can be tilted relative to the homogeneous hypersurfaces. This differs from the perfect fluid case, in which only one space-time admits tilted u/sup i/, as shown by King and Ellis [Commun. Math. Phys. 31, 209 (1973)]. As a consequence, it is shown that all space-times admit nonzero acceleration and heat flow, while a subclass admits nonzero vorticity. The stress π/sub i/j is proportional to the shear sigma/sub i/j by virtue of the invariance of the distribution function. The evolution of tilt and the existence of perfect fluid solutions is also discussed
Ponderomotive forces in electrodynamics of moving media: The Minkowski and Abraham approaches
Nesterenko, V. V.; Nesterenko, A. V.
2016-09-01
In the general setting of the problem, the explicit compact formulae are derived for the ponderomotive forces in the macroscopic electrodynamics of moving media in the Minkowski and Abraham approaches. Taking account of the Minkowski constitutive relations and making use of a special representation for the Abraham energy-momentum tensor enable one to obtain a compact expression for the Abraham force in the case of arbitrary dependence of the medium velocity on spatial coordinates and the time and for nonstationary external electromagnetic field. We term the difference between the ponderomotive forces in the Abraham and Minkowski approaches as the Abraham force not only under consideration of media at rest but also in the case of moving media. The Lorentz force is found which is exerted by external electromagnetic field on the conduction current in a medium, the covariant Ohm law, and the constitutive Minkowski relations being taken into account. The physical argumentation is traced for the definition of the 4-vector of the ponderomotive force as the 4-divergence of the energy-momentum tensor of electromagnetic field in a medium.
Star product realizations of kappa-Minkowski space
DEFF Research Database (Denmark)
Durhuus, Bergfinnur; Sitarz, Andrzej
2013-01-01
We define a family of star products and involutions associated with κ -Minkowski space. Applying corresponding quantization maps we show that these star products restricted to a certain space of Schwartz functions have isomorphic Banach algebra completions. For two particular star products...
Chiral symmetry breaking and confinement in Minkowski space QED2+1
International Nuclear Information System (INIS)
Sauli, V.; Batiz, Z.
2010-01-01
Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e. g. with the standard Euclidean calculation. We have presented for the first analysis of the electron gap equation in Minkowski and Temporal Euclidean space. The dynamical generation of imaginary part of the fermion mass leads to the absence of Khallen-Lehmann representation, providing thus confining solution for all value of m. Apart very small κ the real pole in the propagator is absent as well. Similarly to Euclidean QED3 Minkowski QED2+1 exhibits spontaneous chiral symmetry breaking the mass function has nontrivial solution in the limit m = 0, however the mass is complex function. Furthermore, we compare with QED solved in similar approximation in spacelike Euclidean and Temporal Euclidean space. As a interesting results, although based on the simple ladder approximation, is the proof of the exact equivalence between the theories defined in Minkowski 2+1 and 3D Temporal Euclidean space. We expect large quantitative changes when the polarization effect is taken account, especially the existence of critical number of flavors can be different when compared to the known Euclidean space estimates. Opposite to naive belief we showed and explained that the Wick rotation -the well known calculational trick in quantum theory- provides continuation of Schwinger function of the Euclidean theory which do not correspond with the Greens function calculated directly in the original Minkowski space. We can note our finding has a little to do with the know usefulness of various
Spacetime transformations from a uniformly accelerated frame
International Nuclear Information System (INIS)
Friedman, Yaakov; Scarr, Tzvi
2013-01-01
We use the generalized Fermi–Walker transport to construct a one-parameter family of inertial frames which are instantaneously comoving to a uniformly accelerated observer. We explain the connection between our approach and that of Mashhoon. We show that our solutions of uniformly accelerated motion have constant acceleration in the comoving frame. Assuming the weak hypothesis of locality, we obtain local spacetime transformations from a uniformly accelerated frame K′ to an inertial frame K. The spacetime transformations between two uniformly accelerated frames with the same acceleration are Lorentz. We compute the metric at an arbitrary point of a uniformly accelerated frame. (paper)
Euclidean to Minkowski Bethe-Salpeter amplitude and observables
International Nuclear Information System (INIS)
Carbonell, J.; Frederico, T.; Karmanov, V.A.
2017-01-01
We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)
Euclidean to Minkowski Bethe-Salpeter amplitude and observables
Energy Technology Data Exchange (ETDEWEB)
Carbonell, J. [Universite Paris-Sud, IN2P3-CNRS, Institut de Physique Nucleaire, Orsay Cedex (France); Frederico, T. [Instituto Tecnologico de Aeronautica, DCTA, Sao Jose dos Campos (Brazil); Karmanov, V.A. [Lebedev Physical Institute, Moscow (Russian Federation)
2017-01-15
We propose a method to reconstruct the Bethe-Salpeter amplitude in Minkowski space given the Euclidean Bethe-Salpeter amplitude - or alternatively the light-front wave function - as input. The method is based on the numerical inversion of the Nakanishi integral representation and computing the corresponding weight function. This inversion procedure is, in general, rather unstable, and we propose several ways to considerably reduce the instabilities. In terms of the Nakanishi weight function, one can easily compute the BS amplitude, the LF wave function and the electromagnetic form factor. The latter ones are very stable in spite of residual instabilities in the weight function. This procedure allows both, to continue the Euclidean BS solution in the Minkowski space and to obtain a BS amplitude from a LF wave function. (orig.)
From Euclidean to Minkowski space with the Cauchy-Riemann equations
International Nuclear Information System (INIS)
Gimeno-Segovia, Mercedes; Llanes-Estrada, Felipe J.
2008-01-01
We present an elementary method to obtain Green's functions in non-perturbative quantum field theory in Minkowski space from Green's functions calculated in Euclidean space. Since in non-perturbative field theory the analytical structure of amplitudes often is unknown, especially in the presence of confined fields, dispersive representations suffer from systematic uncertainties. Therefore, we suggest to use the Cauchy-Riemann equations, which perform the analytical continuation without assuming global information on the function in the entire complex plane, but only in the region through which the equations are solved. We use as example the quark propagator in Landau gauge quantum chromodynamics, which is known from lattice and Dyson-Schwinger studies in Euclidean space. The drawback of the method is the instability of the Cauchy-Riemann equations against high-frequency noise,which makes it difficult to achieve good accuracy. We also point out a few curious details related to the Wick rotation. (orig.)
Quantum fluctuations and spontaneous compactification of eleven-dimensional gravity
International Nuclear Information System (INIS)
Nguen Van Hieu.
1985-01-01
The reduction of the eleven-dimensional pure gravity to the field theory in the four-dimensional Minkowski space-time by means of the spontaneous compactification of the extra dimensions is investigated. The contribution of the quantum fluctuations of the eleven-dimen-- sonal second rank symmetric tensor field to the curvatures of the space-time and the compactified space of the extra dimensions are calculated in the one-loop approximation. It is shown that there exist the values of the cosmological constant for which tachions are absent. As a result, self-consistent quantum field theory is obtained in spontaneous compactified Minkowski space M 4 xS 7 ,is where M 4 is Minkowski space-time, and S 7 is seven-dimensional sphere
Memory as persona non grata in the work of Eugène Minkowski: a historical approach.
Vaz, João M
2016-09-01
Memory is both ubiquitous and persona non grata in the work of Eugène Minkowski. Despite the relevance of memory in the works of those who influenced him, in particular Bergson, Minkowski nonetheless repeatedly overlooked its importance in his writings. To the reader of his work this fact is as much evident as unaccounted for - both by prior research and by Minkowski himself. I shall try to prove that this disregard for memory was conditio sine qua non of Minkowski's first synthesis of Bleuler and Bergson in a 1921 article, which resulted in his famous concept of loss of vital contact with reality and which he equated with schizophrenia. Moreover, this historical approach will, on the one hand, explain the fragmentary use made by Minkowski of the philosophy of Bergson and, on the other, shed light on central aspects of his Le temps vécu of 1933 that an exclusively philosophical analysis cannot reveal. © The Author(s) 2016.
General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem I
Gardner, Richard J.; Hug, Daniel; Weil, Wolfgang; Xing, Sudan; Ye, Deping
2018-01-01
The general volume of a star body, a notion that includes the usual volume, the $q$th dual volumes, and many previous types of dual mixed volumes, is introduced. A corresponding new general dual Orlicz curvature measure is defined that specializes to the $(p,q)$-dual curvature measures introduced recently by Lutwak, Yang, and Zhang. General variational formulas are established for the general volume of two types of Orlicz linear combinations. One of these is applied to the Minkowski problem f...
Inextendibilty of the Maximal Global Hyperbolic Development in Electrogowdy spacetimes
Directory of Open Access Journals (Sweden)
Nungesser Ernesto
2013-09-01
Full Text Available The problem of determinism in General Relativity appears even if one assumes that the spacetime is globally hyperbolic, i.e. that it contains a hypersurface that is intersected by any causal curve exactly once. The strong cosmic censorship hypothesis is essentially the hypothesis that General Relativity is a predictable theory and thus a crucial issue in Classical General Relativity. We sketch here the proof for the case of Electrogowdy spacetimes.
Topology of classical vacuum space-time
International Nuclear Information System (INIS)
Cho, Y.M.
2007-04-01
We present a topological classification of classical vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology π 3 (S 3 ) = π 3 (S 2 ). Viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group, we construct all possible vacuum gravitational connections which give a vanishing curvature tensor. With this we show that the vacuum connection has the knot topology, the same topology which describes the multiple vacua of SU(2) gauge theory. We discuss the physical implications of our result in quantum gravity. (author)
Spacetime coarse grainings in nonrelativistic quantum mechanics
International Nuclear Information System (INIS)
Hartle, J.B.
1991-01-01
Sum-over-histories generalizations of nonrelativistic quantum mechanics are explored in which probabilities are predicted, not just for alternatives defined on spacelike surfaces, but for alternatives defined by the behavior of spacetime histories with respect to spacetime regions. Closed, nonrelativistic systems are discussed whose histories are paths in a given configuration space. The action and the initial quantum state are assumed fixed and given. A formulation of quantum mechanics is used which assigns probabilities to members of sets of alternative coarse-grained histories of the system, that is, to the individual classes of a partition of its paths into exhaustive and exclusive classes. Probabilities are assigned to those sets which decohere, that is, whose probabilities are consistent with the sum rules of probability theory. Coarse graining by the behavior of paths with respect to regions of spacetime is described. For example, given a single region, the set of all paths may be partitioned into those which never pass through the region and those which pass through the region at least once. A sum-over-histories decoherence functional is defined for sets of alternative histories coarse-grained by spacetime regions. Techniques for the definition and effective computation of the relevant sums over histories by operator-product formulas are described and illustrated by examples. Methods based on Euclidean stochastic processes are also discussed and illustrated. Models of decoherence and measurement for spacetime coarse grainings are described. Issues of causality are investigated. Such spacetime generalizations of nonrelativistic quantum mechanics may be useful models for a generalized quantum mechanics of spacetime geometry
Space-like surfaces with free boundary in the Lorentz-Minkowski space
International Nuclear Information System (INIS)
López, R; Pyo, J
2012-01-01
We investigate a variational problem in the Lorentz-Minkowski space L 3 whose critical points are space-like surfaces with a constant mean curvature and making a constant contact angle with a given support surface along its common boundary. We show that if the support surface is a pseudosphere, then the surface is a planar disc or a hyperbolic cap. We also study the problem of space-like hypersurfaces with free boundary in the higher dimensional Lorentz-Minkowski space L n+1 . (paper)
Realizations of κ-Minkowski space, Drinfeld twists, and related symmetry algebras
Energy Technology Data Exchange (ETDEWEB)
Juric, Tajron; Meljanac, Stjepan; Pikutic, Danijel [Ruder Boskovic Institute, Theoretical Physics Division, Zagreb (Croatia)
2015-11-15
Realizations of κ-Minkowski space linear in momenta are studied for time-, space- and light-like deformations. We construct and classify all such linear realizations and express them in terms of the gl(n) generators. There are three one-parameter families of linear realizations for timelike and space-like deformations, while for light-like deformations, there are only four linear realizations. The relation between a deformed Heisenberg algebra, the star product, the coproduct of momenta, and the twist operator is presented. It is proved that for each linear realization there exists a Drinfeld twist satisfying normalization and cocycle conditions. κ-Deformed igl(n)-Hopf algebras are presented for all cases. The κ-Poincare-Weyl and κ-Poincare-Hopf algebras are discussed. The left-right dual κ-Minkowski algebra is constructed from the transposed twists. The corresponding realizations are nonlinear. All Drinfeld twists related to κ-Minkowski space are obtained from our construction. Finally, some physical applications are discussed. (orig.)
Realizations of κ-Minkowski space, Drinfeld twists, and related symmetry algebras
International Nuclear Information System (INIS)
Juric, Tajron; Meljanac, Stjepan; Pikutic, Danijel
2015-01-01
Realizations of κ-Minkowski space linear in momenta are studied for time-, space- and light-like deformations. We construct and classify all such linear realizations and express them in terms of the gl(n) generators. There are three one-parameter families of linear realizations for timelike and space-like deformations, while for light-like deformations, there are only four linear realizations. The relation between a deformed Heisenberg algebra, the star product, the coproduct of momenta, and the twist operator is presented. It is proved that for each linear realization there exists a Drinfeld twist satisfying normalization and cocycle conditions. κ-Deformed igl(n)-Hopf algebras are presented for all cases. The κ-Poincare-Weyl and κ-Poincare-Hopf algebras are discussed. The left-right dual κ-Minkowski algebra is constructed from the transposed twists. The corresponding realizations are nonlinear. All Drinfeld twists related to κ-Minkowski space are obtained from our construction. Finally, some physical applications are discussed. (orig.)
Space-Time Crystal and Space-Time Group.
Xu, Shenglong; Wu, Congjun
2018-03-02
Crystal structures and the Bloch theorem play a fundamental role in condensed matter physics. We extend the static crystal to the dynamic "space-time" crystal characterized by the general intertwined space-time periodicities in D+1 dimensions, which include both the static crystal and the Floquet crystal as special cases. A new group structure dubbed a "space-time" group is constructed to describe the discrete symmetries of a space-time crystal. Compared to space and magnetic groups, the space-time group is augmented by "time-screw" rotations and "time-glide" reflections involving fractional translations along the time direction. A complete classification of the 13 space-time groups in one-plus-one dimensions (1+1D) is performed. The Kramers-type degeneracy can arise from the glide time-reversal symmetry without the half-integer spinor structure, which constrains the winding number patterns of spectral dispersions. In 2+1D, nonsymmorphic space-time symmetries enforce spectral degeneracies, leading to protected Floquet semimetal states. We provide a general framework for further studying topological properties of the (D+1)-dimensional space-time crystal.
Experimental demonstration of metamaterial "multiverse" in a ferrofluid.
Smolyaninov, Igor I; Yost, Bradley; Bates, Evan; Smolyaninova, Vera N
2013-06-17
Extraordinary light rays propagating inside a hyperbolic metamaterial look similar to particle world lines in a 2 + 1 dimensional Minkowski spacetime. Magnetic nanoparticles in a ferrofluid are known to form nanocolumns aligned along the magnetic field, so that a hyperbolic metamaterial may be formed at large enough nanoparticle concentration nH. Here we investigate optical properties of such a metamaterial just below nH. While on average such a metamaterial is elliptical, thermal fluctuations of nanoparticle concentration lead to transient formation of hyperbolic regions (3D Minkowski spacetimes) inside this metamaterial. Thus, thermal fluctuations in a ferrofluid look similar to creation and disappearance of individual Minkowski spacetimes (universes) in the cosmological multiverse. This theoretical picture is supported by experimental measurements of polarization-dependent optical transmission of a cobalt based ferrofluid at 1500 nm.
Geodesics in Goedel-type space-times
International Nuclear Information System (INIS)
Calvao, M.O.; Soares, I.D.; Tiomno, J.
1988-01-01
The geodesic curves of the homogeneous Goedel-type space-times, which constitute a two-parameter ({ l and Ω}) class of solutions presented to several theories of gravitation (general relativity, Einstein-Cartan and higher derivative) are investigated. The qualitative properties of those curves by means of the introduction of an effective potential and then accomplish the analytical integration of the equations of motion are examined. It is shown that some of the qualitative features of the free motion in Godel's universe (l 2 =2Ω 2 ) are preserved in all space-times, namely the projections of the geodesics onto the 2-surface (r,ψ) are simple closed curves, and the geodesics for which the ratio of azymuthal angular momentum to total energy, υ is equal to zero always cross the origin r = o. However, two new cases appear: (i) radially unbounded geodesics with υ assuming any (real) value, which may occur only for the causal space-times (l 2 ≥ 4 Ω 2 ), and (ii) geodesics with υ bounded both below and above, which always occur for the circular family (l 2 [pt
Texture classification using non-Euclidean Minkowski dilation
Florindo, Joao B.; Bruno, Odemir M.
2018-03-01
This study presents a new method to extract meaningful descriptors of gray-scale texture images using Minkowski morphological dilation based on the Lp metric. The proposed approach is motivated by the success previously achieved by Bouligand-Minkowski fractal descriptors on texture classification. In essence, such descriptors are directly derived from the morphological dilation of a three-dimensional representation of the gray-level pixels using the classical Euclidean metric. In this way, we generalize the dilation for different values of p in the Lp metric (Euclidean is a particular case when p = 2) and obtain the descriptors from the cumulated distribution of the distance transform computed over the texture image. The proposed method is compared to other state-of-the-art approaches (such as local binary patterns and textons for example) in the classification of two benchmark data sets (UIUC and Outex). The proposed descriptors outperformed all the other approaches in terms of rate of images correctly classified. The interesting results suggest the potential of these descriptors in this type of task, with a wide range of possible applications to real-world problems.
Non-self-dual nonlinear gravitons
International Nuclear Information System (INIS)
Yasskin, P.B.; Isenberg, J.A.
1982-01-01
Penrose has given a twistor description of all self-dual complex Riemannian space-times. This construction is modified to characterize all complex Riemannian space-times and all complex teleparallel space-times. This construction may be useful in finding non-self-dual solutions to the gravitational field equations (Einstein's or otherwise) without or with sources. It may also lead to a nonperturbative method for computing path integrals. Whereas Penrose shows that a self-dual space-time may be specified by a deformation of projective twistor space (the set of α planes in complex Minkowski space), it is found that a Riemannian or teleparallel space-time may be described by a deformation of projective ambitwistor space (the set of null geodesics in complex Minkowski space). (author)
Power Allocation Strategies for Distributed Space-Time Codes in Amplify-and-Forward Mode
Directory of Open Access Journals (Sweden)
Are Hjørungnes
2009-01-01
Full Text Available We consider a wireless relay network with Rayleigh fading channels and apply distributed space-time coding (DSTC in amplify-and-forward (AF mode. It is assumed that the relays have statistical channel state information (CSI of the local source-relay channels, while the destination has full instantaneous CSI of the channels. It turns out that, combined with the minimum SNR based power allocation in the relays, AF DSTC results in a new opportunistic relaying scheme, in which the best relay is selected to retransmit the source's signal. Furthermore, we have derived the optimum power allocation between two cooperative transmission phases by maximizing the average received SNR at the destination. Next, assuming M-PSK and M-QAM modulations, we analyze the performance of cooperative diversity wireless networks using AF opportunistic relaying. We also derive an approximate formula for the symbol error rate (SER of AF DSTC. Assuming the use of full-diversity space-time codes, we derive two power allocation strategies minimizing the approximate SER expressions, for constrained transmit power. Our analytical results have been confirmed by simulation results, using full-rate, full-diversity distributed space-time codes.
Visualization of Minkowski operations by computer graphics techniques
Roerdink, J.B.T.M.; Blaauwgeers, G.S.M.; Serra, J; Soille, P
1994-01-01
We consider the problem of visualizing 3D objects defined as a Minkowski addition or subtraction of elementary objects. It is shown that such visualizations can be obtained by using techniques from computer graphics such as ray tracing and Constructive Solid Geometry. Applications of the method are
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Zahn, J.W.
2006-12-15
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the {phi}{sup 3} and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space
International Nuclear Information System (INIS)
Zahn, J.W.
2006-12-01
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the Φ 3 and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
Minkowski Functionals and Cluster Analysis for CMB Maps
Novikov, D.; Feldman, Hume A.; Shandarin, Sergei F.
We suggest novel statistics for the CMB maps that are sensitive to non-Gaussian features. These statistics are natural generalizations of the geometrical and topological methods that have been already used in cosmology such as the cumulative distribution function and genus. We compute the distribution functions of the Partial Minkowski Functionals for the excursion set above or bellow a constant temperature threshold. Minkowski Functionals are additive and are translationally and rotationally invariant. Thus, they can be used for patchy and/or incomplete coverage. The technique is highly efficient computationally (it requires only O(N) operations, where N is the number of pixels per one threshold level). Further, the procedure makes it possible to split large data sets into smaller subsets. The full advantage of these statistics can be obtained only on very large data sets. We apply it to the 4-year DMR COBE data corrected for the Galaxy contamination as an illustration of the technique.
Energy conditions of non-singular black hole spacetimes in conformal gravity
International Nuclear Information System (INIS)
Toshmatov, Bobir; Bambi, Cosimo; Ahmedov, Bobomurat; Abdujabbarov, Ahmadjon; Stuchlik, Zdenek
2017-01-01
Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)
Energy conditions of non-singular black hole spacetimes in conformal gravity
Energy Technology Data Exchange (ETDEWEB)
Toshmatov, Bobir [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic); Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); Bambi, Cosimo [Fudan University, Department of Physics, Center for Field Theory and Particle Physics, Shanghai (China); Eberhard-Karls Universitaet Tuebingen, Theoretical Astrophysics, Tuebingen (Germany); Ahmedov, Bobomurat [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Abdujabbarov, Ahmadjon [Ulugh Beg Astronomical Institute, Tashkent (Uzbekistan); National University of Uzbekistan, Tashkent (Uzbekistan); Tashkent University of Information Technologies, Tashkent (Uzbekistan); Stuchlik, Zdenek [Silesian University in Opava, Faculty of Philosophy and Science, Institute of Physics, Opava (Czech Republic)
2017-08-15
Conformal gravity can elegantly solve the problem of spacetime singularities present in Einstein's gravity. For every physical spacetime, there is an infinite family of conformally equivalent singularity-free metrics. In the unbroken phase, every non-singular metric is equivalent and can be used to infer the physical properties of the spacetime. In the broken phase, a Higgs-like mechanism should select a certain vacuum, which thus becomes the physical one. However, in the absence of the complete theoretical framework we do not know how to select the right vacuum. In this paper, we study the energy conditions of non-singular black hole spacetimes obtained in conformal gravity assuming they are solutions of Einstein's gravity with an effective energy-momentum tensor. We check whether such conditions can be helpful to select the vacuum of the broken phase. (orig.)
Special relativity of Kaluza-Klein
International Nuclear Information System (INIS)
Maia, M.D.
1984-01-01
Kaluza-Klein theory is formulated from the point of view of the Gauss geometry of embedded manifolds. According to this view, space-time is regarded as locally and isometrically embedded in the high dimensional space predicted by that theory. The high dimensional Minkowski space is considered as a particular solution of the high dimensional vacuum Einstein's equations and it is assumed to represent the ground state of the theory. In this particular case it is shown that the compactification of the space of internal variables follows from the second quadratic forms of the Gaussian geometry of space-time. The Gauss-Codazzi-Ricci integrability conditions are interpreted as the field equations for a low energy observer. The space-time reduced Einstein-Hilbert action is interpreted as an integral equation on the size of the internal space. 13 references
Spontaneously broken spacetime symmetries and the role of inessential Goldstones
Klein, Remko; Roest, Diederik; Stefanyszyn, David
2017-10-01
In contrast to internal symmetries, there is no general proof that the coset construction for spontaneously broken spacetime symmetries leads to universal dynamics. One key difference lies in the role of Goldstone bosons, which for spacetime symmetries includes a subset which are inessential for the non-linear realisation and hence can be eliminated. In this paper we address two important issues that arise when eliminating inessential Goldstones. The first concerns the elimination itself, which is often performed by imposing so-called inverse Higgs constraints. Contrary to claims in the literature, there are a series of conditions on the structure constants which must be satisfied to employ the inverse Higgs phenomenon, and we discuss which parametrisation of the coset element is the most effective in this regard. We also consider generalisations of the standard inverse Higgs constraints, which can include integrating out inessential Goldstones at low energies, and prove that under certain assumptions these give rise to identical effective field theories for the essential Goldstones. Secondly, we consider mappings between non-linear realisations that differ both in the coset element and the algebra basis. While these can always be related to each other by a point transformation, remarkably, the inverse Higgs constraints are not necessarily mapped onto each other under this transformation. We discuss the physical implications of this non-mapping, with a particular emphasis on the coset space corresponding to the spontaneous breaking of the Anti-De Sitter isometries by a Minkowski probe brane.
Is the shell-focusing singularity of Szekeres space-time visible?
International Nuclear Information System (INIS)
Nolan, Brien C; Debnath, Ujjal
2007-01-01
The visibility of the shell-focusing singularity in Szekeres space-time--which represents quasispherical dust collapse--has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second nonparallel radial geodesic, then the space-time is spherically symmetric, and so is a Lemaitre-Tolman-Bondi space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for nonradial null geodesics in the axially symmetric case and in the general (nonaxially symmetric) case, and suggest a possible approach
Twistor space, Minkowski space and the conformal group
van den Broek, P.M.
1983-01-01
It is shown that the conformal group of compactified Minkowski space is isomorphic to a group of rays of semilinear transformations of twistor space. The action of the conformal group on twistor space is given by an explicit realisation of this isomorphism. In this way we determine the
Gravastars with higher dimensional spacetimes
Ghosh, Shounak; Ray, Saibal; Rahaman, Farook; Guha, B. K.
2018-07-01
We present a new model of gravastar in the higher dimensional Einsteinian spacetime including Einstein's cosmological constant Λ. Following Mazur and Mottola (2001, 2004) we design the star with three specific regions, as follows: (I) Interior region, (II) Intermediate thin spherical shell and (III) Exterior region. The pressure within the interior region is equal to the negative matter density which provides a repulsive force over the shell. This thin shell is formed by ultra relativistic plasma, where the pressure is directly proportional to the matter-energy density which does counter balance the repulsive force from the interior whereas the exterior region is completely vacuum assumed to be de Sitter spacetime which can be described by the generalized Schwarzschild solution. With this specification we find out a set of exact non-singular and stable solutions of the gravastar which seems physically very interesting and reasonable.
Lorentz covariant tempered distributions in two-dimensional space-time
International Nuclear Information System (INIS)
Zinov'ev, Yu.M.
1989-01-01
The problem of describing Lorentz covariant distributions without any spectral condition has hitherto remained unsolved even for two-dimensional space-time. Attempts to solve this problem have already been made. Zharinov obtained an integral representation for the Laplace transform of Lorentz invariant distributions with support in the product of two-dimensional future light cones. However, this integral representation does not make it possible to obtain a complete description of the corresponding Lorentz invariant distributions. In this paper the author gives a complete description of Lorentz covariant distributions for two-dimensional space-time. No spectral conditions is assumed
Radiation forces and the Abraham-Minkowski problem
Brevik, Iver
2018-04-01
Recent years have witnessed a number of beautiful experiments in radiation optics. Our purpose with this paper is to highlight some developments of radiation pressure physics in general, and thereafter to focus on the importance of the mentioned experiments in regard to the classic Abraham-Minkowski problem. That means, what is the “correct” expression for electromagnetic momentum density in continuous matter. In our opinion, one often sees that authors over-interpret the importance of their experimental findings with respect to the momentum problem. Most of these experiments are actually unable to discriminate between these energy-momentum tensors at all, since they can be easily described in terms of force expressions that are common for Abraham and Minkowski. Moreover, we emphasize the inherent ambiguity in applying the formal conservation principles to the radiation field in a dielectric, the reason being that the electromagnetic field in matter is only a subsystem which has to be supplemented by the mechanical subsystem to be closed. Finally, we make some suggestions regarding the connection between macroscopic electrodynamics and the Casimir effect, suggesting that there is a limit for the magnitudes of the cutoff parameters in QFT related to surface tension in ordinary hydromechanics.
Asymptotically flat structure of hypergravity in three spacetime dimensions
Energy Technology Data Exchange (ETDEWEB)
Fuentealba, Oscar [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile); Departamento de Física, Universidad de Concepción,Casilla 160-C, Concepción (Chile); Matulich, Javier; Troncoso, Ricardo [Centro de Estudios Científicos (CECs),Av. Arturo Prat 514, Valdivia (Chile)
2015-10-02
The asymptotic structure of three-dimensional hypergravity without cosmological constant is analyzed. In the case of gravity minimally coupled to a spin-5/2 field, a consistent set of boundary conditions is proposed, being wide enough so as to accommodate a generic choice of chemical potentials associated to the global charges. The algebra of the canonical generators of the asymptotic symmetries is given by a hypersymmetric nonlinear extension of BMS{sub 3}. It is shown that the asymptotic symmetry algebra can be recovered from a subset of a suitable limit of the direct sum of the W{sub (2,4)} algebra with its hypersymmetric extension. The presence of hypersymmetry generators allows to construct bounds for the energy, which turn out to be nonlinear and saturate for spacetimes that admit globally-defined “Killing vector-spinors”. The null orbifold or Minkowski spacetime can then be seen as the corresponding ground state in the case of fermions that fulfill periodic or antiperiodic boundary conditions, respectively. The hypergravity theory is also explicitly extended so as to admit parity-odd terms in the action. It is then shown that the asymptotic symmetry algebra includes an additional central charge, being proportional to the coupling of the Lorentz-Chern-Simons form. The generalization of these results in the case of gravity minimally coupled to arbitrary half-integer spin fields is also carried out. The hypersymmetry bounds are found to be given by a suitable polynomial of degree s+(1/2) in the energy, where s is the spin of the fermionic generators.
Planck-scale-modified dispersion relations in FRW spacetime
Rosati, Giacomo; Amelino-Camelia, Giovanni; Marcianò, Antonino; Matassa, Marco
2015-12-01
In recent years, Planck-scale modifications of the dispersion relation have been attracting increasing interest also from the viewpoint of possible applications in astrophysics and cosmology, where spacetime curvature cannot be neglected. Nonetheless, the interplay between Planck-scale effects and spacetime curvature is still poorly understood, particularly in cases where curvature is not constant. These challenges have been so far postponed by relying on an ansatz, first introduced by Jacob and Piran. We propose here a general strategy of analysis of the effects of modifications of the dispersion relation in Friedmann-Robertson-Walker spacetimes, applicable both to cases where the relativistic equivalence of frames is spoiled ("preferred-frame scenarios") and to the alternative possibility of "DSR-relativistic theories," theories that are fully relativistic but with relativistic laws deformed so that the modified dispersion relation is observer independent. We show that the Jacob-Piran ansatz implicitly assumes that spacetime translations are not affected by the Planck scale, while under rather general conditions, the same Planck-scale quantum-spacetime structures producing modifications of the dispersion relation also affect translations. Through the explicit analysis of one of the effects produced by modifications of the dispersion relation, an effect amounting to Planck-scale corrections to travel times, we show that our concerns are not merely conceptual but rather can have significant quantitative implications.
On thick domain walls in general relativity
Goetz, Guenter; Noetzold, Dirk
1989-01-01
Planar scalar field configurations in general relativity differ considerably from those in flat space. It is shown that static domain walls of finite thickness in curved space-time do not possess a reflection symmetry. At infinity, the space-time tends to the Taub vacuum on one side of the wall and to the Minkowski vacuum (Rindler space-time) on the other. Massive test particles are always accelerated towards the Minkowski side, i.e., domain walls are attractive on the Taub side, but repulsive on the Minkowski side (Taub-vacuum cleaner). It is also proved that the pressure in all directions is always negative. Finally, a brief comment is made concerning the possibility of infinite, i.e., bigger than horizon size, domain walls in our universe. All of the results are independent of the form of the potential V(phi) greater than or equal to 0 of the scalar field phi.
Gravitational wave extraction based on Cauchy-characteristic extraction and characteristic evolution
Energy Technology Data Exchange (ETDEWEB)
Babiuc, Maria [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States); Szilagyi, Bela [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, PA 15260 (United States); Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany); Hawke, Ian [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany); School of Mathematics, University of Southampton, Southampton SO17 1BJ (United Kingdom); Zlochower, Yosef [Department of Physics and Astronomy, and Center for Gravitational Wave Astronomy, University of Texas at Brownsville, Brownsville, TX 78520 (United States)
2005-12-07
We implement a code to find the gravitational news at future null infinity by using data from a Cauchy code as boundary data for a characteristic code. This technique of Cauchy-characteristic extraction (CCE) allows for the unambiguous extraction of gravitational waves from numerical simulations. We first test the technique on non-radiative spacetimes: Minkowski spacetime, perturbations of Minkowski spacetime and static black hole spacetimes in various gauges. We show the convergence and limitations of the algorithm and illustrate its success in cases where other wave extraction methods fail. We further apply our techniques to a standard radiative test case for wave extraction, a linearized Teukolsky wave, presenting our results in comparison to the Zerilli technique, and we argue for the advantages of our method of extraction.
Brownian motion, Minkowski space and principle of special relativity
International Nuclear Information System (INIS)
Caubet, J.-P.
1977-01-01
From the assumption that the brownian diffusion locally behaves like an ideal gas (pressure being inversely proportional to volume according to Boyle's law) one can deduce the signature +++- of the Minkowski space, the Lorentz addition of velocities, and the principle of special relativity [fr
Asymptotic structure of isolated systems
International Nuclear Information System (INIS)
Schmidt, B.G.
1979-01-01
The main methods to formulate asymptotic flatness conditions are introduced and motivation and basic ideas are emphasized. Any asymptotic flatness condition proposed up to now describes space-times which behave somehow like Minkowski space, and a very explicit exposition of the structure at infinity of Minkowski space is given. This structure is used to describe the asymptotic behaviour of fields on Minkowski space in a frame-dependent way. The definition of null infinity for curved space-time according to Penrose is given and attempts to define spacelike infinity are outlined. The conformal bundle approach to the formulation of asymptotic behaviour is described and its relation to null and spacelike infinity is given, as far as known. (Auth.)
Twistor space, Minkowski space and the conformal group
International Nuclear Information System (INIS)
Broek, P.M. van den
1983-01-01
It is shown that the conformal group of compactified Minkowski space is isomorphic to a group of rays of semilinear transformations of twistor space. The action of the conformal group on twistor space is given by an explicit realisation of this isomorphism. In this way we determine the transformation of twistor space under space inversion and time inversion. (orig.)
Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes
International Nuclear Information System (INIS)
Nagar, Alessandro; Rezzolla, Luciano
2005-01-01
The theory of gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes is now well established. Yet, as different notations and conventions have been used throughout the years, the literature on the subject is often confusing and sometimes confused. The purpose of this review is to review and collect the relevant expressions related to the Regge-Wheeler and Zerilli equations for the odd and even-parity perturbations of a Schwarzschild spacetime. Special attention is paid to the form they assume in the presence of matter-sources and, for the two most popular conventions in the literature, to the asymptotic expressions and gravitational-wave amplitudes. Besides pointing out some inconsistencies in the literature, the expressions collected here could serve as a quick reference for the calculation of the perturbations of a Schwarzschild black-hole spacetime driven by generic sources and for those approaches in which gravitational waves are extracted from numerically generated spacetimes. (topical review)
Environmental Controls on Space-Time Biodiversity Patterns in the Amazon
Porporato, A. M.; Bonetti, S.; Feng, X.
2014-12-01
The Amazon/Andes territory is characterized by the highest biodiversity on Earth and understanding how all these ecological niches and different species originated and developed is an open challenge. The niche perspective assumes that species have evolved and occupy deterministically different roles within its environment. This view differs from that of the neutral theories, which assume ecological equivalence between all species but incorporates stochastic demographic processes along with long-term migration and speciation rates. Both approaches have demonstrated tremendous power in predicting aspects species biodiversity. By combining tools from both approaches, we use modified birth and death processes to simulate plant species diversification in the Amazon/Andes and their space-time ecohydrological controls. By defining parameters related to births and deaths as functions of available resources, we incorporate the role of space-time resource variability on niche formation and community composition. We also explicitly include the role of a heterogeneous landscape and topography. The results are discussed in relation to transect datasets from neotropical forests.
A new method for calculation of traces of Dirac γ-matrices in Minkowski space
International Nuclear Information System (INIS)
Bondarev, Alexander L.
2006-01-01
This paper presents some relations for orthonormal bases in the Minkowski space and isotropic tetrads constructed from the vectors of these bases. As an example of an application of the obtained formulae, in particular recursion relations, a new method is proposed to calculate traces of Dirac γ-matrices in the Minkowski space. Compared to the classical algorithms, the new method results in more compact expressions for the traces. Specifically, it may be easily implemented as a simple yet efficient computer algorithm
Classification of non-Riemannian doubled-yet-gauged spacetime
Energy Technology Data Exchange (ETDEWEB)
Morand, Kevin [Universidad Andres Bello, Departamento de Ciencias Fisicas, Santiago de Chile (Chile); Universidad Tecnica Federico Santa Maria, Centro Cientifico-Tecnologico de Valparaiso, Departamento de Fisica, Valparaiso (Chile); Park, Jeong-Hyuck [Sogang University, Department of Physics, Seoul (Korea, Republic of); Institute for Basic Science (IBS), Center for Theoretical Physics of the Universe, Seoul (Korea, Republic of)
2017-10-15
Assuming O(D,D) covariant fields as the 'fundamental' variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n, anti n), 0 ≤ n + anti n ≤ D. Upon these backgrounds, strings become chiral and anti-chiral over n and anti n directions, respectively, while particles and strings are frozen over the n + anti n directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis-Ooguri non-relativistic string, (D-1, 0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, (0, 1) leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as D = 10, (3, 3) may open a new scheme for the dimensional reduction from ten to four. (orig.)
A multi-element cosmological model with a complex space-time topology
Kardashev, N. S.; Lipatova, L. N.; Novikov, I. D.; Shatskiy, A. A.
2015-02-01
Wormhole models with a complex topology having one entrance and two exits into the same space-time of another universe are considered, as well as models with two entrances from the same space-time and one exit to another universe. These models are used to build a model of a multi-sheeted universe (a multi-element model of the "Multiverse") with a complex topology. Spherical symmetry is assumed in all the models. A Reissner-Norström black-hole model having no singularity beyond the horizon is constructed. The strength of the central singularity of the black hole is analyzed.
Exact interior solutions in 2 + 1-dimensional spacetime
Energy Technology Data Exchange (ETDEWEB)
Rahaman, Farook; Bhar, Piyali [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Biswas, Ritabrata [Indian Institute of Engineering Sceince and Technology Shibpur, Howrah, West Bengal (India); Usmani, A.A. [Aligarh Muslim University, Department of Physics, Aligarh, Uttar Pradesh (India)
2014-04-15
We provide a new class of exact solutions for the interior in 2 + 1-dimensional spacetime. The solutions obtained for the perfect fluid model both with and without cosmological constant (Λ) are found to be regular and singularity free. It assumes very simple analytical forms that help us to study the various physical properties of the configuration. Solutions without Λ are found to be physically acceptable. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Nomura, Yasunori [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, Kashiwa 277-8583 (Japan); Salzetta, Nico, E-mail: nsalzetta@berkeley.edu [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States); Sanches, Fabio; Weinberg, Sean J. [Berkeley Center for Theoretical Physics, Department of Physics, University of California, Berkeley, CA 94720 (United States); Theoretical Physics Group, Lawrence Berkeley National Laboratory, Berkeley, CA 94720 (United States)
2016-12-10
We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.
Emergent/quantum gravity: macro/micro structures of spacetime
International Nuclear Information System (INIS)
Hu, B L
2009-01-01
Emergent gravity views spacetime as an entity emergent from a more complete theory of interacting fundamental constituents valid at much finer resolution or higher energies, usually assumed to be above the Planck energy. In this view general relativity is an effective theory valid only at long wavelengths and low energies. We describe the tasks of emergent gravity from any ('top-down') candidate theory for the microscopic structure of spacetime (quantum gravity), namely, identifying the conditions and processes or mechanisms whereby the familiar macroscopic spacetime described by general relativity and matter content described by quantum field theory both emerge with high probability and reasonable robustness. We point out that this task may not be so easy as commonly conjured (as implied in the 'theory of everything') because there are emergent phenomena which cannot simply be deduced from a given micro-theory. Going in the opposite direction ('bottom-up') is the task of quantum gravity, i.e., finding a theory for the microscopic structure of spacetime, which, in this new view, cannot come from quantizing the metric or connection forms because they are the collective variables which are meaningful only for the macroscopic theory (valid below the Planck energy). This task looks very difficult or almost impossible because it entails reconstructing lost information. We point out that the situation may not be so hopeless if we ask the right questions and have the proper tools for what we want to look for. We suggest pathways to move 'up' (in energy) from the given macroscopic conditions of classical gravity and quantum field theory to the domain closer to the micro-macro interface where spacetime emerged and places to look for clues or tell-tale signs at low energy where one could infer indirectly some salient features of the micro-structure of spacetime.
The Nature of the Cosmological Constant Problem
Maia, M. D.; Capistrano, A. J. S.; Monte, E. M.
General relativity postulates the Minkowski space-time as the standard (flat) geometry against which we compare all curved space-times and also as the gravitational ground state where particles, quantum fields and their vacua are defined. On the other hand, experimental evidences tell that there exists a non-zero cosmological constant, which implies in a deSitter ground state, which not compatible with the assumed Minkowski structure. Such inconsistency is an evidence of the missing standard of curvature in Riemann's geometry, which in general relativity manifests itself in the form of the cosmological constant problem. We show how the lack of a curvature standard in Riemann's geometry can be fixed by Nash's theorem on metric perturbations. The resulting higher dimensional gravitational theory is more general than general relativity, similar to brane-world gravity, but where the propagation of the gravitational field along the extra dimensions is a mathematical necessity, rather than a postulate. After a brief introduction to Nash's theorem, we show that the vacuum energy density must remain confined to four-dimensional space-times, but the cosmological constant resulting from the contracted Bianchi identity represents a gravitational term which is not confined. In this case, the comparison between the vacuum energy and the cosmological constant in general relativity does not make sense. Instead, the geometrical fix provided by Nash's theorem suggests that the vacuum energy density contributes to the perturbations of the gravitational field.
Quantum gravity effects in Myers-Perry space-times
International Nuclear Information System (INIS)
Litim, Daniel F.; Nikolakopoulos, Konstantinos
2014-01-01
We study quantum gravity effects for Myers-Perry black holes assuming that the leading contributions arise from the renormalization group evolution of Newton’s coupling. Provided that gravity weakens following the asymptotic safety conjecture, we find that quantum effects lift a degeneracy of higher-dimensional black holes, and dominate over kinematical ones induced by rotation, particularly for small black hole mass, large angular momentum, and higher space-time dimensionality. Quantum-corrected space-times display inner and outer horizons, and show the existence of a black hole of smallest mass in any dimension. Ultra-spinning solutions no longer persist. Thermodynamic properties including temperature, specific heat, the Komar integrals, and aspects of black hole mechanics are studied as well. Observing a softening of the ring singularity, we also discuss the validity of classical energy conditions
Nomura, Yasunori; Rath, Pratik; Salzetta, Nico
2018-05-01
The past decade has seen a tremendous effort toward unraveling the relationship between entanglement and emergent spacetime. These investigations have revealed that entanglement between holographic degrees of freedom is crucial for the existence of bulk spacetime. We examine this connection from the other end of the entanglement spectrum and clarify the assertion that maximally entangled states have no reconstructable spacetime. To do so, we first define the conditions for bulk reconstructability. Under these terms, we scrutinize two cases of maximally entangled holographic states. One is the familiar example of AdS black holes; these are dual to thermal states of the boundary conformal field theory. Sending the temperature to the cutoff scale makes the state maximally entangled and the respective black hole consumes the spacetime. We then examine the de Sitter limit of Friedmann-Robertson-Walker (FRW) spacetimes. This limit is maximally entangled if one formulates the boundary theory on the holographic screen. Paralleling the anti-de Sitter (AdS) black hole, we find the resulting reconstructable region of spacetime vanishes. Motivated by these results, we prove a theorem showing that maximally entangled states have no reconstructable spacetime. Evidently, the emergence of spacetime is endemic to intermediate entanglement. By studying the manner in which intermediate entanglement is achieved, we uncover important properties about the boundary theory of FRW spacetimes. With this clarified understanding, our final discussion elucidates the natural way in which holographic Hilbert spaces may house states dual to different geometries. This paper provides a coherent picture clarifying the link between spacetime and entanglement and develops many promising avenues of further work.
Electromagnetic momentum in magnetic media and the Abraham-Minkowski controversy
Energy Technology Data Exchange (ETDEWEB)
Jimenez, J L [Departamento de Fisica, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana, Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Apartado Postal 21-463, Mexico DF, 04000 (Mexico); Campos, I [Departamento de Fisica, Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Apartado Postal 21-463, Mexico DF, 04000 (Mexico); Lopez-Marino, M A, E-mail: jlj@xanum.uam.mx, E-mail: iecampos@prodigy.net.mx, E-mail: malm@itesm.mx [Departamento de Ingenieria, Tecnologico de Monterrey, Campus Central de Veracruz, Av. E. Garza Sada 1, Apartado Postal 314, Cordoba, Veracruz, 94500 (Mexico)
2011-05-15
We explore the consequences of a force density, - (1)/c ({partial_derivative}M)/{partial_derivative}t x E, studied by some authors, for the device designed by Lai (1980 Am. J. Phys. 48 658) to analyse which definition of electromagnetic momentum density, either Minkowski's or Abraham's, is consistent with mechanical torques that arise from the change in time of a magnetic field, which produces an induced electric field that acts on free and polarization charges. It is found that Minkowski's definition is consistent with the mechanical torques associated with free charges, while Abraham's is consistent with mechanical torques associated with both free and polarization charges. We show that with this new force density Lai's work (1980 Am. J. Phys. 48 658) can be extended to include magnetic media. The results are consistent with Abraham's definition of electromagnetic momentum density, extending in this way its usefulness to magnetic media.
Quantum tasks in Minkowski space
International Nuclear Information System (INIS)
Kent, Adrian
2012-01-01
The fundamental properties of quantum information and its applications to computing and cryptography have been greatly illuminated by considering information-theoretic tasks that are provably possible or impossible within non-relativistic quantum mechanics. I describe here a general framework for defining tasks within (special) relativistic quantum theory and illustrate it with examples from relativistic quantum cryptography and relativistic distributed quantum computation. The framework gives a unified description of all tasks previously considered and also defines a large class of new questions about the properties of quantum information in relation to Minkowski causality. It offers a way of exploring interesting new fundamental tasks and applications, and also highlights the scope for a more systematic understanding of the fundamental information-theoretic properties of relativistic quantum theory. (paper)
A few properties of a certain class of degenerate space-times
International Nuclear Information System (INIS)
Kowalczynski, J.K.; Plebanski, J.F.
1977-01-01
The properties are studied of a class of space-times determined by assuming the shape of the metric form ds 2 including disposable coordinate functions. It has been found that this class includes degenerate space-times with geodetic, null, shear-free congruence with nonvanishing expansion. The theorem has been proved that this class of solutions of the Einstein equations can easily be expanded to solutions of Einstein-Maxwell equations with a fairly general electromagnetic field. For a selected subclass relations are given between the functions determining the metric form, and two new explicit solutions with arbitrary functions of the Einstein-Maxwell equations with a cosmological constant are found. (author)
Quantum fields in curved space
International Nuclear Information System (INIS)
Birrell, N.D.; Davies, P.C.W.
1982-01-01
The book presents a comprehensive review of the subject of gravitational effects in quantum field theory. Quantum field theory in Minkowski space, quantum field theory in curved spacetime, flat spacetime examples, curved spacetime examples, stress-tensor renormalization, applications of renormalization techniques, quantum black holes and interacting fields are all discussed in detail. (U.K.)
Quantum heating as an alternative of reheating
Akhmedov, Emil T.; Bascone, Francesco
2018-02-01
To model a realistic situation for the beginning we consider massive real scalar ϕ4 theory in a (1 +1 )-dimensional asymptotically static Minkowski spacetime with an intermediate stage of expansion. To have an analytic headway we assume that scalars have a big mass. At past and future infinities of the background we have flat Minkowski regions which are joint by the inflationary expansion region. We use the tree-level Keldysh propagator in the theory in question to calculate the expectation value of the stress-energy tensor which is, thus, due to the excitations of the zero-point fluctuations. Then we show that even for large mass, if the de Sitter expansion stage is long enough, the quantum loop corrections to the expectation value of the stress-energy tensor are not negligible in comparison with the tree-level contribution. That is revealed itself via the excitation of the higher-point fluctuations of the exact modes: during the expansion stage a nonzero particle number density for the exact modes is generated. This density is not Planckian and serves as a quench which leads to a thermalization in the out Minkowski stage.
Singularities of lightcone pedals of spacelike curves in Lorentz-Minkowski 3-space
Directory of Open Access Journals (Sweden)
Chen Liang
2016-01-01
Full Text Available In this paper, geometric properties of spacelike curves on a timelike surface in Lorentz-Minkowski 3-space are investigated by applying the singularity theory of smooth functions from the contact viewpoint.
κ-Minkowski and Snyder algebra from reparametrization symmetry
International Nuclear Information System (INIS)
Chandrasekhar, Chatterjee; Sunandan, Gangopadhyay
2008-01-01
Recently, motivated by the ideas of quantum gravity, a generalization of Special Relativity known as Doubly Special Relativity has been proposed. The most popular model is the Magueijo-Smolin model. We derive non commuting phase-space structures which are combinations of both the κ-Minkowski and the Snyder algebra by exploiting the re-parametrisation symmetry of the recently proposed Lagrangian for a point particle satisfying the exact Doubly Special Relativity dispersion relation in the Magueijo-Smolin framework
Confined gluon from Minkowski space continuation of the PT-BFM SDE solution
Czech Academy of Sciences Publication Activity Database
Šauli, Vladimír
2012-01-01
Roč. 39, č. 3 (2012), 035003/1-035003/16 ISSN 0954-3899 Institutional support: RVO:61389005 Keywords : Minkowski pace * effective QCD * gluon mass generation Subject RIV: BE - Theoretical Physics Impact factor: 5.326, year: 2012
Electromagnetic Momentum in Magnetic Media and the Abraham-Minkowski Controversy
Jimenez, J. L.; Campos, I.; Lopez-Marino, M. A.
2011-01-01
We explore the consequences of a force density, [image omitted], studied by some authors, for the device designed by Lai (1980 "Am. J. Phys. 48" 658) to analyse which definition of electromagnetic momentum density, either Minkowski's or Abraham's, is consistent with mechanical torques that arise from the change in time of a magnetic field, which…
Einstein’s physical chronogeometry
Directory of Open Access Journals (Sweden)
Mario Bacelar Valente
Full Text Available ABSTRACT In Einstein’s physical geometry, the geometry of space and the uniformity of time are taken to be non-conventional. However, due to the stipulation of the isotropy of the one-way speed of light in the synchronization of clocks (or definition of simultaneity, as it stands, Einstein’s views do not seem to apply to the whole of the Minkowski space-time. In this work we will see how Einstein’s views can be applied to the Minkowski space-time. In this way, when adopting Einstein’s views, chronogeometry is a physical chronogeometry.
International Nuclear Information System (INIS)
Hartle, J.B.
1995-01-01
In usual quantum theory, the information available about a quantum system is defined in terms of the density matrix describing it on a spacelike surface. This definition must be generalized for extensions of quantum theory which neither require, nor always permit, a notion of state on a spacelike surface. In particular, it must be generalized for the generalized quantum theories appropriate when spacetime geometry fluctuates quantum mechanically or when geometry is fixed but not foliable by spacelike surfaces. This paper introduces a four-dimensional notion of the information available about a quantum system's boundary conditions in the various sets of decohering, coarse-grained histories it may display. This spacetime notion of information coincides with the familiar one when quantum theory is formulable in terms of states on spacelike surfaces but generalizes this notion when it cannot be so formulated. The idea of spacetime information is applied in several contexts: When spacetime geometry is fixed the information available through alternatives restricted to a fixed spacetime region is defined. The information available through histories of alternatives of general operators is compared to that obtained from the more limited coarse grainings of sum-over-histories quantum mechanics that refer only to coordinates. The definition of information is considered in generalized quantum theories. We consider as specific examples time-neutral quantum mechanics with initial and final conditions, quantum theories with nonunitary evolution, and the generalized quantum frameworks appropriate for quantum spacetime. In such theories complete information about a quantum system is not necessarily available on any spacelike surface but must be searched for throughout spacetime. The information loss commonly associated with the ''evolution of pure states into mixed states'' in black hole evaporation is thus not in conflict with the principles of generalized quantum mechanics
Can De Sitter spacetime be a final state of the contracting universe
International Nuclear Information System (INIS)
Berezin, V.A.
1984-01-01
This chapter attempts to phenomenologically describe the final stage of the Universe contraction. A model equation of state is used to demonstrate that during a cosmological contraction a de Sitter spacetime may be produced. It is shown that a equilibrium thermodynamic description of the matter in cosmological models leads to the absence of particle creation. It is proposed that these nonequilibrium processes be taken into account by introducing a new additional thermodynamic variable showing the explicit time dependence of all thermodynamic potentials into the thermodynamic relations. The spacetime is assumed to be homogeneous and isotropic, and the energy momentum tensor includes not only the energy density and pressure for the matter and radiation, but it also includes contributions due to vacuum polarization by correspondent fields. It is demonstrated that it is possible to reach in principle the de Sitter spacetime as the limit of the contraction
Arguments for the compactness and multiple connectivity of our cosmic spacetime
International Nuclear Information System (INIS)
El Naschie, M.S.
2009-01-01
Some global topological as well as quantative arguments are given, indicating that our universe is most probably compact, multiply connected and without boundaries. The analysis leading to this tentative conclusion is based on a combination of Nash Euclidean embedding theorems, the local isomorphism theorem, cosmic crystallography and the theory of fractal-Cantorian spacetime. It is shown that the correct topological dimension D = 4 of space is derived from the Euclidean embedding of spacetime quanta when the corresponding manifold is assumed to be compact. This and other conclusions regarding multi-connectivity seems to reinforce the findings of relatively recent research results on topological cosmology by Luminet et al. (see Nature 425;9 Oct. 2003:593-95).
International Nuclear Information System (INIS)
Winicour, Jeffrey
2017-01-01
An algebraic-hyperbolic method for solving the Hamiltonian and momentum constraints has recently been shown to be well posed for general nonlinear perturbations of the initial data for a Schwarzschild black hole. This is a new approach to solving the constraints of Einstein’s equations which does not involve elliptic equations and has potential importance for the construction of binary black hole data. In order to shed light on the underpinnings of this approach, we consider its application to obtain solutions of the constraints for linearized perturbations of Minkowski space. In that case, we find the surprising result that there are no suitable Cauchy hypersurfaces in Minkowski space for which the linearized algebraic-hyperbolic constraint problem is well posed. (note)
$\\kappa$-Minkowski star product in any dimension from symplectic realization
Pachol, Anna; Vitale, Patrizia
2015-01-01
We derive an explicit expression for the star product reproducing the $\\kappa$-Minkowski Lie algebra in any dimension $n$. The result is obtained by suitably reducing the Wick-Voros star product defined on $\\mathbb{C}^{d}_\\theta$ with $n=d+1$. It is thus shown that the new star product can be obtained from a Jordanian twist.
An imbedding of Lorentzian manifolds
International Nuclear Information System (INIS)
Kim, Do-Hyung
2009-01-01
A new method for imbedding a Lorentzian manifold with a non-compact Cauchy surface is presented. As an application, it is shown that any two-dimensional globally hyperbolic spacetime with a non-compact Cauchy surface can be causally isomorphically imbedded into two-dimensional Minkowski spacetime.
Linearization instability for generic gravity in AdS spacetime
Altas, Emel; Tekin, Bayram
2018-01-01
In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure of the linear perturbation theory by showing that a certain quadratic (integral) constraint on the linearized solutions is not satisfied. For non-compact Cauchy surfaces, the situation is different and for example, Minkowski space having a non-compact Cauchy surface, is linearization stable. Here we study, the linearization instability in generic metric theories of gravity where Einstein's theory is modified with additional curvature terms. We show that, unlike the case of general relativity, for modified theories even in the non-compact Cauchy surface cases, there are some theories which show linearization instability about their anti-de Sitter backgrounds. Recent D dimensional critical and three dimensional chiral gravity theories are two such examples. This observation sheds light on the paradoxical behavior of vanishing conserved charges (mass, angular momenta) for non-vacuum solutions, such as black holes, in these theories.
Classical and semi-classical solutions of the Yang--Mills theory
International Nuclear Information System (INIS)
Jackiw, R.; Nohl, C.; Rebbi, C.
1977-12-01
This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator
Zero mean curvature surfaces of mixed type in Minkowski space
International Nuclear Information System (INIS)
Klyachin, V A
2003-01-01
We investigate zero mean curvature surfaces in the Minkowski space R 3 1 such that their first fundamental quadratic form changes signature. Part of such a surface is space-like and part is time-like. We obtain complete information about the structure of the set of points where the surface changes type and prove the related existence and uniqueness theorems
Analysis of image heterogeneity using 2D Minkowski functionals detects tumor responses to treatment.
Larkin, Timothy J; Canuto, Holly C; Kettunen, Mikko I; Booth, Thomas C; Hu, De-En; Krishnan, Anant S; Bohndiek, Sarah E; Neves, André A; McLachlan, Charles; Hobson, Michael P; Brindle, Kevin M
2014-01-01
The acquisition of ever increasing volumes of high resolution magnetic resonance imaging (MRI) data has created an urgent need to develop automated and objective image analysis algorithms that can assist in determining tumor margins, diagnosing tumor stage, and detecting treatment response. We have shown previously that Minkowski functionals, which are precise morphological and structural descriptors of image heterogeneity, can be used to enhance the detection, in T1 -weighted images, of a targeted Gd(3+) -chelate-based contrast agent for detecting tumor cell death. We have used Minkowski functionals here to characterize heterogeneity in T2 -weighted images acquired before and after drug treatment, and obtained without contrast agent administration. We show that Minkowski functionals can be used to characterize the changes in image heterogeneity that accompany treatment of tumors with a vascular disrupting agent, combretastatin A4-phosphate, and with a cytotoxic drug, etoposide. Parameterizing changes in the heterogeneity of T2 -weighted images can be used to detect early responses of tumors to drug treatment, even when there is no change in tumor size. The approach provides a quantitative and therefore objective assessment of treatment response that could be used with other types of MR image and also with other imaging modalities. Copyright © 2013 Wiley Periodicals, Inc.
Dynamics in non-globally-hyperbolic static spacetimes: III. Anti-de Sitter spacetime
International Nuclear Information System (INIS)
Ishibashi, Akihiro; Wald, Robert M
2004-01-01
In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a well-defined dynamics. Nevertheless, AdS spacetime is static, so the possible rules of dynamics for a field satisfying a linear wave equation are constrained by our previous general analysis-given in paper II-where it was shown that the possible choices of dynamics correspond to choices of positive, self-adjoint extensions of a certain differential operator, A. In the present paper, we reduce the analysis of electromagnetic and gravitational perturbations in AdS spacetime to scalar wave equations. We then apply our general results to analyse the possible dynamics of scalar, electromagnetic and gravitational perturbations in AdS spacetime. In AdS spacetime, the freedom (if any) in choosing self-adjoint extensions of A corresponds to the freedom (if any) in choosing suitable boundary conditions at infinity, so our analysis determines all the possible boundary conditions that can be imposed at infinity. In particular, we show that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbations, and depending on the number of spacetime dimensions and type of mode for electromagnetic and gravitational perturbations
Light cones in relativity: Real, complex, and virtual, with applications
International Nuclear Information System (INIS)
Adamo, T. M.; Newman, E. T.
2011-01-01
We study geometric structures associated with shear-free null geodesic congruences in Minkowski space-time and asymptotically shear-free null geodesic congruences in asymptotically flat space-times. We show how in both the flat and asymptotically flat settings, complexified future null infinity I C + acts as a ''holographic screen,'' interpolating between two dual descriptions of the null geodesic congruence. One description constructs a complex null geodesic congruence in a complex space-time whose source is a complex worldline, a virtual source as viewed from the holographic screen. This complex null geodesic congruence intersects the real asymptotic boundary when its source lies on a particular open-string type structure in the complex space-time. The other description constructs a real, twisting, shear-free or asymptotically shear-free null geodesic congruence in the real space-time, whose source (at least in Minkowski space) is in general a closed-string structure: the caustic set of the congruence. Finally we show that virtually all of the interior space-time physical quantities that are identified at null infinity I + (center of mass, spin, angular momentum, linear momentum, and force) are given kinematic meaning and dynamical descriptions in terms of the complex worldline.
Revisiting the conformal invariance of the scalar field: From Minkowski space to de Sitter space
International Nuclear Information System (INIS)
Huguet, E.; Queva, J.; Renaud, J.
2008-01-01
In this article, we clarify the link between the conformal (i.e. Weyl) correspondence from the Minkowski space to the de Sitter space and the conformal [i.e. SO(2,d)] invariance of the conformal scalar field on both spaces. We exhibit the realization on de Sitter space of the massless scalar representation of SO(2,d). It is obtained from the corresponding representation in Minkowski space through an intertwining operator inherited from the Weyl relation between the two spaces. The de Sitter representation is written in a form which allows one to take the point of view of a Minkowskian observer who sees the effect of curvature through additional terms
International Nuclear Information System (INIS)
Harada, Tomohiro; Nakao, Ken-ichi
2004-01-01
It is still uncertain whether the cosmic censorship conjecture is true or not. To get a new insight into this issue, we propose the concept of the border of spacetime as a generalization of the spacetime singularity and discuss its visibility. The visible border, corresponding to the naked singularity, is not only relevant to mathematical completeness of general relativity but also a window into new physics in strongly curved spacetimes, which is in principle observable
Macroscopic Spacetime Shortcuts in the Manyfold Universe
Loup, F
2004-01-01
Recently the idea of a Manyfold Universe was proposed by some authors to explain Dark Matter . In this study we assume that the Standard Model(SM) of particles and fields with gravity propagating in the Higher Dimensional Spacetime(Bulk) while other interactions are confined to 3+1 Einsteinian spacetime(Brane) is not due to open strings and closed loops but instead is due to the capability of gravity as the weakest and "smallest" interaction to penetrate these small Bulk size ($10^{-31}$m to $10^{-35}$m) while protons,neutrons and other interactions stronger and "larger" than gravity do not "fits" in the size of the Bulk and remains trapped on the Brane and we present a equation to justify this point of view. Our picture relies over the geometrical beauty of the Manyfold Universe proposal that Dark Matter is chemically identical to ordinary matter but lies on other Folds. Also the geometrical point of view for the small size of the Bulk eliminates the need of trapping mechanisms to confine matter in the Brane...
International Nuclear Information System (INIS)
Doplicher, S.
1996-01-01
We review some recent result and work in progress on the quantum structure of spacetime at scales comparable with the Planck length; the models discussed here are operationally motivated by the limitations in the accuracy of localization of events in spacetime imposed by the interplay between quantum mechanics and classical general relativity. (orig.)
International Nuclear Information System (INIS)
Raine, D.J.; Heller, M.
1981-01-01
Analyzing the development of the structure of space-time from the theory of Aristotle to the present day, the present work attempts to sketch a science of relativistic mechanics. The concept of relativity is discussed in relation to the way in which space-time splits up into space and time, and in relation to Mach's principle concerning the relativity of inertia. Particular attention is given to the following topics: Aristotelian dynamics Copernican kinematics Newtonian dynamics the space-time of classical dynamics classical space-time in the presence of gravity the space-time of special relativity the space-time of general relativity solutions and problems in general relativity Mach's principle and the dynamics of space-time theories of inertial mass the integral formation of general relativity and the frontiers of relativity
Algebrodynamics over complex space and phase extension of the Minkowski geometry
International Nuclear Information System (INIS)
Kassandrov, V. V.
2009-01-01
First principles should predetermine physical geometry and dynamics both together. In the 'algebrodynamics' they follow solely from the properties of biquaternion algebra B and the analysis over B. We briefly present the algebrodynamics over Minkowski background based on a nonlinear generalization to B of the Cauchi-Riemann analyticity conditions. Further, we consider the effective real geometry uniquely resulting from the structure of B multiplication and found it to be of the Minkowski type, with an additional phase invariant. Then we pass to study the primordial dynamics that takes place in the complex B space and brings into consideration a number of remarkable structures: an ensemble of identical correlated matter pre-elements ('duplicons'), caustic-like signals (interaction carriers), a concept of random complex time resulting in irreversibility of physical time at macrolevel, etc. In partucular, the concept of 'dimerous electron' naturally arises in the framework of complex algebrodynamics and, together with the above-mentioned phase invariant, allows for a novel approach to explanation of quantum interference phenomena alternative to recently accepted wave-particle dualism paradigm.
On the structure and applications of the Bondi-Metzner-Sachs group
Alessio, Francesco; Esposito, Giampiero
This work is a pedagogical review dedicated to a modern description of the Bondi-Metzner-Sachs (BMS) group. Minkowski space-time has an interesting and useful group of isometries, but, for a generic space-time, the isometry group is simply the identity and hence provides no significant informations. Yet symmetry groups have important role to play in physics; in particular, the Poincaré group describing the isometries of Minkowski space-time plays a role in the standard definitions of energy-momentum and angular-momentum. For this reason alone it would seem to be important to look for a generalization of the concept of isometry group that can apply in a useful way to suitable curved space-times. The curved space-times that will be taken into account are the ones that suitably approach, at infinity, Minkowski space-time. In particular we will focus on asymptotically flat space-times. In this work, the concept of asymptotic symmetry group of those space-times will be studied. In the first two sections we derive the asymptotic group following the classical approach which was basically developed by Bondi, van den Burg, Metzner and Sachs. This is essentially the group of transformations between coordinate systems of a certain type in asymptotically flat space-times. In the third section the conformal method and the notion of “asymptotic simplicity” are introduced, following mainly the works of Penrose. This section prepares us for another derivation of the BMS group which will involve the conformal structure, and is thus more geometrical and fundamental. In the subsequent sections we discuss the properties of the BMS group, e.g. its algebra and the possibility to obtain as its subgroup the Poincaré group, as we may expect. The paper ends with a review of the BMS invariance properties of classical gravitational scattering discovered by Strominger, that are finding application to black hole physics and quantum gravity in the literature.
Topological properties of a curved spacetime
Agrawal, Gunjan; Shrivastava, Sampada; Godani, Nisha; Sinha, Soami Pyari
2017-12-01
The present paper aims at the study of a topology on Lorentzian manifolds, defined by Göbel [4] using the ideas of Zeeman [16]. Observing that on the Minkowski space it is the same as Zeeman's time topology, it has been found that a Lorentzian manifold with this topology is path connected, nonfirst countable and nonsimply connected while the Minkowski space with time topology is, in addition nonregular and separable. Furthermore, using the notion of Zeno sequences it is obtained that a compact set does not contain a nonempty open set and that a set is compact if and only if each of its infinite subsets has a limit point if and only if each of its sequences has a convergent subsequence.
Energy Technology Data Exchange (ETDEWEB)
Smolyaninov, Igor I., E-mail: smoly@umd.edu
2014-11-15
Modern advances in transformation optics and electromagnetic metamaterials made possible experimental demonstrations of highly unusual curvilinear “optical spaces”, such as various geometries necessary for electromagnetic cloaking. Recently we demonstrated that mapping light intensity in a hyperbolic metamaterial may also model the flow of time in an effective (2+1) dimensional Minkowski spacetime. Curving such an effective spacetime creates experimental model of a toy “big bang”. Here we demonstrate that at low light levels this model may be used to emulate a fully covariant version of quantum mechanics in a (2+1) dimensional Minkowski spacetime. When quantum mechanical description is applied near the toy “big bang”, the Everett's “universal wave function” formalism arises naturally, in which the wave function of the model “universe” appears to be a quantum superposition of mutually orthogonal “parallel universe” states.
Bubble Collision in Curved Spacetime
International Nuclear Information System (INIS)
Hwang, Dong-il; Lee, Bum-Hoon; Lee, Wonwoo; Yeom, Dong-han
2014-01-01
We study vacuum bubble collisions in curved spacetime, in which vacuum bubbles were nucleated in the initial metastable vacuum state by quantum tunneling. The bubbles materialize randomly at different times and then start to grow. It is known that the percolation by true vacuum bubbles is not possible due to the exponential expansion of the space among the bubbles. In this paper, we consider two bubbles of the same size with a preferred axis and assume that two bubbles form very near each other to collide. The two bubbles have the same field value. When the bubbles collide, the collided region oscillates back-and-forth and then the collided region eventually decays and disappears. We discuss radiation and gravitational wave resulting from the collision of two bubbles
Quantum interest in (3+1)-dimensional Minkowski space
International Nuclear Information System (INIS)
Abreu, Gabriel; Visser, Matt
2009-01-01
The so-called 'quantum inequalities', and the 'quantum interest conjecture', use quantum field theory to impose significant restrictions on the temporal distribution of the energy density measured by a timelike observer, potentially preventing the existence of exotic phenomena such as 'Alcubierre warp drives' or 'traversable wormholes'. Both the quantum inequalities and the quantum interest conjecture can be reduced to statements concerning the existence or nonexistence of bound states for a certain one-dimensional quantum mechanical pseudo-Hamiltonian. Using this approach, we shall provide a simple variational proof of one version of the quantum interest conjecture in (3+1)-dimensional Minkowski space.
Revised Robertson's test theory of special relativity: space-time structure and dynamics
International Nuclear Information System (INIS)
Vargas, J.G.; Torr, D.G.
1986-01-01
The experimental testing of the Lorentz transformations is based on a family of sets of coordinate transformations that do not comply in general with the principle of equivalence of the inertial frames. The Lorentz and Galilean sets of transformations are the only member sets of the family that satisfy this principle. In the neighborhood of regular points of space-time, all members in the family are assumed to comply with local homogeneity of space-time and isotropy of space in at least one free-falling elevator, to be denoted as Robertson's ab initio rest frame (H.P. Robertson, Rev. Mod. Phys. 21, 378 (1949)). Without any further assumptions, it is shown that Robertson's rest frame becomes a preferred frame for all member sets of the Robertson family except for, again, Galilean and Einstein's relativities. If one now assumes the validity of Maxwell-Lorentz electrodynamics in the preferred frame, a different electrodynamics spontaneously emerges for each set of transformations. The flat space-time of relativity retains its relevance, which permits an obvious generalization, in a Robertson context, of Dirac's theory of the electron and Einstein's gravitation. The family of theories thus obtained constitutes a covering theory of relativistic physics. A technique is developed to move back and forth between Einstein's relativity and the different members of the family of theories. It permits great simplifications in the analysis of relativistic experiments with relevant ''Robertson's subfamilies.'' It is shown how to adapt the Clifford algebra version of standard physics for use with the covering theory and, in particular, with the covering Dirac theory
Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
The space-time model according to dimensional continuous space-time theory
International Nuclear Information System (INIS)
Martini, Luiz Cesar
2014-01-01
This article results from the Dimensional Continuous Space-Time Theory for which the introductory theoretician was presented in [1]. A theoretical model of the Continuous Space-Time is presented. The wave equation of time into absolutely stationary empty space referential will be described in detail. The complex time, that is the time fixed on the infinite phase time speed referential, is deduced from the New View of Relativity Theory that is being submitted simultaneously with this article in this congress. Finally considering the inseparable Space-Time is presented the duality equation wave-particle.
A (star)-BASED MINKOWSKI'S INEQUALITY FOR SUGENO FRACTIONAL INTEGRAL OF ORDER alpha > 0
Czech Academy of Sciences Publication Activity Database
Babkhani, A.; Agahi, H.; Mesiar, Radko
2015-01-01
Roč. 18, č. 4 (2015), s. 862-874 ISSN 1311-0454 Institutional support: RVO:67985556 Keywords : fuzzy integral * Sugeno fractional integral * Minkowski's inequality Subject RIV: BA - General Mathematics Impact factor: 2.246, year: 2015 http://library.utia.cas.cz/separaty/2015/E/mesiar-0446629.pdf
On Bäcklund transformation and vortex filament equation for null Cartan curve in Minkowski 3-space
Energy Technology Data Exchange (ETDEWEB)
Grbović, Milica, E-mail: milica.grbovic@kg.ac.rs; Nešović, Emilija, E-mail: nesovickg@sbb.rs [University of Kragujevac, Faculty of Science, Department of Mathematics and Informatics (Serbia)
2016-12-15
In this paper we introduce Bäcklund transformation of a null Cartan curve in Minkowski 3-space as a transformation which maps a null Cartan helix to another null Cartan helix, congruent to the given one. We also give the sufficient conditions for a transformation between two null Cartan curves in the Minkowski 3-space such that these curves have equal constant torsions. By using the Da Rios vortex filament equation, based on localized induction approximation, we derive the vortex filament equation for a null Cartan curve and obtain evolution equation for it’s torsion. As an application, we show that Cartan’s frame vectors generate new solutions of the Da Rios vortex filament equation.
Optimized Ultrawideband and Uniplanar Minkowski Fractal Branch Line Coupler
Directory of Open Access Journals (Sweden)
Mohammad Jahanbakht
2012-01-01
Full Text Available The non-Euclidean Minkowski fractal geometry is used in design, optimization, and fabrication of an ultrawideband (UWB branch line coupler. Self-similarities of the fractal geometries make them act like an infinite length in a finite area. This property creates a smaller design with broader bandwidth. The designed 3 dB microstrip coupler has a single layer and uniplanar platform with quite easy fabrication process. This optimized 180° coupler also shows a perfect isolation and insertion loss over the UWB frequency range of 3.1–10.6 GHz.
Perturbations of higher-dimensional spacetimes
Energy Technology Data Exchange (ETDEWEB)
Durkee, Mark; Reall, Harvey S, E-mail: M.N.Durkee@damtp.cam.ac.uk, E-mail: H.S.Reall@damtp.cam.ac.uk [DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom)
2011-02-07
We discuss linearized gravitational perturbations of higher-dimensional spacetimes. For algebraically special spacetimes (e.g. Myers-Perry black holes), we show that there exist local gauge invariant quantities linear in the metric perturbation. These are the higher-dimensional generalizations of the 4D Newman-Penrose scalars that (in an algebraically special vacuum spacetime) satisfy decoupled equations of motion. We show that decoupling occurs in more than four dimensions if, and only if, the spacetime admits a null geodesic congruence with vanishing expansion, rotation and shear. Decoupling of electromagnetic perturbations occurs under the same conditions. Although these conditions are not satisfied in black hole spacetimes, they are satisfied in the near-horizon geometry of an extreme black hole.
Properties of the eleven dimensional supermembrane theory
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Townsend, P.K.
1987-09-01
We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N=8 world volume (rigid) supersymmetry in a ''physical'' gauge; we also present the field equations and transformation rules in a ''lightcone'' gauge. We semiclassically quantize the closed toroidal supermembrane on a spacetime (Minkowski) 4 x (flat 7-torus), and review some mathematical results that are relevant for path integral quantization. (author). 52 refs, 1 fig
Minkowski metrics in creating universal ranking algorithms
Directory of Open Access Journals (Sweden)
Andrzej Ameljańczyk
2014-06-01
Full Text Available The paper presents a general procedure for creating the rankings of a set of objects, while the relation of preference based on any ranking function. The analysis was possible to use the ranking functions began by showing the fundamental drawbacks of commonly used functions in the form of a weighted sum. As a special case of the ranking procedure in the space of a relation, the procedure based on the notion of an ideal element and generalized Minkowski distance from the element was proposed. This procedure, presented as universal ranking algorithm, eliminates most of the disadvantages of ranking functions in the form of a weighted sum.[b]Keywords[/b]: ranking functions, preference relation, ranking clusters, categories, ideal point, universal ranking algorithm
Dimensional reduction from entanglement in Minkowski space
International Nuclear Information System (INIS)
Brustein, Ram; Yarom, Amos
2005-01-01
Using a quantum field theoretic setting, we present evidence for dimensional reduction of any sub-volume of Minkowksi space. First, we show that correlation functions of a class of operators restricted to a sub-volume of D-dimensional Minkowski space scale as its surface area. A simple example of such area scaling is provided by the energy fluctuations of a free massless quantum field in its vacuum state. This is reminiscent of area scaling of entanglement entropy but applies to quantum expectation values in a pure state, rather than to statistical averages over a mixed state. We then show, in a specific case, that fluctuations in the bulk have a lower-dimensional representation in terms of a boundary theory at high temperature. (author)
Cauchy horizons in Gowdy spacetimes
International Nuclear Information System (INIS)
Chrusciel, Piotr T; Lake, Kayll
2004-01-01
We analyse exhaustively the structure of non-degenerate Cauchy horizons in Gowdy spacetimes, and we establish existence of a large class of non-polarized Gowdy spacetimes with such horizons. Our results here, together with the deep new results of Ringstroem, establish strong cosmic censorship in (toroidal) Gowdy spacetimes
Geometry of Kaluza-Klein theory. I. Basic setting
International Nuclear Information System (INIS)
Maia, M.D.
1985-01-01
Kaluza-Klein space theory is derived from the hypothesis that the four-dimensional space-time is locally and isometrically embedded in a high-dimensional space which presumably originated at the big bang. For mathematical simplicity the high-dimensional space is taken to be a flat, Minkowski space with 14 dimensions assumed to be the ground state of the theory. The resulting metric is more general than the usual zero-mode metric ansatz but it reduces to the latter in the low-energy sector of the theory. The compactification of the internal space results from the existence of the second quadratic form of the embedded V 4 . A simple model of spherical compact space is considered as a working example, where the spontaneous compactification is a hyperbolic function of the strength of the gravitational field. The symmetry group of the embedding is a combined symmetry which breaks into P 4 x SO(10) in the flat limit of the space-time
Toward the classification of differential calculi on κ-Minkowski space and related field theories
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Jurić, Tajron; Meljanac, Stjepan; Pikutić, Danijel [Ruđer Bošković Institute, Theoretical Physics Division,Bijenička c.54, HR-10002 Zagreb (Croatia); Štrajn, Rina [Dipartimento di Matematica e Informatica, Università di Cagliari,viale Merello 92, I-09123 Cagliari (Italy); INFN, Sezione di Cagliari,Cagliari (Italy)
2015-07-13
Classification of differential forms on κ-Minkowski space, particularly, the classification of all bicovariant differential calculi of classical dimension is presented. By imposing super-Jacobi identities we derive all possible differential algebras compatible with the κ-Minkowski algebra for time-like, space-like and light-like deformations. Embedding into the super-Heisenberg algebra is constructed using non-commutative (NC) coordinates and one-forms. Particularly, a class of differential calculi with an undeformed exterior derivative and one-forms is considered. Corresponding NC differential calculi are elaborated. Related class of new Drinfeld twists is proposed. It contains twist leading to κ-Poincaré Hopf algebra for light-like deformation. Corresponding super-algebra and deformed super-Hopf algebras, as well as the symmetries of differential algebras are presented and elaborated. Using the NC differential calculus, we analyze NC field theory, modified dispersion relations, and discuss further physical applications.
Spatial infinity in higher dimensional spacetimes
International Nuclear Information System (INIS)
Shiromizu, Tetsuya; Tomizawa, Shinya
2004-01-01
Motivated by recent studies on the uniqueness or nonuniqueness of higher dimensional black hole spacetime, we investigate the asymptotic structure of spatial infinity in n-dimensional spacetimes (n≥4). It turns out that the geometry of spatial infinity does not have maximal symmetry due to the nontrivial Weyl tensor (n-1) C abcd in general. We also address static spacetime and its multipole moments P a 1 a 2 ···a s . Contrasting with four dimensions, we stress that the local structure of spacetimes cannot be unique under fixed multipole moments in static vacuum spacetimes. For example, we consider the generalized Schwarzschild spacetimes which are deformed black hole spacetimes with the same multipole moments as spherical Schwarzschild black holes. To specify the local structure of the static vacuum solution we need some additional information, at least the Weyl tensor (n-2) C abcd at spatial infinity
Wu, Ning
2012-01-01
When we discuss problems on gravity, we can not avoid some fundamental physical problems, such as space-time, inertia, and inertial reference frame. The goal of this paper is to discuss the logic system of gravity theory and the problems of space-time, inertia, and inertial reference frame. The goal of this paper is to set up the theory on space-time in gauge theory of gravity. Based on this theory, it is possible for human kind to manipulate physical space-time on earth, and produce a machin...
Spinors in self-dual Yang-Mills fields in minkowski space
International Nuclear Information System (INIS)
Pervushin, V.N.
1981-01-01
Yang-Mills theory with infrared divergences removed by spontaneous vacuum symmetry breaking is considered. The corresponding vacuum fields are self-dual and are defined in the Minkowski space. The complete set of solutions of Dirac equations with self-dual fields, depending on certain arbitrary function, is found. Physical observables (charge, energy, spin) for the spinor fields within the self-dual vacuum are calculated and a Hermitean Hamiltonian is obtained. The physical picture corresponds to a relativistic generalization of the hadron bag model [ru
Gravitational Lensing from a Spacetime Perspective
Directory of Open Access Journals (Sweden)
Perlick Volker
2004-09-01
Full Text Available The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of lightlike geodesics of a metric of Lorentzian signature. It includes the basic equations and the relevant techniques for calculating the position, the shape, and the brightness of images in an arbitrary general-relativistic spacetime. It also includes general theorems on the classification of caustics, on criteria for multiple imaging, and on the possible number of images. The general results are illustrated with examples of spacetimes where the lensing features can be explicitly calculated, including the Schwarzschild spacetime, the Kerr spacetime, the spacetime of a straight string, plane gravitational waves, and others.
Positioning in a flat two-dimensional space-time: The delay master equation
International Nuclear Information System (INIS)
Coll, Bartolome; Ferrando, Joan Josep; Morales-Lladosa, Juan Antonio
2010-01-01
The basic theory on relativistic positioning systems in a two-dimensional space-time has been presented in two previous papers [B. Coll, J. J. Ferrando, and J. A. Morales, Phys. Rev. D 73, 084017 (2006); ibid.74, 104003 (2006)], where the possibility of making relativistic gravimetry with these systems has been analyzed by considering specific examples. Here, generic relativistic positioning systems in the Minkowski plane are studied. The information that can be obtained from the data received by a user of the positioning system is analyzed in detail. In particular, it is shown that the accelerations of the emitters and of the user along their trajectories are determined by the sole knowledge of the emitter positioning data and of the acceleration of only one of the emitters. Moreover, as a consequence of the so-called master delay equation, the knowledge of this acceleration is only required during an echo interval, i.e., the interval between the emission time of a signal by an emitter and its reception time after being reflected by the other emitter. These results are illustrated with the obtention of the dynamics of the emitters and of the user from specific sets of data received by the user.
Directory of Open Access Journals (Sweden)
Petré Frederik
2004-01-01
Full Text Available In the downlink of DS-CDMA, frequency-selectivity destroys the orthogonality of the user signals and introduces multiuser interference (MUI. Space-time chip equalization is an efficient tool to restore the orthogonality of the user signals and suppress the MUI. Furthermore, multiple-input multiple-output (MIMO communication techniques can result in a significant increase in capacity. This paper focuses on space-time block coding (STBC techniques, and aims at combining STBC techniques with the original single-antenna DS-CDMA downlink scheme. This results into the so-called space-time block coded DS-CDMA downlink schemes, many of which have been presented in the past. We focus on a new scheme that enables both the maximum multiantenna diversity and the maximum multipath diversity. Although this maximum diversity can only be collected by maximum likelihood (ML detection, we pursue suboptimal detection by means of space-time chip equalization, which lowers the computational complexity significantly. To design the space-time chip equalizers, we also propose efficient pilot-based methods. Simulation results show improved performance over the space-time RAKE receiver for the space-time block coded DS-CDMA downlink schemes that have been proposed for the UMTS and IS-2000 W-CDMA standards.
All partial breakings in ${\\cal N}=2$ supergravity with a single hypermultiplet arXiv
Antoniadis, Ignatios; Petropoulos, P. Marios; Siampos, Konstantinos
We consider partial supersymmetry breaking in ${\\cal N}=2$ supergravity coupled to a single vector and a single hypermultiplet. This breaking pattern is in principle possible if the quaternion-K\\"ahler space of the hypermultiplet admits (at least) one pair of commuting isometries. For this class of manifolds, explicit metrics exist and we analyse a generic electro-magnetic (dyonic) gauging of the isometries. An example of partial breaking in Minkowski spacetime has been found long ago by Ferrara, Girardello and Porrati, using the gauging of two translation isometries on $SO(4,1)/SO(4)$. We demonstrate that no other example of partial breaking of ${\\cal N}=2$ supergravity in Minkowski spacetime exists. We also examine partial-breaking vacua in anti-de Sitter spacetime that are much less constrained and exist generically even for electric gaugings. On $SO(4,1)/SO(4)$, we construct the partially-broken solution and its global limit which is the Antoniadis-Partouche-Taylor model.
Another two dark energy models motivated from Karolyhazy uncertainty relation
Energy Technology Data Exchange (ETDEWEB)
Sun, Cheng-Yi; Yang, Wen-Li; Song, Yu. [Northwest University, Institute of Modern Physics, Xian (China); Yue, Rui-Hong [Ningbo University, Faculty of Science, Ningbo (China)
2012-03-15
The Karolyhazy uncertainty relation indicates that there exists a minimal detectable cell {delta}t{sup 3} over the region t{sup 3} in Minkowski space-time. Due to the energy-time uncertainty relation, the energy of the cell {delta}t {sup 3} cannot be less {delta}t{sup -1}. Then we get a new energy density of metric fluctuations of Minkowski spacetime as {delta}t{sup -4}. Motivated by the energy density, we propose two new dark-energy models. One model is characterized by the age of the universe and the other is characterized by the conformal age of the universe. We find that in the two models, the dark energy mimics a cosmological constant in the late time. (orig.)
Dynamical system analysis of interacting models
Carneiro, S.; Borges, H. A.
2018-01-01
We perform a dynamical system analysis of a cosmological model with linear dependence between the vacuum density and the Hubble parameter, with constant-rate creation of dark matter. We show that the de Sitter spacetime is an asymptotically stable critical point, future limit of any expanding solution. Our analysis also shows that the Minkowski spacetime is an unstable critical point, which eventually collapses to a singularity. In this way, such a prescription for the vacuum decay not only predicts the correct future de Sitter limit, but also forbids the existence of a stable Minkowski universe. We also study the effect of matter creation on the growth of structures and their peculiar velocities, showing that it is inside the current errors of redshift space distortions observations.
On Minkowski decomposition of Okounkov bodies on a Del Pezzo surface
Directory of Open Access Journals (Sweden)
Patrycja Łuszcz-Świdecka
2011-03-01
Full Text Available We show that on a blow up of $P^2$ in $3$ general points there exists a finite set of nef divisors $P_1,ldots,P_s$ such that the Okounkov body $Delta(D$ of an arbitrary effective $R$--divisor $D$ on $X$ is the Minkowski sum Delta(D=sum_{i=1}^s a_iDelta(P_i (1 with non-negative coefficients $a_i in R_{geq 0}$.
Some properties of spatially homogeneous spacetimes
International Nuclear Information System (INIS)
Coomer, G.C.
1979-01-01
This paper discusses two features of the universe which are influenced in a fundamental way by the spacetime geometry of the universe. The first is the growth of density fluctuations in the early stages of the evolution of the universe. The second is the propagation of electromagnetic radiation in the universe. A spatially homogeneous universe is assumed in both discussions. The gravitational instability theory of galaxy formation is investigated for a viscous fluid and for a charged, conducting fluid with a magnetic field added as a perturbation. It is found that the growth rate of density perturbations in both cases is lower than in the perfect fluid case. Spatially homogeneous but nonisotropic spacetimes are investigated next. Two perfect fluid solutions of Einstein's field equations are found which have spacelike hypersurfaces with Bianchi type II geometry. An expression for the spectrum of the cosmic microwave background radiation in a spatially homogeneous but nonisotropic universe is found. The expression is then used to determine the angular distribution of the intensity of the radiation in the simpler of the two solutions. When accepted values of the matter density and decoupling temperature are inserted into this solution, values for the age of the universe and the time of decoupling are obtained which agree reasonably well with the values of the standard model of the universe
International Nuclear Information System (INIS)
Ramos, Tomas; Rubilar, Guillermo F.; Obukhov, Yuri N.
2011-01-01
Highlights: → The definition of the momentum of light inside matter is studied. → Fully relativistic analysis of the dielectric 'Einstein box' thought experiment. → Minkowski, Abraham and the total energy-momentum tensors are derived in detail. → Some assumptions hidden in the usual Einstein box argument are identified. → The Abraham momentum is not uniquely selected as the momentum of light in this case. - Abstract: We analyse the 'Einstein box' thought experiment and the definition of the momentum of light inside matter. We stress the importance of the total energy-momentum tensor of the closed system (electromagnetic field plus material medium) and derive in detail the relativistic expressions for the Abraham and Minkowski momenta, together with the corresponding balance equations for an isotropic and homogeneous medium. We identify some assumptions hidden in the Einstein box argument, which make it weaker than it is usually recognized. In particular, we show that the Abraham momentum is not uniquely selected as the momentum of light in this case.
A new construction of rational electromagnetic knots
Lechtenfeld, Olaf; Zhilin, Gleb
2018-06-01
We set up a correspondence between solutions of the Yang-Mills equations on R ×S3 and in Minkowski spacetime via de Sitter space. Some known Abelian and non-Abelian exact solutions are rederived. For the Maxwell case we present a straightforward algorithm to generate an infinite number of explicit solutions, with fields and potentials in Minkowski coordinates given by rational functions of increasing complexity. We illustrate our method with a nontrivial example.
Anisotropic compacts stars on paraboloidal spacetime with linear equation of state
Energy Technology Data Exchange (ETDEWEB)
Thomas, V.O. [The Maharaja Sayajirao University of Baroda, Department of Mathematics, Faculty of Science, Vadodara, Gujarat (India); Pandya, D.M. [Pandit Deendayal Petroleum University, Department of Mathematics and Computer Science, Gandhinagar, Gujarat (India)
2017-06-15
New exact solutions of Einstein's field equations (EFEs) by assuming a linear equation of state, p{sub r} = α(ρ-ρ{sub R}), where p{sub r} is the radial pressure and ρ{sub R} is the surface density, are obtained on the background of a paraboloidal spacetime. By assuming estimated mass and radius of strange star candidate 4U 1820-30, various physical and energy conditions are used for estimating the range of parameter α. The suitability of the model for describing pulsars like PSR J1903+327, Vela X-1, Her X-1 and SAX J1808.4-3658 has been explored and respective ranges of α, for which all physical and energy conditions are satisfied throughout the distribution, are obtained. (orig.)
Spinorial relativistic rotator: the transformation from quasi-Newtonian to Minkowski coordinates
International Nuclear Information System (INIS)
Biedenharn, L.C.; Bohm, A.; Tarlini, M.; van Dam, H.; Mukunda, N.
1983-12-01
There exists a remarkably close relationship between the operator algebra of the Dirac equation and the corresponding operators of the spinorial relativistic rotator (an indecomposable object lying on a mass-spin Regge trajectory). The analog of the Foldy-Wouthuysen transformation (more generally, the transformation between quasi-Newtonian and Minkowski coordinates) is constructed and explicit results are discussed for the spin and position operators. Zitterbewegung is shown to exist for a system having only positive energies. 31 references
Statistics from dynamics in curved spacetime
International Nuclear Information System (INIS)
Parker, L.; Wang, Y.
1989-01-01
We consider quantum fields of spin 0, 1/2, 1, 3/2, and 2 with a nonzero mass in curved spacetime. We show that the dynamical Bogolubov transformations associated with gravitationally induced particle creation imply the connection between spin and statistics: By embedding two flat regions in a curved spacetime, we find that only when one imposes Bose-Einstein statistics for an integer-spin field and Fermi-Dirac statistics for a half-integer-spin field in the first flat region is the same type of statistics propagated from the first to the second flat region. This derivation of the flat-spacetime spin-statistics theorem makes use of curved-spacetime dynamics and does not reduce to any proof given in flat spacetime. We also show in the same manner that parastatistics, up to the fourth order, are consistent with the dynamical evolution of curved spacetime
The bicovariant differential calculus on the κ-Poincare group and on the κ-Minkowski space
International Nuclear Information System (INIS)
Kosinski, P.; Maslanka, P.; Sobczyk, J.
1996-01-01
The bicovariant differential calculus on the four-dimensional κ-Poincare group and the corresponding Lie-algebra-like structure are described. The differential calculus on the n-dimensional κ-Minkowski space covariant under the action of the κ-Poincare group was constructed. 5 refs
Minkowski vacuum transitions in (nongeometric) flux compactifications
International Nuclear Information System (INIS)
Herrera-Suarez, Wilberth; Loaiza-Brito, Oscar
2010-01-01
In this work we study the generalization of twisted homology to geometric and nongeometric backgrounds. In the process, we describe the necessary conditions to wrap a network of D-branes on twisted cycles. If the cycle is localized in time, we show how by an instantonic brane mediation, some D-branes transform into fluxes on different backgrounds, including nongeometric fluxes. As a consequence, we show that in the case of a IIB six-dimensional torus compactification on a simple orientifold, the flux superpotential is not invariant by this brane-flux transition, allowing the connection among different Minkowski vacuum solutions. For the case in which nongeometric fluxes are turned on, we also discuss some topological restrictions for the transition to occur. In this context, we show that there are some vacuum solutions protected to change by a brane-flux transition.
Relativistic Landau levels in the rotating cosmic string spacetime
Energy Technology Data Exchange (ETDEWEB)
Cunha, M.S. [Universidade Estadual do Ceara, Grupo de Fisica Teorica (GFT), Fortaleza, CE (Brazil); Muniz, C.R. [Universidade Estadual do Ceara, Faculdade de Educacao, Ciencias e Letras de Iguatu, Iguatu, CE (Brazil); Christiansen, H.R. [Instituto Federal de Ciencia, Educacao e Tecnologia, IFCE Departamento de Fisica, Sobral (Brazil); Bezerra, V.B. [Universidade Federal da Paraiba-UFPB, Departamento de Fisica, Caixa Postal 5008, Joao Pessoa, PB (Brazil)
2016-09-15
In the spacetime induced by a rotating cosmic string we compute the energy levels of a massive spinless particle coupled covariantly to a homogeneous magnetic field parallel to the string. Afterwards, we consider the addition of a scalar potential with a Coulomb-type and a linear confining term and completely solve the Klein-Gordon equations for each configuration. Finally, assuming rigid-wall boundary conditions, we find the Landau levels when the linear defect is itself magnetized. Remarkably, our analysis reveals that the Landau quantization occurs even in the absence of gauge fields provided the string is endowed with spin. (orig.)
Covariant differential calculus on quantum Minkowski space and the q-analogue of Dirac equation
International Nuclear Information System (INIS)
Song Xingchang; Academia Sinica, Beijing
1992-01-01
The covariant differential calculus on the quantum Minkowski space is presented with the help of the generalized Wess-Zumino method and the quantum Pauli matrices and quantum Dirac matrices are constructed parallel to those in the classical case. Combining these two aspects a q-analogue of Dirac equation follows directly. (orig.)
Re-examination of globally flat space-time.
Directory of Open Access Journals (Sweden)
Michael R Feldman
Full Text Available In the following, we offer a novel approach to modeling the observed effects currently attributed to the theoretical concepts of "dark energy," "dark matter," and "dark flow." Instead of assuming the existence of these theoretical concepts, we take an alternative route and choose to redefine what we consider to be inertial motion as well as what constitutes an inertial frame of reference in flat space-time. We adopt none of the features of our current cosmological models except for the requirement that special and general relativity be local approximations within our revised definition of inertial systems. Implicit in our ideas is the assumption that at "large enough" scales one can treat objects within these inertial systems as point-particles having an insignificant effect on the curvature of space-time. We then proceed under the assumption that time and space are fundamentally intertwined such that time- and spatial-translational invariance are not inherent symmetries of flat space-time (i.e., observable clock rates depend upon both relative velocity and spatial position within these inertial systems and take the geodesics of this theory in the radial Rindler chart as the proper characterization of inertial motion. With this commitment, we are able to model solely with inertial motion the observed effects expected to be the result of "dark energy," "dark matter," and "dark flow." In addition, we examine the potential observable implications of our theory in a gravitational system located within a confined region of an inertial reference frame, subsequently interpreting the Pioneer anomaly as support for our redefinition of inertial motion. As well, we extend our analysis into quantum mechanics by quantizing for a real scalar field and find a possible explanation for the asymmetry between matter and antimatter within the framework of these redefined inertial systems.
Two general classes of self dual, Minkowski propagating wave solutions in Yang Mills gauge theory
International Nuclear Information System (INIS)
Kovacs, E.; Lo, S.Y.
1979-01-01
Two classes of self dual propogating wave solutions to the sourceless field equations in Minkowski space are presented. Some of these solutions can be linearly superposed. These waves can propogate at either the speed of light or at a speed less than that of light
The free Maxwell field in curved spacetime
International Nuclear Information System (INIS)
Kueskue, M.
2001-09-01
The aim of this thesis is to discuss quantizations of the free Maxwell field in flat and curved spacetimes. First we introduce briefly some notions from tensor analysis and the causal structure of spacetime. As an introduction to the main topic, we review some aspects of the two axiomatic quantum field theories, Wightman theory and algebraic quantum field theory. We also give an introduction into concepts of the quantization of fields on curved spacetime backgrounds. Then the wave equation and quantization of the Maxwell field in flat spacetimes is discussed. It follows a review of J. Dimock's quantization of the Maxwell field on curved spacetimes and then we come to our main result: We show explicitly that the Maxwell field, defined by dF=0 and δF=0, has a well posed initial value formulation on arbitrary globally hyperbolic spacetime manifolds. We prove the existence and uniqueness of fundamental solutions without employing a vector potential. Thus our solution is also applicable to spacetimes not satisfying the Poincare lemma and should lead to a quantization of the Maxwell field on non-trivial spacetime backgrounds. This in turn provides the opportunity to investigate physical states on non-trivial spacetime-topologies and could lead to the discovery of new quantum phenomena. (orig.)
Indian Academy of Sciences (India)
dimensional space-time continuum by Minkowski. Unification of electromagnetism and weak interaction was obtained by Glashow, Weinberg and Salam. In 1961, Glashow 1 unified the weak and electromagnetic interactions using the gauge group ...
Description of surfaces associated with Grassmannian sigma models on Minkowski space
International Nuclear Information System (INIS)
Grundland, A.M.; Snobl, L.
2005-01-01
We construct and investigate smooth orientable surfaces in su(N) algebras. The structural equations of surfaces associated with Grassmannian sigma models on Minkowski space are studied using moving frames adapted to the surfaces. The first and second fundamental forms of these surfaces as well as the relations between them as expressed in the Gauss-Weingarten and Gauss-Codazzi-Ricci equations are found. The scalar curvature and the mean curvature vector expressed in terms of a solution of Grassmanian sigma model are obtained
The topology of geodesically complete space-times
International Nuclear Information System (INIS)
Lee, C.W.
1983-01-01
Two theorems are given on the topology of geodesically complete space-times which satisfy the energy condition. Firstly, the condition that a compact embedded 3-manifold in space-time be dentless is defined in terms of causal structure. Then it is shown that a dentless 3-manifold must separate space-time, and that it must enclose a compact portion of space-time. Further, it is shown that if the dentless 3-manifold is homeomorphic to S 3 then the part of space-time that it encloses must be simply connected. (author)
Area law for localization-entropy in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2002-02-01
The previously developed algebraic lightfront holography is used in conjunction with the tensor splitting of the chiral theory on the causal horizon. In this way a universal area law for the entanglement entropy of the vacuum relative to the split (tensor factorized) vacuum is obtained. The universality of the area law is a result of the kinematical structure of the properly defined lightfront degrees of freedom. We consider this entropy associated with causal horizon of the wedge algebra in Minkowski spacetime as an analog of the quantum Bekenstein black hole entropy similar to the way in which the Unruh temperature for the wedge algebra may be viewed as an analog in Minkowski spacetime of the Hawking thermal behavior. My more recent preprint hep-th/20202085 presents other aspects of the same problem. (author)
Singularities in FLRW Spacetimes
Lam, Huibert het; Prokopec, Tom
2017-01-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept
Structure of three-twistor particles
International Nuclear Information System (INIS)
Lukacs, B.; Perjes, Z.; Sebestyen, A.; Newman, E.T.; Porter, J.
1981-11-01
The simplest physical system to have a non-trivial intrinsic structure in Minkowski space-time is a three-twistor particle. The authors investigate this structure and the two pictures of the particle as an extended object in space-time and as a point in unitary space. The effect of twistor translations on the mass triangle defined by the partial centre of mass points in space-time as well as the connections between twistor rotations and the spin are considered and the spin deficiency formula is established. (author)
Properties of the eleven-dimensional supermembrane theory
International Nuclear Information System (INIS)
Bergshoeff, E.; Sezgin, E.; Townsend, P.K.
1988-01-01
We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flate spacetime background, the spacetime supersymmetry becomes an N = 8 world volume (rigid) supersymmetry in a ''physical'' gauge; we also present the field equations and transformation rules in a ''lightcone'' gauge. We semiclassically quantize the closed torodial supermembrane on a spactime (Minkowski) 4 x (flat 7-torus), and review some mathematical results that are relevant for path integral quantization. copyright 1988 Academic Press, Inc
Isolated Minkowski vacua, and stability analysis for an extended brane in the rugby ball
International Nuclear Information System (INIS)
Himmetoglu, Burak; Peloso, Marco
2007-01-01
We study a recently proposed model, where a codimension one brane is wrapped around the axis of symmetry of an internal two-dimensional space compactified by a flux. This construction is free from the problems which plague delta-like, codimension two branes, where only tension can be present. In contrast, arbitrary fields can be localized on this extended brane, and their gravitational interaction is standard 4d gravity at large distances. In the first part of this work, we study the de Sitter (dS) vacua of the model. The landscape of these vacua is characterized by discrete points labeled by two integer numbers, related to the flux responsible for the compactification and to the current of a brane field. A Minkowski external space emerges only for a special ratio between these two integers, and it is therefore (topologically) isolated from the nearby dS solutions. In the second part, we show that the Minkowski vacua are stable under the most generic axially-symmetric perturbations, and we argue that this is sufficient to ensure the overall stability
Isolated Minkowski vacua, and stability analysis for an extended brane in the rugby ball
Energy Technology Data Exchange (ETDEWEB)
Himmetoglu, Burak [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States); Peloso, Marco [School of Physics and Astronomy, University of Minnesota, Minneapolis, MN 55455 (United States)]. E-mail: peloso@physics.umn.edu
2007-06-25
We study a recently proposed model, where a codimension one brane is wrapped around the axis of symmetry of an internal two-dimensional space compactified by a flux. This construction is free from the problems which plague delta-like, codimension two branes, where only tension can be present. In contrast, arbitrary fields can be localized on this extended brane, and their gravitational interaction is standard 4d gravity at large distances. In the first part of this work, we study the de Sitter (dS) vacua of the model. The landscape of these vacua is characterized by discrete points labeled by two integer numbers, related to the flux responsible for the compactification and to the current of a brane field. A Minkowski external space emerges only for a special ratio between these two integers, and it is therefore (topologically) isolated from the nearby dS solutions. In the second part, we show that the Minkowski vacua are stable under the most generic axially-symmetric perturbations, and we argue that this is sufficient to ensure the overall stability.
Isolated Minkowski vacua, and stability analysis for an extended brane in the rugby ball
Himmetoǧlu, Burak; Peloso, Marco
2007-06-01
We study a recently proposed model, where a codimension one brane is wrapped around the axis of symmetry of an internal two-dimensional space compactified by a flux. This construction is free from the problems which plague delta-like, codimension two branes, where only tension can be present. In contrast, arbitrary fields can be localized on this extended brane, and their gravitational interaction is standard 4d gravity at large distances. In the first part of this work, we study the de Sitter (dS) vacua of the model. The landscape of these vacua is characterized by discrete points labeled by two integer numbers, related to the flux responsible for the compactification and to the current of a brane field. A Minkowski external space emerges only for a special ratio between these two integers, and it is therefore (topologically) isolated from the nearby dS solutions. In the second part, we show that the Minkowski vacua are stable under the most generic axially-symmetric perturbations, and we argue that this is sufficient to ensure the overall stability.
Ambient cosmology and spacetime singularities
Antoniadis, Ignatios
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
Mach's principle in spatially homogeneous spacetimes
International Nuclear Information System (INIS)
Tipler, F.J.
1978-01-01
On the basis of Mach's Principle it is concluded that the only singularity-free solution to the empty space Einstein equations is flat space. It is shown that the only singularity-free solution to the empty space Einstein equations which is spatially homogeneous and globally hyperbolic is in fact suitably identified Minkowski space. (Auth.)
Czech Academy of Sciences Publication Activity Database
Hervik, S.; Málek, Tomáš; Pravda, Vojtěch; Pravdová, Alena
2015-01-01
Roč. 32, č. 24 (2015), s. 245012 ISSN 0264-9381 R&D Projects: GA ČR GA13-10042S Institutional support: RVO:67985840 Keywords : einstein spacetimes * generalized gravities * universal spacetimes Subject RIV: BA - General Mathematics Impact factor: 2.837, year: 2015 http://iopscience.iop.org/article/10.1088/0264-9381/32/24/245012
Why we observe an almost classical spacetime
Rosales, Jose-Luis; Sanchez-Gomez, Jose-Luis
1997-01-01
We argue that, in order to obtain decoherence of spacetime, we should consider quantum conformal metric fluctuations of spacetime. This could be the required environment in the problem of selfmeasurement of spacetime in quantum gravity.
Solution of second order supersymmetrical intertwining relations in Minkowski plane
Energy Technology Data Exchange (ETDEWEB)
Ioffe, M. V., E-mail: m.ioffe@spbu.ru; Kolevatova, E. V., E-mail: e.v.kolev@yandex.ru [Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034 (Russian Federation); Nishnianidze, D. N., E-mail: cutaisi@yahoo.com [Saint Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg 199034 (Russian Federation); Akaki Tsereteli State University, 4600 Kutaisi, Georgia (United States)
2016-08-15
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the “metric” matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of “metric” matrices, and their properties are discussed.
Singularities in FLRW spacetimes
het Lam, Huibert; Prokopec, Tomislav
2017-12-01
We point out that past-incompleteness of geodesics in FLRW spacetimes does not necessarily imply that these spacetimes start from a singularity. Namely, if a test particle that follows such a trajectory has a non-vanishing velocity, its energy was super-Planckian at some time in the past if it kept following that geodesic. That indicates a breakdown of the particle's description, which is why we should not consider those trajectories for the definition of an initial singularity. When one only considers test particles that do not have this breakdown of their trajectory, it turns out that the only singular FLRW spacetimes are the ones that have a scale parameter that vanishes at some initial time.
Wismüller, Axel; De, Titas; Lochmüller, Eva; Eckstein, Felix; Nagarajan, Mahesh B.
2017-01-01
The ability of Minkowski Functionals to characterize local structure in different biological tissue types has been demonstrated in a variety of medical image processing tasks. We introduce anisotropic Minkowski Functionals (AMFs) as a novel variant that captures the inherent anisotropy of the underlying gray-level structures. To quantify the anisotropy characterized by our approach, we further introduce a method to compute a quantitative measure motivated by a technique utilized in MR diffusion tensor imaging, namely fractional anisotropy. We showcase the applicability of our method in the research context of characterizing the local structure properties of trabecular bone micro-architecture in the proximal femur as visualized on multi-detector CT. To this end, AMFs were computed locally for each pixel of ROIs extracted from the head, neck and trochanter regions. Fractional anisotropy was then used to quantify the local anisotropy of the trabecular structures found in these ROIs and to compare its distribution in different anatomical regions. Our results suggest a significantly greater concentration of anisotropic trabecular structures in the head and neck regions when compared to the trochanter region (p < 10−4). We also evaluated the ability of such AMFs to predict bone strength in the femoral head of proximal femur specimens obtained from 50 donors. Our results suggest that such AMFs, when used in conjunction with multi-regression models, can outperform more conventional features such as BMD in predicting failure load. We conclude that such anisotropic Minkowski Functionals can capture valuable information regarding directional attributes of local structure, which may be useful in a wide scope of biomedical imaging applications. PMID:29170580
Relativity theory (a bibliography with abstracts). Report for 1970--Feb 77
International Nuclear Information System (INIS)
Grooms, D.W.
1977-04-01
Research studies are presented on special and general relativity. Gravitational theory, field theory, and space--time studies are included, as are studies involving the Minkowski space, the Schrodinger equations, the Dirac equations, and the Lorentz transformations
Ambient cosmology and spacetime singularities
International Nuclear Information System (INIS)
Antoniadis, Ignatios; Cotsakis, Spiros
2015-01-01
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary. (orig.)
Quantum field theory on discrete space-time. II
International Nuclear Information System (INIS)
Yamamoto, H.
1985-01-01
A quantum field theory of bosons and fermions is formulated on discrete Lorentz space-time of four dimensions. The minimum intervals of space and time are assumed to have different values in this paper. As a result the difficulties encountered in the previous paper (complex energy, incompleteness of solutions, and inequivalence between phase representation and momentum representation) are removed. The problem in formulating a field theory of fermions is solved by introducing a new operator and considering a theorem of translation invariance. Any matrix element given by a Feynman diagram is calculated in this theory to give a finite value regardless of the kinds of particles concerned (massive and/or massless bosons and/or fermions)
International Nuclear Information System (INIS)
Strohmaier, Alexander; Verch, Rainer; Wollenberg, Manfred
2002-01-01
We show in this article that the Reeh-Schlieder property holds for states of quantum fields on real analytic curved space-times if they satisfy an analytic microlocal spectrum condition. This result holds in the setting of general quantum field theory, i.e., without assuming the quantum field to obey a specific equation of motion. Moreover, quasifree states of the Klein-Gordon field are further investigated in the present work and the (analytic) microlocal spectrum condition is shown to be equivalent to simpler conditions. We also prove that any quasifree ground or KMS state of the Klein-Gordon field on a stationary real analytic space-time fulfills the analytic microlocal spectrum condition
On ``minimally curved spacetimes'' in general relativity
Dadhich, Naresh
1997-01-01
We consider a spacetime corresponding to uniform relativistic potential analogus to Newtonian potential as an example of ``minimally curved spacetime''. We also consider a radially symmetric analogue of the Rindler spacetime of uniform proper acceleration relative to infinity.
Quantum fields in curved space-times
International Nuclear Information System (INIS)
Ashtekar, A.; Magnon, A.
1975-01-01
The problem of obtaining a quantum description of the (real) Klein-Gordon system in a given curved space-time is discussed. An algebraic approach is used. The *-algebra of quantum operators is constructed explicitly and the problem of finding its *-representation is reduced to that of selecting a suitable complex structure on the real vector space of the solutions of the (classical) Klein-Gordon equation. Since, in a static space-time, there already exists, a satisfactory quantum field theory, in this case one already knows what the 'correct' complex structure is. A physical characterization of this 'correct' complex structure is obtained. This characterization is used to extend quantum field theory to non-static space-times. Stationary space-times are considered first. In this case, the issue of extension is completely straightforward and the resulting theory is the natural generalization of the one in static space-times. General, non-stationary space-times are then considered. In this case the issue of extension is quite complicated and only a plausible extension is presented. Although the resulting framework is well-defined mathematically, the physical interpretation associated with it is rather unconventional. Merits and weaknesses of this framework are discussed. (author)
Energy Technology Data Exchange (ETDEWEB)
Visser, Matt; Bassett, B.A.; Liberati, S
2000-06-01
We argue that 'effective' superluminal travel, potentially caused by the tipping over of light cones in Einstein gravity, is always associated with violations of the null energy condition (NEC). This is most easily seen by working perturbatively around Minkowski spacetime, where we use linearized Einstein gravity to show that the NEC forces the light cones to contract (narrow). Given the NEC, the Shapiro time delay in any weak gravitational field is always a delay relative to the Minkowski background, and never an advance. Furthermore, any object travelling within the lightcones of the weak gravitational field is similarly delayed with respect to the minimum traversal time possible in the background Minkowski geometry.
Some Peculiarities of Newton-Hooke Space-Times
Tian, Yu
2011-01-01
Newton-Hooke space-times are the non-relativistic limit of (anti-)de Sitter space-times. We investigate some peculiar facts about the Newton-Hooke space-times, among which the "extraordinary Newton-Hooke quantum mechanics" and the "anomalous Newton-Hooke space-times" are discussed in detail. Analysis on the Lagrangian/action formalism is performed in the discussion of the Newton-Hooke quantum mechanics, where the path integral point of view plays an important role, and the physically measurab...
Temperature and entropy of Schwarzschild-de Sitter space-time
International Nuclear Information System (INIS)
Shankaranarayanan, S.
2003-01-01
In the light of recent interest in quantum gravity in de Sitter space, we investigate semiclassical aspects of four-dimensional Schwarzschild-de Sitter space-time using the method of complex paths. The standard semiclassical techniques (such as Bogoliubov coefficients and Euclidean field theory) have been useful to study quantum effects in space-times with single horizons; however, none of these approaches seem to work for Schwarzschild-de Sitter space-time or, in general, for space-times with multiple horizons. We extend the method of complex paths to space-times with multiple horizons and obtain the spectrum of particles produced in these space-times. We show that the temperature of radiation in these space-times is proportional to the effective surface gravity--the inverse harmonic sum of surface gravity of each horizon. For the Schwarzschild-de Sitter space-time, we apply the method of complex paths to three different coordinate systems--spherically symmetric, Painleve, and Lemaitre. We show that the equilibrium temperature in Schwarzschild-de Sitter space-time is the harmonic mean of cosmological and event horizon temperatures. We obtain Bogoliubov coefficients for space-times with multiple horizons by analyzing the mode functions of the quantum fields near the horizons. We propose a new definition of entropy for space-times with multiple horizons, analogous to the entropic definition for space-times with a single horizon. We define entropy for these space-times to be inversely proportional to the square of the effective surface gravity. We show that this definition of entropy for Schwarzschild-de Sitter space-time satisfies the D-bound conjecture
Spacetime symmetries and topology in bimetric relativity
Torsello, Francesco; Kocic, Mikica; Högâs, Marcus; Mörtsell, Edvard
2018-04-01
We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.
Methods of approaching decoherence in the flavor sector due to space-time foam
Mavromatos, N. E.; Sarkar, Sarben
2006-08-01
In the first part of this work we discuss possible effects of stochastic space-time foam configurations of quantum gravity on the propagation of “flavored” (Klein-Gordon and Dirac) neutral particles, such as neutral mesons and neutrinos. The formalism is not the usually assumed Lindblad one, but it is based on random averages of quantum fluctuations of space-time metrics over which the propagation of the matter particles is considered. We arrive at expressions for the respective oscillation probabilities between flavors which are quite distinct from the ones pertaining to Lindblad-type decoherence, including in addition to the (expected) Gaussian decay with time, a modification to oscillation behavior, as well as a power-law cutoff of the time-profile of the respective probability. In the second part we consider space-time foam configurations of quantum-fluctuating charged-black holes as a way of generating (parts of) neutrino mass differences, mimicking appropriately the celebrated Mikheyev-Smirnov-Wolfenstein (MSW) effects of neutrinos in stochastically fluctuating random media. We pay particular attention to disentangling genuine quantum-gravity effects from ordinary effects due to the propagation of a neutrino through ordinary matter. Our results are of interest to precision tests of quantum-gravity models using neutrinos as probes.
Exact geodesic distances in FLRW spacetimes
Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri
2017-11-01
Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.
Said-Houari, Belkacem
2012-03-01
In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.
Said-Houari, Belkacem
2012-01-01
In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.
Linearized gravity in terms of differential forms
Baykal, Ahmet; Dereli, Tekin
2017-01-01
A technique to linearize gravitational field equations is developed in which the perturbation metric coefficients are treated as second rank, symmetric, 1-form fields belonging to the Minkowski background spacetime by using the exterior algebra of differential forms.
Fermion systems in discrete space-time
International Nuclear Information System (INIS)
Finster, Felix
2007-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure
Fermion systems in discrete space-time
Energy Technology Data Exchange (ETDEWEB)
Finster, Felix [NWF I - Mathematik, Universitaet Regensburg, 93040 Regensburg (Germany)
2007-05-15
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion Systems in Discrete Space-Time
Finster, Felix
2006-01-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Fermion systems in discrete space-time
Finster, Felix
2007-05-01
Fermion systems in discrete space-time are introduced as a model for physics on the Planck scale. We set up a variational principle which describes a non-local interaction of all fermions. This variational principle is symmetric under permutations of the discrete space-time points. We explain how for minimizers of the variational principle, the fermions spontaneously break this permutation symmetry and induce on space-time a discrete causal structure.
Vacuum quantum effect for curved boundaries in static Robertson-Walker space-time
International Nuclear Information System (INIS)
Setare, M.R.; Sadeghi, J.
2009-01-01
The energy-momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in k=-1 static Robertson-Walker space-time is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. k=-1 Robertson-Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in Robertson-Walker space from the corresponding Rindler counterpart by the conformal transformation.
Deduction of Einstein equation from homogeneity of Riemann spacetime
Ni, Jun
2012-03-01
The symmetry of spacetime translation leads to the energy-momentum conservation. However, the Lagrange depends on spacetime coordinates, which makes the symmetry of spacetime translation different with other symmetry invariant explicitly under symmetry transformation. We need an equation to guarantee the symmetry of spacetime translation. In this talk, I will show that the Einstein equation can be deduced purely from the general covariant principle and the homogeneity of spacetime in the frame of quantum field theory. The Einstein equation is shown to be the equation to guarantee the symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field, only electroweak-strong interactions appear with curved spacetime metric determined by the Einstein equation.. The general covariant principle and the homogeneity of spacetime are merged into one basic principle: Any Riemann spacetime metric guaranteeing the energy-momentum conservation are equivalent, which can be called as the conserved general covariant principle. [4pt] [1] Jun Ni, Chin. Phys. Lett. 28, 110401 (2011).
International Nuclear Information System (INIS)
Lovejoy, S.; Lima, M. I. P. de
2015-01-01
Over the range of time scales from about 10 days to 30–100 years, in addition to the familiar weather and climate regimes, there is an intermediate “macroweather” regime characterized by negative temporal fluctuation exponents: implying that fluctuations tend to cancel each other out so that averages tend to converge. We show theoretically and numerically that macroweather precipitation can be modeled by a stochastic weather-climate model (the Climate Extended Fractionally Integrated Flux, model, CEFIF) first proposed for macroweather temperatures and we show numerically that a four parameter space-time CEFIF model can approximately reproduce eight or so empirical space-time exponents. In spite of this success, CEFIF is theoretically and numerically difficult to manage. We therefore propose a simplified stochastic model in which the temporal behavior is modeled as a fractional Gaussian noise but the spatial behaviour as a multifractal (climate) cascade: a spatial extension of the recently introduced ScaLIng Macroweather Model, SLIMM. Both the CEFIF and this spatial SLIMM model have a property often implicitly assumed by climatologists that climate statistics can be “homogenized” by normalizing them with the standard deviation of the anomalies. Physically, it means that the spatial macroweather variability corresponds to different climate zones that multiplicatively modulate the local, temporal statistics. This simplified macroweather model provides a framework for macroweather forecasting that exploits the system's long range memory and spatial correlations; for it, the forecasting problem has been solved. We test this factorization property and the model with the help of three centennial, global scale precipitation products that we analyze jointly in space and in time
International Nuclear Information System (INIS)
Ivanov, I. P.
2008-01-01
We continue to explore the consequences of the recently discovered Minkowski space structure of the Higgs potential in the two-Higgs-doublet model. Here, we focus on the vacuum properties. The search for extrema of the Higgs potential is reformulated in terms of 3-quadrics in the 3+1-dimensional Minkowski space. We prove that 2HDM cannot have more than two local minima in the orbit space and that a twice-degenerate minimum can arise only via spontaneous violation of a discrete symmetry of the Higgs potential. Investigating topology of the 3-quadrics, we give concise criteria for existence of noncontractible paths in the Higgs orbit space. We also study explicit symmetries of the Higgs potential/Lagrangian and their spontaneous violation from a wider perspective than usual
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes
International Nuclear Information System (INIS)
Schenkel, Alexander
2011-01-01
The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the noncommutative
Noncommutative gravity and quantum field theory on noncummutative curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Schenkel, Alexander
2011-10-24
The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the
Conformal symmetry inheritance in null fluid spacetimes
International Nuclear Information System (INIS)
Tupper, B O J; Keane, A J; Hall, G S; Coley, A A; Carot, J
2003-01-01
We define inheriting conformal Killing vectors for null fluid spacetimes and find the maximum dimension of the associated inheriting Lie algebra. We show that for non-conformally flat null fluid spacetimes, the maximum dimension of the inheriting algebra is seven and for conformally flat null fluid spacetimes the maximum dimension is eight. In addition, it is shown that there are two distinct classes of non-conformally flat generalized plane wave spacetimes which possess the maximum dimension, and one class in the conformally flat case
Causal boundary for stably causal space-times
International Nuclear Information System (INIS)
Racz, I.
1987-12-01
The usual boundary constructions for space-times often yield an unsatisfactory boundary set. This problem is reviewed and a new solution is proposed. An explicit identification rule is given on the set of the ideal points of the space-time. This construction leads to a satisfactory boundary point set structure for stably causal space-times. The topological properties of the resulting causal boundary construction are examined. For the stably causal space-times each causal curve has a unique endpoint on the boundary set according to the extended Alexandrov topology. The extension of the space-time through the boundary is discussed. To describe the singularities the defined boundary sets have to be separated into two disjoint sets. (D.Gy.) 8 refs
Stochastic quantization of geometrodynamic curved space-time
International Nuclear Information System (INIS)
Prugovecki, E.
1981-01-01
It is proposed that quantum rather than classical test particles be used in recent operational definitions of space-time. In the resulting quantum space-time the role of test particle trajectories is taken over by propagators. The introduced co-ordinate values are stochastic rather than deterministic, the afore-mentioned propagators providing probability amplitudes describing fluctuations of measured co-ordinates around their mean values. It is shown that, if a geometrodynamic point of view based on 3 + 1 foliations of space-time is adopted, self-consistent families of propagators for quantum test particles in free fall can be constructed. The resulting formalism for quantum space-time is outlined and the quantization of spatially flat Robertson-Walker space-times is provided as an illustration. (author)
Bliokh, Konstantin Y.; Bekshaev, Aleksandr Y.; Nori, Franco
2017-12-01
We examine the momentum and angular momentum (AM) properties of monochromatic optical fields in dispersive and inhomogeneous isotropic media, using the Abraham- and Minkowski-type approaches, as well as the kinetic (Poynting-like) and canonical (with separate spin and orbital degrees of freedom) pictures. While the kinetic Abraham–Poynting momentum describes the energy flux and the group velocity of the wave, the Minkowski-type quantities, with proper dispersion corrections, describe the actual momentum and AM carried by the wave. The kinetic Minkowski-type momentum and AM densities agree with phenomenological results derived by Philbin. Using the canonical spin–orbital decomposition, previously used for free-space fields, we find the corresponding canonical momentum, spin and orbital AM of light in a dispersive inhomogeneous medium. These acquire a very natural form analogous to the Brillouin energy density and are valid for arbitrary structured fields. The general theory is applied to a non-trivial example of a surface plasmon-polariton (SPP) wave at a metal-vacuum interface. We show that the integral momentum of the SPP per particle corresponds to the SPP wave vector, and hence exceeds the momentum of a photon in the vacuum. We also provide the first accurate calculation of the transverse spin and orbital AM of the SPP. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. Importantly, we present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory also predicts a transverse magnetization in the metal (i.e. a magnetic moment for the SPP) as well as the corresponding direct magnetization current, which provides the difference between the Abraham and Minkowski momenta.
Y Bliokh, Konstantin; Y Bekshaev, Aleksandr; Nori, Franco
2017-12-01
We examine the momentum and angular momentum (AM) properties of monochromatic optical fields in dispersive and inhomogeneous isotropic media, using the Abraham- and Minkowski-type approaches, as well as the kinetic (Poynting-like) and canonical (with separate spin and orbital degrees of freedom) pictures. While the kinetic Abraham-Poynting momentum describes the energy flux and the group velocity of the wave, the Minkowski-type quantities, with proper dispersion corrections, describe the actual momentum and AM carried by the wave. The kinetic Minkowski-type momentum and AM densities agree with phenomenological results derived by Philbin. Using the canonical spin-orbital decomposition, previously used for free-space fields, we find the corresponding canonical momentum, spin and orbital AM of light in a dispersive inhomogeneous medium. These acquire a very natural form analogous to the Brillouin energy density and are valid for arbitrary structured fields. The general theory is applied to a non-trivial example of a surface plasmon-polariton (SPP) wave at a metal-vacuum interface. We show that the integral momentum of the SPP per particle corresponds to the SPP wave vector, and hence exceeds the momentum of a photon in the vacuum. We also provide the first accurate calculation of the transverse spin and orbital AM of the SPP. While the intrinsic orbital AM vanishes, the transverse spin can change its sign depending on the SPP frequency. Importantly, we present both macroscopic and microscopic calculations, thereby proving the validity of the general phenomenological results. The microscopic theory also predicts a transverse magnetization in the metal (i.e. a magnetic moment for the SPP) as well as the corresponding direct magnetization current, which provides the difference between the Abraham and Minkowski momenta.
International Nuclear Information System (INIS)
Racz, I.
1991-09-01
The problem of the existence of local extensions of spacetime is considered. It is shown that for a spacetime including an incomplete inextendible non-coiling causal geodesic curve there exists a particular C k (resp. C k- ) local extension provided that the curvature and its covariant derivatives are well behaved up to order k + 1 (resp. k) along a family of causal geodetics (around the chosen one). (R.P.) 15 refs
On the quantization of spacetime
International Nuclear Information System (INIS)
Banai, M.
1981-01-01
A program of quantization of relativistic local field theories in terms of Hilbert modules over non-commutative Csup*-algebras is outlined. The spacetime of the considered systems should become a ''quantum'' represented by a Hilbert space. Two suggestions are given for the possible determination this quantum spacetime. (author)
Possibility of extending space-time coordinates
International Nuclear Information System (INIS)
Wang Yongcheng.
1993-11-01
It has been shown that one coordinate system can describe a whole space-time region except some supersurfaces on which there are coordinate singularities. The conditions of extending a coordinate from real field to complex field are studied. It has been shown that many-valued coordinate transformations may help us to extend space-time regions and many-valued metric functions may make one coordinate region to describe more than one space-time regions. (author). 11 refs
a Novel 3d Intelligent Fuzzy Algorithm Based on Minkowski-Clustering
Toori, S.; Esmaeily, A.
2017-09-01
Assessing and monitoring the state of the earth surface is a key requirement for global change research. In this paper, we propose a new consensus fuzzy clustering algorithm that is based on the Minkowski distance. This research concentrates on Tehran's vegetation mass and its changes during 29 years using remote sensing technology. The main purpose of this research is to evaluate the changes in vegetation mass using a new process by combination of intelligent NDVI fuzzy clustering and Minkowski distance operation. The dataset includes the images of Landsat8 and Landsat TM, from 1989 to 2016. For each year three images of three continuous days were used to identify vegetation impact and recovery. The result was a 3D NDVI image, with one dimension for each day NDVI. The next step was the classification procedure which is a complicated process of categorizing pixels into a finite number of separate classes, based on their data values. If a pixel satisfies a certain set of standards, the pixel is allocated to the class that corresponds to those criteria. This method is less sensitive to noise and can integrate solutions from multiple samples of data or attributes for processing data in the processing industry. The result was a fuzzy one dimensional image. This image was also computed for the next 28 years. The classification was done in both specified urban and natural park areas of Tehran. Experiments showed that our method worked better in classifying image pixels in comparison with the standard classification methods.
Realization of Robertson-Walker spacetimes as affine hypersurfaces
International Nuclear Information System (INIS)
Chen Bangyen
2007-01-01
Due to the growing interest in embeddings of spacetimes in higher dimensional spaces, we consider a special type of embedding. We prove that Robertson-Walker spacetimes can be embedded as centroaffine hypersurfaces and graph hypersurfaces in some affine spaces in such a way that the induced relative metrics are exactly the Lorentzian metrics on the Robertson-Walker spacetimes. Such realizations allow us to view Robertson-Walker spacetimes and their submanifolds as affine submanifolds in a natural way. Consequently, our realizations make it possible to apply the tools of affine differential geometry to study Robertson-Walker spacetimes and their submanifolds
Semiclassical expanding discrete space-times
International Nuclear Information System (INIS)
Cobb, W.K.; Smalley, L.L.
1981-01-01
Given the close ties between general relativity and geometry one might reasonably expect that quantum effects associated with gravitation might also be tied to the geometry of space-time, namely, to some sort of discreteness in space-time itself. In particular it is supposed that space-time consists of a discrete lattice of points rather than the usual continuum. Since astronomical evidence seems to suggest that the universe is expanding, the lattice must also expand. Some of the implications of such a model are that the proton should presently be stable, and the universe should be closed although the mechanism for closure is quantum mechanical. (author)
Closed Timelike Curves in Type II Non-Vacuum Spacetime
International Nuclear Information System (INIS)
Ahmed, Faizuddin
2017-01-01
Here we present a cyclicly symmetric non-vacuum spacetime, admitting closed timelike curves (CTCs) which appear after a certain instant of time, i.e., a time-machine spacetime. The spacetime is asymptotically flat, free-from curvature singularities and a four-dimensional extension of the Misner space in curved spacetime. The spacetime is of type II in the Petrov classification scheme and the matter field pure radiation satisfy the energy condition. (paper)
Appleby, Stephen; Chingangbam, Pravabati; Park, Changbom; Hong, Sungwook E.; Kim, Juhan; Ganesan, Vidhya
2018-05-01
We apply the Minkowski tensor statistics to two-dimensional slices of the three-dimensional matter density field. The Minkowski tensors are a set of functions that are sensitive to directionally dependent signals in the data and, furthermore, can be used to quantify the mean shape of density fields. We begin by reviewing the definition of Minkowski tensors and introducing a method of calculating them from a discretely sampled field. Focusing on the statistic {W}21,1—a 2 × 2 matrix—we calculate its value for both the entire excursion set and individual connected regions and holes within the set. To study the morphology of structures within the excursion set, we calculate the eigenvalues λ 1, λ 2 for the matrix {W}21,1 of each distinct connected region and hole and measure their mean shape using the ratio β \\equiv . We compare both {W}21,1 and β for a Gaussian field and a smoothed density field generated from the latest Horizon Run 4 cosmological simulation to study the effect of gravitational collapse on these functions. The global statistic {W}21,1 is essentially independent of gravitational collapse, as the process maintains statistical isotropy. However, β is modified significantly, with overdensities becoming relatively more circular compared to underdensities at low redshifts. When applying the statistics to a redshift-space distorted density field, the matrix {W}21,1 is no longer proportional to the identity matrix, and measurements of its diagonal elements can be used to probe the large-scale velocity field.
Spacetime averaging of exotic singularity universes
International Nuclear Information System (INIS)
Dabrowski, Mariusz P.
2011-01-01
Taking a spacetime average as a measure of the strength of singularities we show that big-rips (type I) are stronger than big-bangs. The former have infinite spacetime averages while the latter have them equal to zero. The sudden future singularities (type II) and w-singularities (type V) have finite spacetime averages. The finite scale factor (type III) singularities for some values of the parameters may have an infinite average and in that sense they may be considered stronger than big-bangs.
Simulations of black holes in compactified spacetimes
Energy Technology Data Exchange (ETDEWEB)
Zilhao, Miguel; Herdeiro, Carlos [Centro de Fisica do Porto, Departamento de Fisica e Astronomia, Faculdade de Ciencias da Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto (Portugal); Cardoso, Vitor; Nerozzi, Andrea; Sperhake, Ulrich; Witek, Helvi [Centro Multidisciplinar de Astrofisica, Deptartamento de Fisica, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal); Gualtieri, Leonardo, E-mail: mzilhao@fc.up.pt [Dipartimento di Fisica, Universita di Roma ' Sapienza' and Sezione INFN Roma1, P.A. Moro 5, 00185, Roma (Italy)
2011-09-22
From the gauge/gravity duality to braneworld scenarios, black holes in compactified spacetimes play an important role in fundamental physics. Our current understanding of black hole solutions and their dynamics in such spacetimes is rather poor because analytical tools are capable of handling a limited class of idealized scenarios, only. Breakthroughs in numerical relativity in recent years, however, have opened up the study of such spacetimes to a computational treatment which facilitates accurate studies of a wider class of configurations. We here report on recent efforts of our group to perform numerical simulations of black holes in cylindrical spacetimes.
Time as a geometric property of space
Directory of Open Access Journals (Sweden)
James Michael Chappell
2016-11-01
Full Text Available The proper description of time remains a key unsolved problem in science. Newton conceived of time as absolute and universal which it `flows equably without relation to anything external'}. In the nineteenth century, the four-dimensional algebraic structure of the quaternions developed by Hamilton, inspired him to suggest that they could provide a unified representation of space and time. With the publishing of Einstein's theory of special relativity these ideas then lead to the generally accepted Minkowski spacetime formulation in 1908. Minkowski, though, rejected the formalism of quaternions suggested by Hamilton and adopted rather an approach using four-vectors. The Minkowski framework is indeed found to provide a versatile formalism for describing the relationship between space and time in accordance with Einstein's relativistic principles, but nevertheless fails to provide more fundamental insights into the nature of time itself. In order to answer this question we begin by exploring the geometric properties of three-dimensional space that we model using Clifford geometric algebra, which is found to contain sufficient complexity to provide a natural description of spacetime. This description using Clifford algebra is found to provide a natural alternative to the Minkowski formulation as well as providing new insights into the nature of time. Our main result is that time is the scalar component of a Clifford space and can be viewed as an intrinsic geometric property of three-dimensional space without the need for the specific addition of a fourth dimension.
Constraints on string vacua with spacetime supersymmetry
International Nuclear Information System (INIS)
Banks, T.; California Univ., Santa Cruz; Dixon, L.J.
1988-01-01
We examine the consequences of extended spacetime supersymmetry for classical superstring vacua with four dimensions uncompactified. N=2 spacetime supersymmetry implies that the 'internal' N=1 superconformal algebra with central charge c=6 splits into a piece with c=4 which has N=4 superconformal invariance, and a piece with c=2 which is constructed from two free dimension 1/2 superfields. N=4 spacetime supersymmetry requires that the entire c=6 algebra be represented by six free superfields. Using the world-sheet properties of N=1 spacetime supersymmetric classical vacua, we show that spacetime supersymmetry cannot be continuously broken within a family of classical vacua. Finally, we argue that the effective field theories for classical vacua of superstring theories (whether space time supersymmetric or not) have no continuous global symmetries - all continuous symmetries are gauged. (orig.)
Inflation from Minkowski space
International Nuclear Information System (INIS)
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Uttayarat, Patipan
2014-01-01
We propose a class of scalar models that, once coupled to gravity, lead to cosmologies that smoothly and stably connect an inflationary quasi-de Sitter universe to a low, or even zero-curvature, maximally symmetric spacetime in the asymptotic past, strongly violating the null energy condition ( H-dot ≫H"2) at intermediate times. The models are deformations of the conformal galileon lagrangian and are therefore based on symmetries, both exact and approximate, that ensure the quantum robustness of the whole picture. The resulting cosmological backgrounds can be viewed as regularized extensions of the galilean genesis scenario, or, equivalently, as ‘early-time-complete’ realizations of inflation. The late-time inflationary dynamics possesses phenomenologically interesting properties: it can produce a large tensor-to-scalar ratio within the regime of validity of the effective field theory and can lead to sizeable equilateral nongaussianities.
The Red Queen visits Minkowski space
International Nuclear Information System (INIS)
Low, Robert J
2007-01-01
When Alice went Through the Looking Glass, she found herself in a situation where she had to run as fast as she could in order to stay still. In accordance with the dictum that truth is stranger than fiction, we will see that it is possible to find a situation in special relativity where running towards one's target is actually counter-productive. Although the situation is easily analysed algebraically, the qualitative properties of the analysis are greatly illuminated by the use of spacetime diagrams
GRHydro: a new open-source general-relativistic magnetohydrodynamics code for the Einstein toolkit
International Nuclear Information System (INIS)
Mösta, Philipp; Haas, Roland; Ott, Christian D; Reisswig, Christian; Mundim, Bruno C; Faber, Joshua A; Noble, Scott C; Bode, Tanja; Löffler, Frank; Schnetter, Erik
2014-01-01
We present the new general-relativistic magnetohydrodynamics (GRMHD) capabilities of the Einstein toolkit, an open-source community-driven numerical relativity and computational relativistic astrophysics code. The GRMHD extension of the toolkit builds upon previous releases and implements the evolution of relativistic magnetized fluids in the ideal MHD limit in fully dynamical spacetimes using the same shock-capturing techniques previously applied to hydrodynamical evolution. In order to maintain the divergence-free character of the magnetic field, the code implements both constrained transport and hyperbolic divergence cleaning schemes. We present test results for a number of MHD tests in Minkowski and curved spacetimes. Minkowski tests include aligned and oblique planar shocks, cylindrical explosions, magnetic rotors, Alfvén waves and advected loops, as well as a set of tests designed to study the response of the divergence cleaning scheme to numerically generated monopoles. We study the code’s performance in curved spacetimes with spherical accretion onto a black hole on a fixed background spacetime and in fully dynamical spacetimes by evolutions of a magnetized polytropic neutron star and of the collapse of a magnetized stellar core. Our results agree well with exact solutions where these are available and we demonstrate convergence. All code and input files used to generate the results are available on http://einsteintoolkit.org. This makes our work fully reproducible and provides new users with an introduction to applications of the code. (paper)
Clifford Algebras and magnetic monopoles
International Nuclear Information System (INIS)
Recami, E.
1987-01-01
It is known that the introduction of magnetic monopolies in electromagnetism does still present formal problems from the point of view of classical field theory. The author attempts to overcome at least some of them by making recourse to the Clifford Algebra formalism. In fact, while the events of a two-dimensional Minkowski space-time M(1,1) are sufficiently well represented by ordinary Complex Numbers, when dealing with the events of the four-dimensional Minkowski space M(1,3)identical to M/sub 4/ one has of course to look for hypercomplex numbers or, more generally, for the elements of a Clifford Algebra. The author uses the Clifford Algebras in terms of ''multivectors'', and in particular by Hestenes' language, which suits space-time quite well. He recalls that the Clifford product chiγ is the sum of the internal product chi . γ and of the wedge product chiΛγ
Negative norm states in de Sitter space and QFT without renormalization procedure
International Nuclear Information System (INIS)
Takook, M.V.
2002-01-01
In recent papers, 1,2 it has been shown that the presence of negative norm states or negative frequency solutions are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content of the theory, offers the advantage of eliminating any ultraviolet divergence in the vacuum energy 2 and infrared divergence in the two point function. 3 We attempt here to extend this method to the interacting quantum field in Minkowski space-time. As an illustration of the procedure, we consider the λϕ 4 theory in Minkowski space-time. The mathematical consequences of this method is the disappearance of the ultraviolet divergence to the one-loop approximation. This means, the effect of these auxiliary negative norm states is to allow an automatic renormalization of the theory in this approximation. (author)
Special relativity a heuristic approach
Hassani, Sadri
2017-01-01
Special Relativity: A Heuristic Approach provides a qualitative exposition of relativity theory on the basis of the constancy of the speed of light. Using Einstein's signal velocity as the defining idea for the notion of simultaneity and the fact that the speed of light is independent of the motion of its source, chapters delve into a qualitative exposition of the relativity of time and length, discuss the time dilation formula using the standard light clock, explore the Minkowski four-dimensional space-time distance based on how the time dilation formula is derived, and define the components of the two-dimensional space-time velocity, amongst other topics. Provides a heuristic derivation of the Minkowski distance formula Uses relativistic photography to see Lorentz transformation and vector algebra manipulation in action Includes worked examples to elucidate and complement the topic being discussed Written in a very accessible style
The definition of time and quantum vacuum in 1 + 1 dimensions
International Nuclear Information System (INIS)
Capri, A.Z.; Roy, S.M.
1992-01-01
In this paper, the authors prove that for any (1+ 1)-dimensional globally hyperbolic space-time it is possible to define an instant of time as a special space-like geodesic which is independent of the coordinates chosen. This definition follows uniquely from the requirement of validity of Poincare symmetry in an infinitesimal neighborhood of the hypersurface of instantaneity. The generator associated with time translation then selects the direction of time. This fact permits unambiguous field quantization of this surface. For flat space-time the corresponding time and vacuum coincide with those of Minkowski space-time
Black Hole Space-time In Dark Matter Halo
Xu, Zhaoyi; Hou, Xian; Gong, Xiaobo; Wang, Jiancheng
2018-01-01
For the first time, we obtain the analytical form of black hole space-time metric in dark matter halo for the stationary situation. Using the relation between the rotation velocity (in the equatorial plane) and the spherical symmetric space-time metric coefficient, we obtain the space-time metric for pure dark matter. By considering the dark matter halo in spherical symmetric space-time as part of the energy-momentum tensors in the Einstein field equation, we then obtain the spherical symmetr...
Stochastic space-time and quantum theory
International Nuclear Information System (INIS)
Frederick, C.
1976-01-01
Much of quantum mechanics may be derived if one adopts a very strong form of Mach's principle such that in the absence of mass, space-time becomes not flat, but stochastic. This is manifested in the metric tensor which is considered to be a collection of stochastic variables. The stochastic-metric assumption is sufficient to generate the spread of the wave packet in empty space. If one further notes that all observations of dynamical variables in the laboratory frame are contravariant components of tensors, and if one assumes that a Lagrangian can be constructed, then one can obtain an explanation of conjugate variables and also a derivation of the uncertainty principle. Finally the superposition of stochastic metrics and the identification of root -g in the four-dimensional invariant volume element root -g dV as the indicator of relative probability yields the phenomenon of interference as will be described for the two-slit experiment
Quantum mechanics on noncommutative spacetime
International Nuclear Information System (INIS)
Calmet, Xavier; Selvaggi, Michele
2006-01-01
We consider electrodynamics on a noncommutative spacetime using the enveloping algebra approach and perform a nonrelativistic expansion of the effective action. We obtain the Hamiltonian for quantum mechanics formulated on a canonical noncommutative spacetime. An interesting new feature of quantum mechanics formulated on a noncommutative spacetime is an intrinsic electric dipole moment. We note, however, that noncommutative intrinsic dipole moments are not observable in present experiments searching for an electric dipole moment of leptons or nuclei such as the neutron since they are spin independent. These experiments are sensitive to the energy difference between two states and the noncommutative effect thus cancels out. Bounds on the noncommutative scale found in the literature relying on such intrinsic electric dipole moments are thus incorrect
Extending quantum mechanics entails extending special relativity
International Nuclear Information System (INIS)
Aravinda, S; Srikanth, R
2016-01-01
The complementarity between signaling and randomness in any communicated resource that can simulate singlet statistics is generalized by relaxing the assumption of free will in the choice of measurement settings. We show how to construct an ontological extension for quantum mechanics (QMs) through the oblivious embedding of a sound simulation protocol in a Newtonian spacetime. Minkowski or other intermediate spacetimes are ruled out as the locus of the embedding by virtue of hidden influence inequalities. The complementarity transferred from a simulation to the extension unifies a number of results about quantum non-locality, and implies that special relativity has a different significance for the ontological model and for the operational theory it reproduces. Only the latter, being experimentally accessible, is required to be Lorentz covariant. There may be certain Lorentz non-covariant elements at the ontological level, but they will be inaccessible at the operational level in a valid extension. Certain arguments against the extendability of QM, due to Conway and Kochen (2009) and Colbeck and Renner (2012), are attributed to their assumption that the spacetime at the ontological level has Minkowski causal structure. (paper)
Singularities of spacelike constant mean curvature surfaces in Lorentz-Minkowski space
DEFF Research Database (Denmark)
Brander, David
2011-01-01
We study singularities of spacelike, constant (non-zero) mean curvature (CMC) surfaces in the Lorentz-Minkowski 3-space L-3. We show how to solve the singular Bjorling problem for such surfaces, which is stated as follows: given a real analytic null-curve f(0)(x), and a real analytic null vector...... field v(x) parallel to the tangent field of f(0), find a conformally parameterized (generalized) CMC H surface in L-3 which contains this curve as a singular set and such that the partial derivatives f(x) and f(y) are given by df(0)/dx and v along the curve. Within the class of generalized surfaces...
Symmetry, structure, and spacetime
Rickles, Dean
2007-01-01
In this book Rickles considers several interpretative difficulties raised by gauge-type symmetries (those that correspond to no change in physical state). The ubiquity of such symmetries in modern physics renders them an urgent topic in philosophy of physics. Rickles focuses on spacetime physics, and in particular classical and quantum general relativity. Here the problems posed are at their most pathological, involving the apparent disappearance of spacetime! Rickles argues that both traditional ontological positions should be replaced by a structuralist account according to which relational
Geodesic deviation and Minikowski space
International Nuclear Information System (INIS)
Barraco, D.; Kozameh, C.; Newman, E.T.; Tod, P.
1990-01-01
The authors study the properties of the solution space of local surface-forming null sub-congruences in the neighborhood of a given null geodesic in a pseudo-Riemannian space-time. This solution space is a three-dimensional manifold, naturally endowed with a conformal Minkowski metric
The global monopole spacetime and its topological charge
Tan, Hongwei; Yang, Jinbo; Zhang, Jingyi; He, Tangmei
2018-03-01
We show that the global monopole spacetime is one of the exact solutions of the Einstein equations by treating the matter field as a non-linear sigma model, without the weak field approximation applied in the original derivation by Barriola and Vilenkin. Furthermore, we find the physical origin of the topological charge in the global monopole spacetime. Finally, we generalize the proposal which generates spacetime from thermodynamical laws to the case of spacetime with global monopole charge. Project supported by the National Natural Science Foundation of China (Grant Nos. 11273009 and 11303006).
Stringy models of modified gravity: space-time defects and structure formation
International Nuclear Information System (INIS)
Mavromatos, Nick E.; Sakellariadou, Mairi; Yusaf, Muhammad Furqaan
2013-01-01
Starting from microscopic models of space-time foam, based on brane universes propagating in bulk space-times populated by D0-brane defects (''D-particles''), we arrive at effective actions used by a low-energy observer on the brane world to describe his/her observations of the Universe. These actions include, apart from the metric tensor field, also scalar (dilaton) and vector fields, the latter describing the interactions of low-energy matter on the brane world with the recoiling point-like space-time defect (D-particle). The vector field is proportional to the recoil velocity of the D-particle and as such it satisfies a certain constraint. The vector breaks locally Lorentz invariance, which however is assumed to be conserved on average in a space-time foam situation, involving the interaction of matter with populations of D-particle defects. In this paper we clarify the role of fluctuations of the vector field on structure formation and galactic growth. In particular we demonstrate that, already at the end of the radiation era, the (constrained) vector field associated with the recoil of the defects provides the seeds for a growing mode in the evolution of the Universe. Such a growing mode survives during the matter dominated era, provided the variance of the D-particle recoil velocities on the brane is larger than a critical value. We note that in this model, as a result of specific properties of D-brane dynamics in the bulk, there is no issue of overclosing the brane Universe for large defect densities. Thus, in these models, the presence of defects may be associated with large-structure formation. Although our string inspired models do have (conventional, from a particle physics point of view) dark matter components, nevertheless it is interesting that the role of ''extra'' dark matter is also provided by the population of massive defects. This is consistent with the weakly interacting character of the D-particle defects, which predominantly interact only
Accelerated observers and the notion of singular spacetime
Olmo, Gonzalo J.; Rubiera-Garcia, Diego; Sanchez-Puente, Antonio
2018-03-01
Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and, therefore, observers with arbitrary motions should be able to provide a complete physical description of the world. This suggests that in a regular spacetime, all physically acceptable observers should have complete paths. In this work we explore this idea by studying the motion of accelerated observers in spherically symmetric spacetimes and illustrate it by considering two geodesically complete black hole spacetimes recently described in the literature. We show that for bound and locally unbound accelerations, the paths of accelerated test particles are complete, providing further support to the regularity of such spacetimes.
International Nuclear Information System (INIS)
Dey, Dipanjan
2015-01-01
Dark-matter is a hypothetical matter which can't be seen but around 27% of our universe is made of it. Its distribution, evolution from early stage of our universe to present stage, its particle constituents all these are great unsolved mysteries of modern Cosmology and Astrophysics. In this talk I will introduce a special kind of space-time which is known as Bertrand Space-time (BST). I will show this space-time interestingly shows some dark-matter properties like- flat velocity curve, density profile of Dark-matter, total mass of Dark matter-halo, gravitational lensing etc, for that reason we consider BST is seeded by Dark-matter or it is a space-time of Dark-matter. At last I will show using modified gravity formalism the behaviour of the equation of state parameter of Dark-matter and the behaviour of the Newton's gravitational constant in the vicinity of the singularity. (author)
International Nuclear Information System (INIS)
Tupper, B.O.J.
1983-01-01
The work of a previous article is extended to show that space-times which are the exact solutions of the field equations for a perfect fluid also may be exact solutions of the field equations for a viscous magnetohydrodynamic fluid. Conditions are found for this equivalence to exist and viscous magnetohydrodynamic solutions are found for a number of known perfect fluid space-times. (author)
On Mass, Spacetime Curvature, and Gravity
Janis, Allen I.
2018-01-01
The frequently used analogy of a massive ball distorting an elastic sheet, which is used to illustrate why mass causes spacetime curvature and gravitational attraction, is criticized in this article. A different analogy that draws on the students' previous knowledge of spacetime diagrams in special relativity is suggested.
DEFF Research Database (Denmark)
Brander, David; Rossman, Wayne; Schmitt, Nicholas
2010-01-01
We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space $\\R^{2,1}$. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group $SU_2$ with...
Geometría y física del espacio-tiempo de Minkowski
Xambó Descamps, Sebastián
2017-01-01
El propósito de este artículo es urdir una presentación elemental del espacio-tiempo (en el sentido de Minkowski) que subraye los aspectos geométricos y físicos fundamentales que concurren en su estructura. El lenguaje utilizado es el álgebra lineal y su extensión en el álgebra geométrica. Es el mé- todo que nos parece más idóneo para formular y manejar las transformaciones de Lorentz, la electrodinámica relativista y la teoría del electrón de Dirac. Peer Reviewed
Self-force on an arbitrarily coupled scalar charge in cylindrical thin-shell spacetimes
Energy Technology Data Exchange (ETDEWEB)
Tomasini, C.; Rubin de Celis, E.; Simeone, C. [Universidad de Buenos Aires y IFIBA, CONICET, Ciudad Universitaria, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)
2018-02-15
We consider the arbitrarily coupled field and self-force of a static massless scalar charge in cylindrical spacetimes with one or two asymptotic regions, with the only matter content concentrated in a thin-shell characterized by the trace of the extrinsic curvature jump κ. The self-force is studied numerically and analytically in terms of the curvature coupling ξ. We found the critical values ξ{sub c}{sup (n)} = n/(ρ(r{sub s})κ), with n element of N and ρ(r{sub s}) the metric's profile function at the position of the shell, for which the scalar field is divergent in the background configuration. The pathological behavior is removed by restricting the coupling to a domain of stability. The coupling has a significant influence over the self-force at the vicinities of the shell, and we identified ξ = 1/4 as the value for which the scalar force changes sign at a neighborhood of r{sub s}; if κ(1-4ξ) > 0 the shell acts repulsively as an effective potential barrier, while if κ(1-4ξ) < 0 it attracts the charge as a potential well. The sign of the asymptotic self-force only depends on whether there is an angle deficit or not on the external region where the charge is placed; conical asymptotics produce a leading attractive force, while Minkowski regions produce a repulsive asymptotic self-force. (orig.)
Empty space-times with separable Hamilton-Jacobi equation
International Nuclear Information System (INIS)
Collinson, C.D.; Fugere, J.
1977-01-01
All empty space-times admitting a one-parameter group of motions and in which the Hamilton-Jacobi equation is (partially) separable are obtained. Several different cases of such empty space-times exist and the Riemann tensor is found to be either type D or N. The results presented here complete the search for empty space-times with separable Hamilton-Jacobi equation. (author)
Quantum Spacetime: Mimicry of Paths and Black Holes
Spaans, Marco
2015-08-01
Since its inception, general relativity has been unreceptive to a marriage with the quantum aspects of our universe. Following the ideas of Einstein, one may pursue an approach that allows spacetime itself to take center stage. The quantum properties of matter are then carried by the dynamics of spacetime shape and connectivity. This monograph introduces the reader to the foundations of quantum spacetime in a manner accessible to researchers and students. Likewise, interested laymen that lack a strong background in quantum mechanics or spacetime studies but are keen to learn will find this book worthwhile. It is shown from first principles how spacetime is globally built up by paths which constitute entire histories in four dimensions. The central physical idea is that the collective existence of observers and observed derives from one mimicking the other unremittingly, thereby inducing tangible reality. This world of identity by mimicry creates a multitude of interacting histories. Throughout the text, thought experiments are used to derive physical principles. Obtained results are therefore intuitive and accessible to non-experts. This monograph also discusses consequences of quantum spacetime for black holes, dark energy, inflation, the Higgs boson, and the multiverse.
Space-time and matter in 'prephysics'
International Nuclear Information System (INIS)
Terazawa, Hidezumi.
1985-05-01
Many fundamental questions concerning the space-time and matter are asked and answered in ''prephysics'', a new line of physics (or philosophy but not metaphysics). They include the following: 1) ''Why is our space-time of 4 dimensions.'', 2) ''What is the ultimate form of matter.'' and 3) ''How was our universe created.''. (author)
Finiteness principle and the concept of space-time
International Nuclear Information System (INIS)
Tati, T.
1984-01-01
It is shown that the non-space-time description can be given by a system of axioms under the postulate of a certain number of pre-supposed physical concepts in which space-time is not included. It is found that space-time is a compound concept of presupposed concepts of non-space-time description connected by an additional condition called 'space-time condition'. (L.C.) [pt
Energy Technology Data Exchange (ETDEWEB)
Akkelin, S.V. [Bogolyubov Institute for Theoretical Physics, Kiev (Ukraine); Universitaet Heidelberg, Institut fuer Theoretische Physik, Heidelberg (Germany); GSI Helmholtzzentrum fuer Schwerionenforschung, ExtreMe Matter Institute EMMI, Darmstadt (Germany)
2017-12-15
Ultrarelativistic heavy ion collisions produce a quark-gluon matter which lies in the future light cone originating from given points on the t = z = 0 plane of the Minkowski spacetime manifold. We show that in a weak coupling regime the Minkowski vacuum of massless fields presents itself in the ''Little Bang'' region as a thermal state of low p{sub T} particles, in close analogy to the Unruh effect for uniformly accelerated observers which are causally restricted to a Rindler wedge. It can shed some light on the mechanisms of early time thermalization in ultrarelativistic heavy ion collisions. (orig.)
Natural world physical, brain operational, and mind phenomenal space-time
Fingelkurts, Andrew A.; Fingelkurts, Alexander A.; Neves, Carlos F. H.
2010-06-01
Concepts of space and time are widely developed in physics. However, there is a considerable lack of biologically plausible theoretical frameworks that can demonstrate how space and time dimensions are implemented in the activity of the most complex life-system - the brain with a mind. Brain activity is organized both temporally and spatially, thus representing space-time in the brain. Critical analysis of recent research on the space-time organization of the brain's activity pointed to the existence of so-called operational space-time in the brain. This space-time is limited to the execution of brain operations of differing complexity. During each such brain operation a particular short-term spatio-temporal pattern of integrated activity of different brain areas emerges within related operational space-time. At the same time, to have a fully functional human brain one needs to have a subjective mental experience. Current research on the subjective mental experience offers detailed analysis of space-time organization of the mind. According to this research, subjective mental experience (subjective virtual world) has definitive spatial and temporal properties similar to many physical phenomena. Based on systematic review of the propositions and tenets of brain and mind space-time descriptions, our aim in this review essay is to explore the relations between the two. To be precise, we would like to discuss the hypothesis that via the brain operational space-time the mind subjective space-time is connected to otherwise distant physical space-time reality.
Dual transformations of the non-abelian fields in Minkowsky, Euclid, and Galilei-Newton spaces
International Nuclear Information System (INIS)
Tolkaehev, E.A.; Kurochkin, Y.A.; Trequbovich, A.Y.
1991-01-01
In this paper it is shown that the generalization of the Yang-Mills equations in Minkowsky space to the case of the biquaternions over dual and double numbers enables one to define the corresponding representations of the Galilei and SO(4) groups in a rather natural way. it makes construction of the non-Abelian field equations in Euclidean and Galilei-Newton spaces possible and proves their invariance under generalized dual transformations by use of the analogy with the Abelian gauge
Thermal particle production in two Taub-Nut type spacetimes
International Nuclear Information System (INIS)
Lapedes, A.S.
1976-01-01
The Hartle-Hawking method of deriving black hole radiance has been extended to non-asymptotically flat de Sitter spacetime by Gibbons and Hawking. We extend this work to Taub-Nut spacetime and a related and more physical spacetime constructed from it by Siklos. (orig./BJ) [de
International Nuclear Information System (INIS)
Dodson, C.T.J.
1977-02-01
This is the second part of a monograph intended to be a mathematically rigorous account of the current position of the bundle-completion of spacetime in general relativity; some new material is included
The classification of static plane-symmetric spacetimes
International Nuclear Information System (INIS)
Ziad, M.
1999-01-01
According to the classical literature, here a complete classification of static plane-symmetric spacetimes according to their isometries and metrics is provided,without imposing any restriction on the stress-energy tensor. It turns out that these spacetimes admit G r as the maximal isometry groups whereas their Killing vector fields are obtained. The Einstein field equations are used to discuss the stress energy tensors of the spacetimes admitting higher symmetries along with their Segre' and Plebanski types and finally results are compared with those of Taub, Hall and Steele
Matter fields in curved space-time
International Nuclear Information System (INIS)
Viet, Nguyen Ai; Wali, Kameshwar C.
2000-01-01
We study the geometry of a two-sheeted space-time within the framework of non-commutative geometry. As a prelude to the Standard Model in curved space-time, we present a model of a left- and a right- chiral field living on the two sheeted-space time and construct the action functionals that describe their interactions
Spacetime Dynamics and Slow Neutrino Background
Zhang, Tianxi
2018-06-01
Space is a form of existence of matter, while time is a measure of change of the matter in the space. Issac Newton suggested that the space and time are absolute, not affected by matter and its motion. His first law of motion or the law of inertia says that, without net force acts on it, an object in motion remains the motion in a straight line at a constant speed. Ernest Mach proposed that the inertia of a body results from the gravitational interaction on the body by the rest of the entire universe. As mass is a measure of inertia, Mach’s principle can be simply stated as mass here is affected by matter there. On the basis of Mach’s principle, Albert Einstein considered the space and time to be relative and developed two theories of relativities. One called special relativity describes the effect of motion on spacetime and the other called general relativity describes the effect of matter on spacetime. Recently, the author has further considered reactions of the influenced spacetime on the moving objects, including photons. A moving object including a photon, because of its continuously keeping on displacement, disturbs the rest of the entire universe or distorts/curves the spacetime. The distorted or curved spacetime then generates an effective gravitational force to act back on the moving object or photon, so that reduces the object inertia or photon frequency. Considering the disturbance of spacetime by a photon is extremely weak, the author has modelled the effective gravitational force to be Newtonian and derived a new redshift-distance relation that not only perfectly explained the redshift-distance measurement of distant type Ia supernovae but also inherently obtained Hubble’s law as an approximate at small redshift. In this study, we will further analyse the reaction of the influenced spacetime on moving neutrinos and demonstrate the creation of slow neutrino (or tired neutrino) background that may be gravitationally orbiting around clusters
The variation of the density functions on chaotic spheres in chaotic space-like Minkowski space time
International Nuclear Information System (INIS)
El-Ahmady, A.E.
2007-01-01
In this article we introduce types of chaotic spheres in chaotic space-like Minkowski space time M n+1 . The variations of the density functions under the folding of these chaotic spheres are defined. The foldings restriction imposed on the density function are also discussed. The relations between the folding of geometry and pure chaotic manifolds are deduced. Some theorems concerning these relations are presented
K-causality and degenerate spacetimes
Dowker, H. F.; Garcia, R. S.; Surya, S.
2000-11-01
The causal relation K+ was introduced by Sorkin and Woolgar to extend the standard causal analysis of C2 spacetimes to those that are only C0. Most of their results also hold true in the case of metrics with degeneracies which are C0 but vanish at isolated points. In this paper we seek to examine K+ explicitly in the case of topology-changing `Morse histories' which contain degeneracies. We first demonstrate some interesting features of this relation in globally Lorentzian spacetimes. In particular, we show that K+ is robust and the Hawking and Sachs characterization of causal continuity translates into a natural condition in terms of K+. We then examine K+ in topology-changing Morse spacetimes with the degenerate points excised and then for the Morse histories in which the degenerate points are reinstated. We find further characterizations of causal continuity in these cases.
The Casimir Effect from the Point of View of Algebraic Quantum Field Theory
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, Claudio, E-mail: claudio.dappiaggi@unipv.it; Nosari, Gabriele [Università degli Studi di Pavia, Dipartimento di Fisica (Italy); Pinamonti, Nicola [Università di Genova, Dipartimento di Matematica (Italy)
2016-06-15
We consider a region of Minkowski spacetime bounded either by one or by two parallel, infinitely extended plates orthogonal to a spatial direction and a real Klein-Gordon field satisfying Dirichlet boundary conditions. We quantize these two systems within the algebraic approach to quantum field theory using the so-called functional formalism. As a first step we construct a suitable unital ∗-algebra of observables whose generating functionals are characterized by a labelling space which is at the same time optimal and separating and fulfils the F-locality property. Subsequently we give a definition for these systems of Hadamard states and we investigate explicit examples. In the case of a single plate, it turns out that one can build algebraic states via a pull-back of those on the whole Minkowski spacetime, moreover inheriting from them the Hadamard property. When we consider instead two plates, algebraic states can be put in correspondence with those on flat spacetime via the so-called method of images, which we translate to the algebraic setting. For a massless scalar field we show that this procedure works perfectly for a large class of quasi-free states including the Poincaré vacuum and KMS states. Eventually Wick polynomials are introduced. Contrary to the Minkowski case, the extended algebras, built in globally hyperbolic subregions can be collected in a global counterpart only after a suitable deformation which is expressed locally in terms of a *-isomorphism. As a last step, we construct explicitly the two-point function and the regularized energy density, showing, moreover, that the outcome is consistent with the standard results of the Casimir effect.
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
International Nuclear Information System (INIS)
Pfeifer, Christian
2013-11-01
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
The Finsler spacetime framework. Backgrounds for physics beyond metric geometry
Energy Technology Data Exchange (ETDEWEB)
Pfeifer, Christian
2013-11-15
The fundamental structure on which physics is described is the geometric spacetime background provided by a four dimensional manifold equipped with a Lorentzian metric. Most importantly the spacetime manifold does not only provide the stage for physical field theories but its geometry encodes causality, observers and their measurements and gravity simultaneously. This threefold role of the Lorentzian metric geometry of spacetime is one of the key insides of general relativity. During this thesis we extend the background geometry for physics from the metric framework of general relativity to our Finsler spacetime framework and ensure that the threefold role of the geometry of spacetime in physics is not changed. The geometry of Finsler spacetimes is determined by a function on the tangent bundle and includes metric geometry. In contrast to the standard formulation of Finsler geometry our Finsler spacetime framework overcomes the differentiability and existence problems of the geometric objects in earlier attempts to use Finsler geometry as an extension of Lorentzian metric geometry. The development of our nonmetric geometric framework which encodes causality is one central achievement of this thesis. On the basis of our well-defined Finsler spacetime geometry we are able to derive dynamics for the non-metric Finslerian geometry of spacetime from an action principle, obtained from the Einstein-Hilbert action, for the first time. We can complete the dynamics to a non-metric description of gravity by coupling matter fields, also formulated via an action principle, to the geometry of our Finsler spacetimes. We prove that the combined dynamics of the fields and the geometry are consistent with general relativity. Furthermore we demonstrate how to define observers and their measurements solely through the non-metric spacetime geometry. Physical consequence derived on the basis of our Finsler spacetime are: a possible solution to the fly-by anomaly in the solar system; the
Space-Time Disarray and Visual Awareness
Directory of Open Access Journals (Sweden)
Jan Koenderink
2012-04-01
Full Text Available Local space-time scrambling of optical data leads to violent jerks and dislocations. On masking these, visual awareness of the scene becomes cohesive, with dislocations discounted as amodally occluding foreground. Such cohesive space-time of awareness is technically illusory because ground truth is jumbled whereas awareness is coherent. Apparently the visual field is a construction rather than a (veridical perception.
On the reconstruction of Lifshitz spacetimes
International Nuclear Information System (INIS)
Gentle, Simon A.; Keeler, Cynthia
2016-01-01
We consider the reconstruction of a Lifshitz spacetime from three perspectives: differential entropy (or ‘hole-ography’), causal wedges and entanglement wedges. We find that not all time-varying bulk curves in vacuum Lifshitz can be reconstructed via the differential entropy approach, adding a caveat to the general analysis of http://dx.doi.org/10.1007/JHEP10(2014)149. We show that the causal wedge for Lifshitz spacetimes degenerates, while the entanglement wedge requires the additional consideration of a set of boundary-emanating light-sheets. The need to include bulk surfaces with no clear field theory interpretation in the differential entropy construction and the change in the entanglement wedge formation both serve as warnings against a naive application of holographic entanglement entropy proposals in Lifshitz spacetimes.
Thick domain wall spacetimes with and without reflection symmetry
International Nuclear Information System (INIS)
Melfo, Alejandra; Pantoja, Nelson; Skirzewski, Aureliano
2003-01-01
We show that different thick domain wall spacetimes, for which the scalar field configuration and the potential are the same, can be found as solutions to the coupled Einstein-scalar field equations, depending on whether or not reflection symmetry on the wall is imposed. Spacetimes with reflection symmetry may be dynamic or static, while the asymmetric ones are static. Asymmetric walls are asymptotically flat on one side and reduce to the Taub spacetime on the other. Examples of asymmetric thick walls in D-dimensional spacetimes are given, and previous analysis on the distributional thin-wall limit of the dynamic symmetric thick walls are extended to the asymmetric case. A new family of reflection symmetric, static thick domain wall spacetimes, including previously known Bogomol'nyi-Prasad-Sommerfield walls, is presented
Quaternion wave equations in curved space-time
Edmonds, J. D., Jr.
1974-01-01
The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.
Quantum theory of spinor field in four-dimensional Riemannian space-time
International Nuclear Information System (INIS)
Shavokhina, N.S.
1996-01-01
The review deals with the spinor field in the four-dimensional Riemannian space-time. The field beys the Dirac-Fock-Ivanenko equation. Principles of quantization of the spinor field in the Riemannian space-time are formulated which in a particular case of the plane space-time are equivalent to the canonical rules of quantization. The formulated principles are exemplified by the De Sitter space-time. The study of quantum field theory in the De Sitter space-time is interesting because it itself leads to a method of an invariant well for plane space-time. However, the study of the quantum spinor field theory in an arbitrary Riemannian space-time allows one to take into account the influence of the external gravitational field on the quantized spinor field. 60 refs
Energy Technology Data Exchange (ETDEWEB)
Racz, Istvan, E-mail: iracz@rmki.kfki.h [RMKI, H-1121 Budapest, Konkoly Thege Miklos ut 29-33 (Hungary)
2010-08-07
The global extendibility of smooth causal geodesically incomplete spacetimes is investigated. Denote by {gamma} one of the incomplete non-extendible causal geodesics of a causal geodesically incomplete spacetime (M, g{sub ab}). First, it is shown that it is always possible to select a synchronized family of causal geodesics {Gamma} and an open neighbourhood U of a final segment of {gamma} in M such that U comprises members of {Gamma}, and suitable local coordinates can be defined everywhere on U provided that {gamma} does not terminate either on a tidal force tensor singularity or on a topological singularity. It is also shown that if, in addition, the spacetime (M, g{sub ab}) is globally hyperbolic, and the components of the curvature tensor, and its covariant derivatives up to order k - 1 are bounded on U, and also the line integrals of the components of the kth-order covariant derivatives are finite along the members of {Gamma}-where all the components are meant to be registered with respect to a synchronized frame field on U-then there exists a C{sup k-} extension {Phi} : (M,g{sub ab}) {yields}(M,g{sub ab}) so that for each {gamma}-bar from {Gamma}, which is inextendible in (M, g{sub ab}), the image, {Phi}{gamma}-bar, is extendible in (M,g{sub ab}). Finally, it is also proved that whenever {gamma} does terminate on a topological singularity (M, g{sub ab}) cannot be generic.
Effects related to spacetime foam in particle physics
International Nuclear Information System (INIS)
Kirillov, A.A.
1999-01-01
It is found that the existence of spacetime foam leads to a situation in which the number of fundamental quantum bosonic fields is a variable quantity. The general aspects of an exact theory that allows for a variable number of fields are discussed, and the simplest observable effects generated by the foam are estimated. It is shown that in the absence of processes related to variations in the topology of space, the concept of an effective field can be reintroduced and standard field theory can be restored. However, in the complete theory the ground state is characterized by a nonvanishing particle number density. From the effective-field standpoint, such particles are 'dark'. It is assumed that they comprise dark matter of the universe. The properties of this dark matter are discussed, and so is the possibility of measuring the quantum fluctuation in the field potentials
A short history of fractal-Cantorian space-time
International Nuclear Information System (INIS)
Marek-Crnjac, L.
2009-01-01
The article attempts to give a short historical overview of the discovery of fractal-Cantorian space-time starting from the 17th century up to the present. In the last 25 years a great number of scientists worked on fractal space-time notably Garnet Ord in Canada, Laurent Nottale in France and Mohamed El Naschie in England who gave an exact mathematical procedure for the derivation of the dimensionality and curvature of fractal space-time fuzzy manifold.
Comparison of two Minkowski-space approaches to heavy quarkonia
Energy Technology Data Exchange (ETDEWEB)
Leitao, Sofia; Biernat, Elmar P. [Universidade de Lisboa, CFTP, Instituto Superior Tecnico, Lisbon (Portugal); Li, Yang [Iowa State University, Department of Physics and Astronomy, Ames, IA (United States); College of William and Mary, Department of Physics, Williamsburg, VA (United States); Maris, Pieter; Vary, James P. [Iowa State University, Department of Physics and Astronomy, Ames, IA (United States); Pena, M.T. [Universidade de Lisboa, CFTP, Instituto Superior Tecnico, Lisbon (Portugal); Universidade de Lisboa, Departamento de Fisica, Instituto Superior Tecnico, Lisbon (Portugal); Stadler, Alfred [Universidade de Lisboa, CFTP, Instituto Superior Tecnico, Lisbon (Portugal); Universidade de Evora, Departamento de Fisica, Evora (Portugal)
2017-10-15
In this work we compare mass spectra and decay constants obtained from two recent, independent, and fully relativistic approaches to the quarkonium bound-state problem: the Basis Light-Front Quantization approach, where light-front wave functions are naturally formulated; and, the Covariant Spectator Theory (CST), based on a reorganization of the Bethe-Salpeter equation. Even though conceptually different, both solutions are obtained in Minkowski space. Comparisons of decay constants for more than ten states of charmonium and bottomonium show favorable agreement between the two approaches as well as with experiment where available. We also apply the Brodsky-Huang-Lepage prescription to convert the CST amplitudes into functions of light-front variables. This provides an ideal opportunity to investigate the similarities and differences at the level of the wave functions. Several qualitative features are observed in remarkable agreement between the two approaches even for the rarely addressed excited states. Leading-twist distribution amplitudes as well as parton distribution functions of heavy quarkonia are also analyzed. (orig.)
Space-time neutronic analysis of postulated LOCA's in CANDU reactors
International Nuclear Information System (INIS)
Luxat, J.C.; Frescura, G.M.
1978-01-01
Space-time neutronic behaviour of CANDU reactors is of importance in the analysis and design of reactor safety systems. A methodology has been developed for simulating CANDU space-time neutronics with application to the analysis of postulated LOCA'S. The approach involves the efficient use of a set of computer codes which provide a capability to perform simulations ranging from detailed, accurate 3-dimensional space-time to low-cost survey calculations using point kinetics with some ''effective'' spatial content. A new, space-time kinetics code based upon a modal expansion approach is described. This code provides an inexpensive and relatively accurate scoping tool for detailed 3-dimensional space-time simulations. (author)
Observable Zitterbewegung in curved spacetimes
Energy Technology Data Exchange (ETDEWEB)
Kobakhidze, Archil, E-mail: archilk@physics.usyd.edu.au [ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, NSW 2006 (Australia); Manning, Adrian, E-mail: a.manning@physics.usyd.edu.au [ARC Centre of Excellence for Particle Physics at the Terascale, School of Physics, The University of Sydney, NSW 2006 (Australia); Tureanu, Anca, E-mail: anca.tureanu@helsinki.fi [Department of Physics, University of Helsinki, P.O. Box 64, 00014 Helsinki (Finland)
2016-06-10
Zitterbewegung, as it was originally described by Schrödinger, is an unphysical, non-observable effect. We verify whether the effect can be observed in non-inertial reference frames/curved spacetimes, where the ambiguity in defining particle states results in a mixing of positive and negative frequency modes. We explicitly demonstrate that such a mixing is in fact necessary to obtain the correct classical value for a particle's velocity in a uniformly accelerated reference frame, whereas in cosmological spacetime a particle does indeed exhibit Zitterbewegung.
Observable Zitterbewegung in curved spacetimes
Kobakhidze, Archil; Manning, Adrian; Tureanu, Anca
2016-06-01
Zitterbewegung, as it was originally described by Schrödinger, is an unphysical, non-observable effect. We verify whether the effect can be observed in non-inertial reference frames/curved spacetimes, where the ambiguity in defining particle states results in a mixing of positive and negative frequency modes. We explicitly demonstrate that such a mixing is in fact necessary to obtain the correct classical value for a particle's velocity in a uniformly accelerated reference frame, whereas in cosmological spacetime a particle does indeed exhibit Zitterbewegung.
Spacetimes admitting a universal redshift function
International Nuclear Information System (INIS)
Dautcourt, G.
1987-01-01
The conditions are given for a velocity congruence in a Riemannian spacetime admitting a universal redshift function R. This function allows to calculate in a simple way (as a quotient of R values taken at the emission and registration event) the redshift or blueshift connected with an emitter and observer both following the congruence. Spacetimes and congruences with an universal redshift function are shortly discussed. (author)
On discrete models of space-time
International Nuclear Information System (INIS)
Horzela, A.; Kempczynski, J.; Kapuscik, E.; Georgia Univ., Athens, GA; Uzes, Ch.
1992-02-01
Analyzing the Einstein radiolocation method we come to the conclusion that results of any measurement of space-time coordinates should be expressed in terms of rational numbers. We show that this property is Lorentz invariant and may be used in the construction of discrete models of space-time different from the models of the lattice type constructed in the process of discretization of continuous models. (author)
Ohanian, Hans C
2013-01-01
The third edition of this classic textbook is a quantitative introduction for advanced undergraduates and graduate students. It gently guides students from Newton's gravitational theory to special relativity, and then to the relativistic theory of gravitation. General relativity is approached from several perspectives: as a theory constructed by analogy with Maxwell's electrodynamics, as a relativistic generalization of Newton's theory, and as a theory of curved spacetime. The authors provide a concise overview of the important concepts and formulas, coupled with the experimental results underpinning the latest research in the field. Numerous exercises in Newtonian gravitational theory and Maxwell's equations help students master essential concepts for advanced work in general relativity, while detailed spacetime diagrams encourage them to think in terms of four-dimensional geometry. Featuring comprehensive reviews of recent experimental and observational data, the text concludes with chapters on cosmology an...
Stability of generic thin shells in conformally flat spacetimes
Energy Technology Data Exchange (ETDEWEB)
Amirabi, Z. [Eastern Mediterranean Univ., Gazimagusa (Turkey). Dept. of Physics
2017-07-15
Some important spacetimes are conformally flat; examples are the Robertson-Walker cosmological metric, the Einstein-de Sitter spacetime, and the Levi-Civita-Bertotti-Robinson and Mannheim metrics. In this paper we construct generic thin shells in conformally flat spacetime supported by a perfect fluid with a linear equation of state, i.e., p = ωσ. It is shown that, for the physical domain of ω, i.e., 0 < ω ≤ 1, such thin shells are not dynamically stable. The stability of the timelike thin shells with the Mannheim spacetime as the outer region is also investigated. (orig.)
Scalar fields in black hole spacetimes
Thuestad, Izak; Khanna, Gaurav; Price, Richard H.
2017-07-01
The time evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, timelike infinity, and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index ℓ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.
International Nuclear Information System (INIS)
Bakulev, A. P.; Mikhailov, S. V.; Stefanis, N. G.
2007-01-01
We work out and discuss the Minkowski version of fractional analytic perturbation theory for QCD observables, recently developed and presented by us for the Euclidean region. The original analytic approach to QCD, initiated by Shirkovand Solovtsov, is summarized and relations to other proposals to achieve an analytic strong coupling are pointed out. The developed framework is applied to the Higgs boson decay into a bb pair, using recent results for the massless correlator of two quark scalar currents in the MS scheme.We present calculations for the decay width within the Minkowski version off ractional analytic perturbation theory including those non-power-series contributions that correspond to the O(α s 3 )-terms, also taking into account evolution effects of the running coupling and the b-quark-mass renormalization. Comparisons with previous results within standard QCD perturbation theory are performed and the differences are pointed out. The interplay between effects originating from the analyticity requirement and the analytic continuation from the spacelike to the timelike region and those due to the evolution of the heavy-quark mass is addressed, highlighting the differences from the conventional QCD perturbation theory
Free and constrained symplectic integrators for numerical general relativity
International Nuclear Information System (INIS)
Richter, Ronny; Lubich, Christian
2008-01-01
We consider symplectic time integrators in numerical general relativity and discuss both free and constrained evolution schemes. For free evolution of ADM-like equations we propose the use of the Stoermer-Verlet method, a standard symplectic integrator which here is explicit in the computationally expensive curvature terms. For the constrained evolution we give a formulation of the evolution equations that enforces the momentum constraints in a holonomically constrained Hamiltonian system and turns the Hamilton constraint function from a weak to a strong invariant of the system. This formulation permits the use of the constraint-preserving symplectic RATTLE integrator, a constrained version of the Stoermer-Verlet method. The behavior of the methods is illustrated on two effectively (1+1)-dimensional versions of Einstein's equations, which allow us to investigate a perturbed Minkowski problem and the Schwarzschild spacetime. We compare symplectic and non-symplectic integrators for free evolution, showing very different numerical behavior for nearly-conserved quantities in the perturbed Minkowski problem. Further we compare free and constrained evolution, demonstrating in our examples that enforcing the momentum constraints can turn an unstable free evolution into a stable constrained evolution. This is demonstrated in the stabilization of a perturbed Minkowski problem with Dirac gauge, and in the suppression of the propagation of boundary instabilities into the interior of the domain in Schwarzschild spacetime
Space-Time Diffeomorphisms in Noncommutative Gauge Theories
Directory of Open Access Journals (Sweden)
L. Román Juarez
2008-07-01
Full Text Available In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007, 10367–10382] we have shown how for canonical parametrized field theories, where space-time is placed on the same footing as the other fields in the theory, the representation of space-time diffeomorphisms provides a very convenient scheme for analyzing the induced twisted deformation of these diffeomorphisms, as a result of the space-time noncommutativity. However, for gauge field theories (and of course also for canonical geometrodynamics where the Poisson brackets of the constraints explicitely depend on the embedding variables, this Poisson algebra cannot be connected directly with a representation of the complete Lie algebra of space-time diffeomorphisms, because not all the field variables turn out to have a dynamical character [Isham C.J., Kuchar K.V., Ann. Physics 164 (1985, 288–315, 316–333]. Nonetheless, such an homomorphic mapping can be recuperated by first modifying the original action and then adding additional constraints in the formalism in order to retrieve the original theory, as shown by Kuchar and Stone for the case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical Quantum Gravity 4 (1987, 319–328]. Making use of a combination of all of these ideas, we are therefore able to apply our canonical reparametrization approach in order to derive the deformed Lie algebra of the noncommutative space-time diffeomorphisms as well as to consider how gauge transformations act on the twisted algebras of gauge and particle fields. Thus, hopefully, adding clarification on some outstanding issues in the literature concerning the symmetries for gauge theories in noncommutative space-times.
Spacetimes foliated by Killing horizons
International Nuclear Information System (INIS)
Pawlowski, Tomasz; Lewandowski, Jerzy; Jezierski, Jacek
2004-01-01
It seems to be expected that a horizon of a quasi-local type, such as a Killing or an isolated horizon, by analogy with a globally defined event horizon, should be unique in some open neighbourhood in the spacetime, provided the vacuum Einstein or the Einstein-Maxwell equations are satisfied. The aim of our paper is to verify whether that intuition is correct. If one can extend a so-called Kundt metric, in such a way that its null, shear-free surfaces have spherical spacetime sections, the resulting spacetime is foliated by so-called non-expanding horizons. The obstacle is Kundt's constraint induced at the surfaces by the Einstein or the Einstein-Maxwell equations, and the requirement that a solution be globally defined on the sphere. We derived a transformation (reflection) that creates a solution to Kundt's constraint out of data defining an extremal isolated horizon. Using that transformation, we derived a class of exact solutions to the Einstein or Einstein-Maxwell equations of very special properties. Each spacetime we construct is foliated by a family of the Killing horizons. Moreover, it admits another, transversal Killing horizon. The intrinsic and extrinsic geometries of the transversal Killing horizon coincide with the one defined on the event horizon of the extremal Kerr-Newman solution. However, the Killing horizon in our example admits yet another Killing vector tangent to and null at it. The geometries of the leaves are given by the reflection
Energy Technology Data Exchange (ETDEWEB)
Kirchbach, M. [Instituto de Fisica, UASLP, San Luis Potosi (Mexico); Compean, C.B. [Instituto Tecnologico de San Luis Potosi, Soledad de Graciano Sanchez (Mexico)
2017-04-15
In the article under discussion the analysis of the spectra of the unflavored mesons lead us to some intriguing insights into the possible geometry of space-time outside the causal Minkowski light cone and into the nature of strong interactions. In applying the potential theory concept of geometrization of interactions, we showed that the meson masses are best described by a confining potential composed by the centrifugal barrier on the three-dimensional spherical space, S{sup 3}, and of a charge-dipole potential constructed from the Green function to the S{sup 3} Laplacian. The dipole potential emerged in view of the fact that S{sup 3} does not support single-charges without violation of the Gauss theorem and the superposition principle, thus providing a natural stage for the description of the general phenomenon of confined charge-neutral systems. However, in the original article we did not relate the charge-dipoles on S{sup 3} to the color neutral mesons, and did not express the magnitude of the confining dipole potential in terms of the strong coupling α{sub S} and the number of colors, N{sub c}, the subject of the addendum. To the amount S{sup 3} can be thought of as the unique closed space-like geodesic of a four-dimensional de Sitter space-time, dS{sub 4}, we hypothesized the space-like region outside the causal Einsteinian light cone (it describes virtual processes, among them interactions) as the (1+4)-dimensional subspace of the conformal (2+4) space-time, foliated with dS{sub 4} special relativity for strong interaction processes. The potential designed in this way predicted meson spectra of conformal degeneracy patterns, and in accord with the experimental observations. We now extract the α{sub s} values in the infrared from data on meson masses. The results obtained are compatible with the α{sub s} estimates provided by other approaches. (orig.)
Spinor Field Nonlinearity and Space-Time Geometry
Saha, Bijan
2018-03-01
Within the scope of Bianchi type VI,VI0,V, III, I, LRSBI and FRW cosmological models we have studied the role of nonlinear spinor field on the evolution of the Universe and the spinor field itself. It was found that due to the presence of non-trivial non-diagonal components of the energy-momentum tensor of the spinor field in the anisotropic space-time, there occur some severe restrictions both on the metric functions and on the components of the spinor field. In this report we have considered a polynomial nonlinearity which is a function of invariants constructed from the bilinear spinor forms. It is found that in case of a Bianchi type-VI space-time, depending of the sign of self-coupling constants, the model allows either late time acceleration or oscillatory mode of evolution. In case of a Bianchi VI 0 type space-time due to the specific behavior of the spinor field we have two different scenarios. In one case the invariants constructed from bilinear spinor forms become trivial, thus giving rise to a massless and linear spinor field Lagrangian. This case is equivalent to the vacuum solution of the Bianchi VI 0 type space-time. The second case allows non-vanishing massive and nonlinear terms and depending on the sign of coupling constants gives rise to accelerating mode of expansion or the one that after obtaining some maximum value contracts and ends in big crunch, consequently generating space-time singularity. In case of a Bianchi type-V model there occur two possibilities. In one case we found that the metric functions are similar to each other. In this case the Universe expands with acceleration if the self-coupling constant is taken to be a positive one, whereas a negative coupling constant gives rise to a cyclic or periodic solution. In the second case the spinor mass and the spinor field nonlinearity vanish and the Universe expands linearly in time. In case of a Bianchi type-III model the space-time remains locally rotationally symmetric all the time
Galilean generalized Robertson-Walker spacetimes: A new family of Galilean geometrical models
de la Fuente, Daniel; Rubio, Rafael M.
2018-02-01
We introduce a new family of Galilean spacetimes, the Galilean generalized Robertson-Walker spacetimes. This new family is relevant in the context of a generalized Newton-Cartan theory. We study its geometrical structure and analyse the completeness of its inextensible free falling observers. This sort of spacetimes constitutes the local geometric model of a much wider family of spacetimes admitting certain conformal symmetry. Moreover, we find some sufficient geometric conditions which guarantee a global splitting of a Galilean spacetime as a Galilean generalized Robertson-Walker spacetime.
The signature triality of Majorana-Weyl spacetimes
International Nuclear Information System (INIS)
Andrade, M.A. de; Rojas, M.; Toppan, F.
2000-05-01
The Higher dimensional Majorana-Weyl spacetimes present space-time dualities which are induced by the Spin (8) triality automorphisms. Different signature versions of theories such as 10-dimensional SYM's superstrings, five-branes, F-theory, are shown to be interconnected via the S 3 permutation group. Bilinear and trilinear invariants under spacetime triality are introduced and their possible relevance in building models possessing a space-versus-time exchange symmetry is discussed. Moreover the Cartan's vector/chiral spinor/antichiral spinor triality of SO (8) and SO(4,4) is analyzed in detail and explicit formulas are produced in a Majorana-Weyl basis. This paper is the extended version of hep-th/9907148. (author)
Null Geodesic Congruences, Asymptotically-Flat Spacetimes and Their Physical Interpretation
Directory of Open Access Journals (Sweden)
Timothy M. Adamo
2009-09-01
Full Text Available A priori, there is nothing very special about shear-free or asymptotically shear-free null geodesic congruences. Surprisingly, however, they turn out to possess a large number of fascinating geometric properties and to be closely related, in the context of general relativity, to a variety of physically significant effects. It is the purpose of this paper to try to fully develop these issues. This work starts with a detailed exposition of the theory of shear-free and asymptotically shear-free null geodesic congruences, i.e., congruences with shear that vanishes at future conformal null infinity. A major portion of the exposition lies in the analysis of the space of regular shear-free and asymptotically shear-free null geodesic congruences. This analysis leads to the space of complex analytic curves in complex Minkowski space. They in turn play a dominant role in the applications. The applications center around the problem of extracting interior physical properties of an asymptotically-flat spacetime directly from the asymptotic gravitational (and Maxwell field itself, in analogy with the determination of total charge by an integral over the Maxwell field at infinity or the identification of the interior mass (and its loss by (Bondi’s integrals of the Weyl tensor, also at infinity. More specifically, we will see that the asymptotically shear-free congruences lead us to an asymptotic definition of the center-of-mass and its equations of motion. This includes a kinematic meaning, in terms of the center-of-mass motion, for the Bondi three-momentum. In addition, we obtain insights into intrinsic spin and, in general, angular momentum, including an angular-momentum–conservation law with well-defined flux terms. When a Maxwell field is present, the asymptotically shear-free congruences allow us to determine/define at infinity a center-of-charge world line and intrinsic magnetic dipole moment.
Conformal mechanics in Newton-Hooke spacetime
International Nuclear Information System (INIS)
Galajinsky, Anton
2010-01-01
Conformal many-body mechanics in Newton-Hooke spacetime is studied within the framework of the Lagrangian formalism. Global symmetries and Noether charges are given in a form convenient for analyzing the flat space limit. N=2 superconformal extension is built and a new class on N=2 models related to simple Lie algebras is presented. A decoupling similarity transformation on N=2 quantum mechanics in Newton-Hooke spacetime is discussed.
GRPIC modeling of jets from accretion disks
International Nuclear Information System (INIS)
Watson, M.
2008-01-01
An algorithm is presented that incorporates the tensor form of Maxwell's equations in an electromagnetic particle-in-cell algorithm. The code simplifies to Schwarzschild space-time for the absence of a spinning central mass and to Minkowski space-time if no central mass is present. The current density is calculated using the curved space-time of the metric. The algorithm described here is part of a core software engine developed for plasma simulation in an environment around a spinning central mass. The versatility of the algorithm allows for calculations without spin. Because the algorithm uses a general metric explicitly for the description of the space-time, this algorithm can be used as a general relativistic particle-in-cell (GRPIC) code. We have studied the particle dynamics within the negative energy region of the ergosphere. (author)
Quantum Dynamics of Test Particle in Curved Space-Time
International Nuclear Information System (INIS)
Piechocki, W.
2002-01-01
To reveal the nature of space-time singularities of removable type we examine classical and quantum dynamics of a free particle in the Sitter type spacetimes. Consider space-times have different topologies otherwise are isometric. Our systems are integrable and we present analytic solutions of the classical dynamics. We quantize the systems by making use of the group theoretical method: we find an essentially self-adjoint representation of the algebra of observables integrable to the irreducible unitarity representation of the symmetry group of each consider gravitational system. The massless particle dynamics is obtained in the zero-mass limit of the massive case. Global properties of considered gravitational systems are of primary importance for the quantization procedure. Systems of a particle in space-times with removable singularities appear to be quantizable. We give specific proposal for extension of our analysis to space-times with essential type singularities. (author)
On the Gauss Map of Surfaces of Revolution with Lightlike Axis in Minkowski 3-Space
Directory of Open Access Journals (Sweden)
Minghao Jin
2013-01-01
Full Text Available By studying the Gauss map G and Laplace operator Δh of the second fundamental form h, we will classify surfaces of revolution with a lightlike axis in 3-dimensional Minkowski space and also obtain the surface of Enneper of the 2nd kind, the surface of Enneper of the 3rd kind, the de Sitter pseudosphere, and the hyperbolic pseudosphere that satisfy condition ΔhG=ΛG, Λ being a 3×3 real matrix.
Investigation of a Complex Space-Time Metric to Describe Precognition of the Future
Rauscher, Elizabeth A.; Targ, Russell
2006-10-01
For more than 100 years scientists have attempted to determine the truth or falsity of claims that some people are able to describe and experience events or information blocked from ordinary perception. For the past 25 years, the authors of this paper - together with researchers in laboratories around the world — have carried out experiments in remote viewing. The evidence for this mode of perception, or direct knowing of distant events and objects, has convinced us of the validity of these claims. It has been widely observed that the accuracy and reliability of this sensory awareness does not diminish with either electromagnetic shielding, nor with increases in temporal or spatial separation between the percipient and the target to be described. Modern physics describes such a time-and-space independent connection between percipient and target as nonlocal. In this paper we present a geometrical model of space-time, which has already been extensively studied in the technical literature of mathematics and physics. This eight-dimensional metric is known as "complex Minkowski space," and has been shown to be consistent with our present understanding of the equations of Newton, Maxwell, Einstein, and Schrödinger. It also has the interesting property of allowing a connection of zero distance between points in the complex manifold, which appear to be separate from one another in ordinary observation. We propose a model that describes the major elements of experimental parapsychology, and at the same time is consistent with the present highly successful structure of modern physics.
Spontaneous CP violation from a quaternionic Kaluza-Klein theory
International Nuclear Information System (INIS)
Hanlon, B.E.; Joshi, G.C.
1991-01-01
Motivated by the isomorphism between the universal covering group of the six dimensional Lorentz group and the special linear group over the quaternions, a locally quaternionic covariant quantum mechanics is postulated to exist in six space-time dimensions. Compactifying onto the space-time M 4 x S 2 complex theory is retrieved on the four dimensional Minkowski space with the essential quaternionic nature confined to S 2 . Quaternionic spinors are introduced and a dimensionally reduced theory recovered which exhibits a CP violating effect via spontaneous symmetry breaking. 20 refs
A spin-4 analog of 3D massive gravity
Bergshoeff, Eric A.; Kovacevic, Marija; Rosseel, Jan; Townsend, Paul K.; Yin, Yihao
2011-01-01
A sixth-order, but ghost-free, gauge-invariant action is found for a fourth-rank symmetric tensor potential in a three-dimensional (3D) Minkowski spacetime. It propagates two massive modes of spin 4 that are interchanged by parity and is thus a spin-4 analog of linearized 'new massive gravity'. Also
On the Robinson theorem and shearfree geodesic null congruences
International Nuclear Information System (INIS)
Tafel, J.
1985-01-01
Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions. (orig.)
Relativity theory (a bibliography with abstracts). Report for 1970--1976
International Nuclear Information System (INIS)
Grooms, D.W.
1976-03-01
Research studies are presented on special and general relativity. Gravitational theory, field theory, and space--time studies are included as are studies involving the Minkowski space, the Schrodinger equations, the Dirac equations, and the Lorentz transformations. (This updated bibliography contains 136 abstracts, 4 of which are new entries to the previous edition.)
Is physical space unique or optional
International Nuclear Information System (INIS)
Ekstein, H.; Centre National de la Recherche Scientifique, 13 - Marseille
1975-02-01
There are two concepts of the physical space-time. One, S(F), is that of a fixed arena in which events take place. The other S(D), is that of a space-time shaped by events. The second depends on the state (initial conditions) or on the external field, the first does not. The main assertions of the present paper are: 1) the fixed space-time S(F) is neither incompatibles with nor made superfluous, by Einstein's theory. S(F) is experimentally explorable, unique, and probably identical with Minkowski space M. 2) The dynamical space S(D) is largely optional. It can be chosen to be M, but the natural choice is Einstein's pseudo-Riemanian manifold [fr
International Nuclear Information System (INIS)
Namsrai, K.
1988-01-01
The review presents systematically the results of studies which develop an idea of quantum properties of space-time in the microworld or near exotic objects (black holes, magnetic monopoles and others). On the basis of this idea motion equations of nonrelativistic and relativistic particles are studied. It is shown that introducing concept of quantum space-time at small distances (or near superdense matter) leads to an additional force giving rise to appearance of spiral-like behaviour of a particle along its classical trajectory. Given method is generalized to nonrelativistic quantum mechanics and to motion of a particle in gravitational force. In the latter case, there appears to be an antigravitational effect in the motion of a particle leading to different value of free-fall time (at least for gravitational force of exotic objects) for particles with different masses. Gravitational consequences of quantum space-time and tensor structures of physical quantities are investigated in detail. From experimental data on testing relativity and anisotropy of inertia estimation L ≤ 10 -22 cm on the value of the fundamental length is obtained. (author)
Quantum space-times in the year 2002
Indian Academy of Sciences (India)
These ideas of space-time are suggested from developments in fuzzy physics, string theory, and deformation quantization. The review focuses on the ideas coming from fuzzy physics. We ﬁnd models of quantum space-time like fuzzy 4 on which states cannot be localized, but which ﬂuctuate into other manifolds like CP3.
Space-time design of the public city
Thomaier, Susanne; Könecke, Benjamin; Zedda, Roberto; Stabilini, Stefano
2013-01-01
Time has become an increasingly important topic in urban studies and urban planning. The spatial-temporal interplay is not only of relevance for the theory of urban development and urban politics, but also for urban planning and governance. The space-time approach focuses on the human being with its various habits and routines in the city. Understanding and taking those habits into account in urban planning and public policies offers a new way to improve the quality of life in our cities. Adapting the supply and accessibility of public spaces and services to the inhabitants’ space-time needs calls for an integrated approach to the physical design of urban space and to the organization of cities. In the last two decades the body of practical and theoretical work on urban space-time topics has grown substantially. The book offers a state of the art overview of the theoretical reasoning, the development of new analytical tools, and practical experience of the space-time design of public cities in major Europea...
Some spacetimes with higher rank Killing-Staeckel tensors
International Nuclear Information System (INIS)
Gibbons, G.W.; Houri, T.; Kubiznak, D.; Warnick, C.M.
2011-01-01
By applying the lightlike Eisenhart lift to several known examples of low-dimensional integrable systems admitting integrals of motion of higher-order in momenta, we obtain four- and higher-dimensional Lorentzian spacetimes with irreducible higher-rank Killing tensors. Such metrics, we believe, are first examples of spacetimes admitting higher-rank Killing tensors. Included in our examples is a four-dimensional supersymmetric pp-wave spacetime, whose geodesic flow is superintegrable. The Killing tensors satisfy a non-trivial Poisson-Schouten-Nijenhuis algebra. We discuss the extension to the quantum regime.
Conserved quantities for stationary Einstein-Maxwell space-times
International Nuclear Information System (INIS)
Esposito, F.P.; Witten, L.
1978-01-01
It is shown that every stationary Einstein-Maxwell space-time has eight divergence-free vector fields and these are isolated in general form. The vector fields and associated conserved quantities are calculated for several families of space-times. (Auth.)
International Nuclear Information System (INIS)
Urano, Miho; Tomimatsu, Akira; Saida, Hiromi
2009-01-01
The mechanical first law (MFL) of black hole spacetimes is a geometrical relation which relates variations of the mass parameter and horizon area. While it is well known that the MFL of an asymptotic flat black hole is equivalent to its thermodynamical first law, however we do not know the detail of the MFL of black hole spacetimes with a cosmological constant which possess a black hole and cosmological event horizons. This paper aims to formulate an MFL of the two-horizon spacetimes. For this purpose, we try to include the effects of two horizons in the MFL. To do so, we make use of the Iyer-Wald formalism and extend it to regard the mass parameter and the cosmological constant as two independent variables which make it possible to treat the two horizons on the same footing. Our extended Iyer-Wald formalism preserves the existence of the conserved Noether current and its associated Noether charge, and gives an abstract form of the MFL of black hole spacetimes with a cosmological constant. Then, as a representative application of this formalism, we derive the MFL of the Schwarzschild-de Sitter (SdS) spacetime. Our MFL of the SdS spacetime relates the variations of three quantities: the mass parameter, the total area of the two horizons and the volume enclosed by the two horizons. If our MFL is regarded as a thermodynamical first law of the SdS spacetime, it offers a thermodynamically consistent description of the SdS black hole evaporation process: the mass decreases while the volume and the entropy increase. In our suggestion, a generalized second law is not needed to ensure the second law of SdS thermodynamics for its evaporation process.
The memory effect for particle scattering in even spacetime dimensions
Garfinkle, David; Hollands, Stefan; Ishibashi, Akihiro; Tolish, Alexander; Wald, Robert M.
2017-07-01
We explicitly calculate the gravitational wave memory effect for classical point particle sources in linearized gravity off an even dimensional Minkowski background. We show that there is no memory effect in d > 4 dimensions, in agreement with the general analysis of Hollands et al (2016 arXiv:1612.03290).
Feynman propagator and space-time transformation technique
International Nuclear Information System (INIS)
Nassar, A.B.
1987-01-01
We evaluate the exact propagator for the time-dependent two-dimensional charged harmonic oscillator in a time-varying magnetic field, by taking direct recourse to the corresponding Schroedinger equation. Through the usage of an appropriate space-time transformation, we show that such a propagator can be obtained from the free propagator in the new space-time coordinate system. (orig.)
Mechanics and Newton-Cartan-like gravity on the Newton-Hooke space-time
International Nuclear Information System (INIS)
Tian Yu; Guo Hanying; Huang Chaoguang; Xu Zhan; Zhou Bin
2005-01-01
We focus on the dynamical aspects on Newton-Hooke space-time NH + mainly from the viewpoint of geometric contraction of the de Sitter spacetime with Beltrami metric. (The term spacetime is used to denote a space with non-degenerate metric, while the term space-time is used to denote a space with degenerate metric.) We first discuss the Newton-Hooke classical mechanics, especially the continuous medium mechanics, in this framework. Then, we establish a consistent theory of gravity on the Newton-Hooke space-time as a kind of Newton-Cartan-like theory, parallel to the Newton's gravity in the Galilei space-time. Finally, we give the Newton-Hooke invariant Schroedinger equation from the geometric contraction, where we can relate the conservative probability in some sense to the mass density in the Newton-Hooke continuous medium mechanics. Similar consideration may apply to the Newton-Hooke space-time NH - contracted from anti-de Sitter spacetime
Solutions of weakened field equations in Gödel space-time
Directory of Open Access Journals (Sweden)
Aditya Mani Mishra
2019-04-01
Full Text Available We have solved Weakened field equations, collected work of Lovelock for cylindrically symmetric G¨odel type spacetime. A comparative study of these solutions to solution of Einstein’s field equation have shown. Conformality of Gödel spacetime has discussed with vanishing and non-vanishing scalar curvature of the spacetime.
Spinorial space-time and the origin of Quantum Mechanics. The dynamical role of the physical vacuum
International Nuclear Information System (INIS)
Gonzalez-Mestres, Luis
2016-01-01
Is Quantum Mechanics really and ultimate principle of Physics described by a set of intrinsic exact laws? Are standard particles the ultimate constituents of matter? The two questions appear to be closely related, as a preonic structure of the physical vacuum would have an influence on the properties of quantum particles. Although the first preon models were just « quark-like » and assumed preons to be direct constituents of the conventional « elementary » particles, we suggested in 1995 that preons could instead be constituents of the physical vacuum (the superbradyon hypothesis). Standard particles would then be excitations of the preonic vacuum and have substantially different properties from those of preons themselves (critical speed…). The standard laws of Particle Physics would be approximate expressions generated from basic preon dynamics. In parallel, the mathematical properties of space-time structures such as the spinoral space-time (SST) we introduced in 1996-97 can have strong implications for Quantum Mechanics and even be its real origin. We complete here our recent discussion of the subject by pointing out that: i) Quantum Mechanics corresponds to a natural set of properties of vacuum excitations in the presence of a SST geometry ; ii) the recently observed entanglement at long distances would be a logical property if preons are superluminal (superbradyons), so that superluminal signals and correlations can propagate in vacuum ; iii) in a specific description, the function of space-time associated to the extended internal structure of a spin-1/2 particle at very small distances may be incompatible with a continuous motion at space and time scales where the internal structure of vacuum can be felt. In the dynamics associated to iii), and using the SST approach to space-time, a contradiction can appear between macroscopic and microscopic space-times due to an overlap in the time variable directly related to the fact that a spinorial function takes
The inverse spatial Laplacian of spherically symmetric spacetimes
International Nuclear Information System (INIS)
Fernandes, Karan; Lahiri, Amitabha
2017-01-01
We derive the inverse spatial Laplacian for static, spherically symmetric backgrounds by solving Poisson’s equation for a point source. This is different from the electrostatic Green function, which is defined on the four dimensional static spacetime, while the equation we consider is defined on the spatial hypersurface of such spacetimes. This Green function is relevant in the Hamiltonian dynamics of theories defined on spherically symmetric backgrounds, and closed form expressions for the solutions we find are absent in the literature. We derive an expression in terms of elementary functions for the Schwarzschild spacetime, and comment on the relation of this solution with the known Green function of the spacetime Laplacian operator. We also find an expression for the Green function on the static pure de-Sitter space in terms of hypergeometric functions. We conclude with a discussion of the constraints of the electromagnetic field. (paper)
Directory of Open Access Journals (Sweden)
Ronald E. Meyers
2015-03-01
Full Text Available We report on an experimental and theoretical investigation of quantum imaging where the images are stored in both space and time. Ghost images of remote objects are produced with either one or two beams of chaotic laser light generated by a rotating ground glass and two sensors measuring the reference field and bucket field at different space-time points. We further observe that the ghost images translate depending on the time delay between the sensor measurements. The ghost imaging experiments are performed both with and without turbulence. A discussion of the physics of the space-time imaging is presented in terms of quantum nonlocal two-photon analysis to support the experimental results. The theoretical model includes certain phase factors of the rotating ground glass. These experiments demonstrated a means to investigate the time and space aspects of ghost imaging and showed that ghost imaging contains more information per measured photon than was previously recognized where multiple ghost images are stored within the same ghost imaging data sets. This suggests new pathways to explore quantum information stored not only in multi-photon coincidence information but also in time delayed multi-photon interference. The research is applicable to making enhanced space-time quantum images and videos of moving objects where the images are stored in both space and time.
Stress tensor fluctuations in de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Pérez-Nadal, Guillem; Verdaguer, Enric [Departament de Física Fonamental and Institut de Ciències del Cosmos, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain); Roura, Albert, E-mail: guillem@ffn.ub.es, E-mail: albert.roura@aei.mpg.de, E-mail: enric.verdaguer@ub.edu [Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476 Golm (Germany)
2010-05-01
The two-point function of the stress tensor operator of a quantum field in de Sitter spacetime is calculated for an arbitrary number of dimensions. We assume the field to be in the Bunch-Davies vacuum, and formulate our calculation in terms of de Sitter-invariant bitensors. Explicit results for free minimally coupled scalar fields with arbitrary mass are provided. We find long-range stress tensor correlations for sufficiently light fields (with mass m much smaller than the Hubble scale H), namely, the two-point function decays at large separations like an inverse power of the physical distance with an exponent proportional to m{sup 2}/H{sup 2}. In contrast, we show that for the massless case it decays at large separations like the fourth power of the physical distance. There is thus a discontinuity in the massless limit. As a byproduct of our work, we present a novel and simple geometric interpretation of de Sitter-invariant bitensors for pairs of points which cannot be connected by geodesics.
Quantum mechanics in fractional and other anomalous spacetimes
Calcagni, Gianluca; Nardelli, Giuseppe; Scalisi, Marco
2012-01-01
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the wave-functions minimizing the uncertainty are found. In spite of the
Construction of spacetimes from initial data
International Nuclear Information System (INIS)
Isenberg, J.A.
1979-01-01
As relativistic effects become more accessible to physical experiment and observation, it becomes important to be able to theoretically analyze the behavior of relativistic model systems designed to incorporate such measurable effects. This dissertation describes in detail the initial value (IV) procedure for carrying out such analyses (i.e., for ''building spacetimes''). We report progress--of the author as well as others--in all of these areas: (1) The generalized Bergmann-Dirac (BD) procedure can be used to systematically translate any theory into 3+1 form. (2) The York procedure turns the constraints of Einstein's theory into a set of four elliptic equations for four unknowns (with the rest of the initial data ''relatively free''). (3) The maximal and K-foliation schemes appear to give preferred kinematics for the generic spacetimes one might build. We discuss the sense in which these foliations are preferred, and compare them with others. We then show how to find maximal and K-surfaces, both in a given spacetime (e.g. Schwarzschild) and in one being built from scratch. (4) Many physically interesting systems have symmetries which considerably simplify the equations. After discussing how, in general, one can build symmetries into initial data, and how one can use them to simplify the analysis, we look at a particular example symmetry: spacetimes with two space-like translation Killing Vectors. (''2T'')
Quantum space-time and gravitational consequences
International Nuclear Information System (INIS)
Namsrai, K.
1986-01-01
Relativistic particle dynamics and basic physical quantities for the general theory of gravity are reconstructed from a quantum space-time point of view. An additional force caused by quantum space-time appears in the equation of particle motion, giving rise to a reformulation of the equivalence principle up to values of O(L 2 ), where L is the fundamental length. It turns out that quantum space-time leads to quantization of gravity, i.e. the metric tensor g/sub uv/ (/ZETA/) becomes operator-valued and is not commutative at different points x/sup micro/ and y/sup micro/ in usual space-time on a large scale, and its commutator depending on the ''vielbein'' field (gaugelike graviton field) is proportional to L 2 multiplied by a translationinvariant wave function propagated between points x/sup micro/ and y/sup micro/. In the given scheme, there appears to be an antigravitational effect in the motion of a particle in the gravitational force. This effect depends on the value of particle mass; when a particle is heavy its free-fall time is long compared to that for a light-weight particle. The problem of the change of time scale and the anisotropy of inertia are discussed. From experimental data from testing of the latter effect it follows that L ≤ 10 -22 cm
Circular motion and Polish Doughnuts in NUT spacetime
Jefremov, Paul I.
The astrophysical relevance of the NUT spacetime(s) is a matter of debate due to pathological properties exhibited by this solution. However, if it is realised in nature, then we should look for the characteristic imprints of it on possible observations. One of the major sources of data on black hole astrophysics is the accretion process. Using a simple but fully analytical ``Polish Doughnuts'' model of accretion disk one gets both qualitative and quantitative differences from the Kerr spacetime produced by the presence of the gravitomagnetic charge. The present paper is based on our work Jefremov & Perlick (2016).
The causal structure of spacetime is a parameterized Randers geometry
Energy Technology Data Exchange (ETDEWEB)
Skakala, Jozef; Visser, Matt, E-mail: jozef.skakala@msor.vuw.ac.nz, E-mail: matt.visser@msor.vuw.ac.nz [School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, PO Box 600, Wellington (New Zealand)
2011-03-21
There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.
The causal structure of spacetime is a parameterized Randers geometry
International Nuclear Information System (INIS)
Skakala, Jozef; Visser, Matt
2011-01-01
There is a well-established isomorphism between stationary four-dimensional spacetimes and three-dimensional purely spatial Randers geometries-these Randers geometries being a particular case of the more general class of three-dimensional Finsler geometries. We point out that in stably causal spacetimes, by using the (time-dependent) ADM decomposition, this result can be extended to general non-stationary spacetimes-the causal structure (conformal structure) of the full spacetime is completely encoded in a parameterized (t-dependent) class of Randers spaces, which can then be used to define a Fermat principle, and also to reconstruct the null cones and causal structure.
A composite model of the space-time and 'colors'
International Nuclear Information System (INIS)
Terazawa, Hidezumi.
1987-03-01
A pregeometric and pregauge model of the space-time and ''colors'' in which the space-time metric and ''color'' gauge fields are both composite is presented. By the non-triviality of the model, the number of space-time dimensions is restricted to be not larger than the number of ''colors''. The long conjectured space-color correspondence is realized in the model action of the Nambu-Goto type which is invariant under both general-coordinate and local-gauge transformations. (author)
Axiomatics of uniform space-time models
International Nuclear Information System (INIS)
Levichev, A.V.
1983-01-01
The mathematical statement of space-time axiomatics of the special theory of relativity is given; it postulates that the space-time M is the binding single boundary Hausedorf local-compact four-dimensional topological space with the given order. The theorem is proved: if the invariant order in the four-dimensional group M is given by the semi-group P, which contingency K contains inner points , then M is commutative. The analogous theorem is correct for the group of two and three dimensionalities
A Minkowski Fractal Circularly Polarized Antenna for RFID Reader
Directory of Open Access Journals (Sweden)
Yanzhong Yu
2014-11-01
Full Text Available A design of fractal-like antenna with circular polarization for radio frequency identification (RFID reader applications is presented in this article. The modified Minkowski fractal structure is adopted as radiating patch for size reduction and broadband operation. A corner-truncated technology and a slot-opened method are employed to realize circular polarization and improve the gain of the proposed antenna, respectively. The proposed antenna is analyzed and optimized by HFSS. Return loss and maximum gain of the optimized antenna achieve to -22.2 dB and 1.12 dB at 920 MHz, respectively. The optimized design has an axial ratio (AR of 1.2 dB at central frequency of 920 MHz and impedance bandwidth (S11<=-10 dB of 40 MHz (4.3 %. Its input impedance is (57.9-j2.6 W that is close to input impedance of coaxial line (50 W. Numerical results demonstrate that the optimized antenna exhibits acceptable performances and may satisfy requirements of RFID reader applications.
Tensor Minkowski Functionals: first application to the CMB
Energy Technology Data Exchange (ETDEWEB)
Ganesan, Vidhya [Indian Institute of Astrophysics, Koramangala II Block, Bangalore 560 034 (India); Chingangbam, Pravabati, E-mail: vidhya@iiap.res.in, E-mail: prava@iiap.res.in [Indian Institute of Science, C.V. Raman Ave, Bangalore 560 012 (India)
2017-06-01
Tensor Minkowski Functionals (TMFs) are tensor generalizations of the usual Minkowski Functionals which are scalar quantities. We introduce them here for use in cosmological analysis, in particular to analyze the Cosmic Microwave Background (CMB) radiation. They encapsulate information about the shapes of structures and the orientation of distributions of structures. We focus on one of the TMFs, namely W {sub 2}{sup 1,1}, which is the (1,1) rank tensor generalization of the genus. The ratio of the eigenvalues of the average of W {sub 2}{sup 1,1} over all structures, α, encodes the net orientation of the structures; and the average of the ratios of the eigenvalues of W {sub 2}{sup 1,1} for each structure, β, encodes the net intrinsic anisotropy of the structures. We have developed a code that computes W {sub 2}{sup 1,1}, and from it α and β, for a set of structures on the 2-dimensional Euclidean plane. We use it to compute α and β as functions of chosen threshold levels for simulated Gaussian and isotropic CMB temperature and E mode fields. We obtain the value of α to be one for both temperature and E mode, which means that we recover the statistical isotropy of density fluctuations that we input in the simulations. We find that the standard ΛCDM model predicts a charateristic shape of β for temperature and E mode as a function of the threshold, and the average over thresholds is β∼ 0.62 for temperature and β∼ 0.63 for E mode. Accurate measurements of α and β can be used to test the standard model of cosmology and to search for deviations from it. For this purpose we compute α and β for temperature and E mode data of various data sets from PLANCK mission. We compare the values measured from observed data with those obtained from simulations to which instrument beam and noise characteristics of the 44GHz frequency channel have been added (which are provided as part of the PLANCK data release). We find very good agreement of β and α between all
Thermal dimension of quantum spacetime
Energy Technology Data Exchange (ETDEWEB)
Amelino-Camelia, Giovanni, E-mail: amelino@roma1.infn.it [Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy); Brighenti, Francesco [Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom); Dipartimento di Fisica e Astronomia dell' Università di Bologna and Sez. Bologna INFN, Via Irnerio 46, 40126 Bologna (Italy); Gubitosi, Giulia [Theoretical Physics, Blackett Laboratory, Imperial College, London, SW7 2BZ (United Kingdom); Santos, Grasiele [Dipartimento di Fisica, Università “La Sapienza” and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)
2017-04-10
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular for various scenarios of “dynamical dimensional reduction” which have been discussed in the literature. We are here concerned with the fact that the related research effort has been based mostly on analyses of the “spectral dimension”, which involves an unphysical Euclideanization of spacetime and is highly sensitive to the off-shell properties of a theory. As here shown, different formulations of the same physical theory can have wildly different spectral dimension. We propose that dynamical dimensional reduction should be described in terms of the “thermal dimension” which we here introduce, a notion that only depends on the physical content of the theory. We analyze a few models with dynamical reduction both of the spectral dimension and of our thermal dimension, finding in particular some cases where thermal and spectral dimension agree, but also some cases where the spectral dimension has puzzling properties while the thermal dimension gives a different and meaningful picture.
Temporal and spatial foliations of spacetimes.
Herold, H.
For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.
Tension perturbations of black brane spacetimes
International Nuclear Information System (INIS)
Traschen, Jennie; Fox, Daniel
2004-01-01
We consider black brane spacetimes that have at least one spatial translation Killing field that is tangent to the brane. A new parameter, the tension of a spacetime, is defined. The tension parameter is associated with spatial translations in much the same way that the ADM mass is associated with the time translation Killing field. In this work, we explore the implications of the spatial translation symmetry for small perturbations around a background black brane. For static-charged black branes we derive a law which relates the tension perturbation to the surface gravity times the change in the horizon area, plus terms that involve variations in the charges and currents. We find that as a black brane evaporates the tension decreases. We also give a simple derivation of a first law for black brane spacetimes. These constructions hold when the background stress-energy is governed by a Hamiltonian, and the results include arbitrary perturbative stress-energy sources
Translational spacetime symmetries in gravitational theories
International Nuclear Information System (INIS)
Petti, R J
2006-01-01
How to include spacetime translations in fibre bundle gauge theories has been a subject of controversy, because spacetime symmetries are not internal symmetries of the bundle structure group. The standard method for including affine symmetry in differential geometry is to define a Cartan connection on an affine bundle over spacetime. This is equivalent to (1) defining an affine connection on the affine bundle, (2) defining a zero section on the associated affine vector bundle and (3) using the affine connection and the zero section to define an 'associated solder form', whose lift to a tensorial form on the frame bundle becomes the solder form. The zero section reduces the affine bundle to a linear bundle and splits the affine connection into translational and homogeneous parts; however, it violates translational equivariance/gauge symmetry. This is the natural geometric framework for Einstein-Cartan theory as an affine theory of gravitation. The last section discusses some alternative approaches that claim to preserve translational gauge symmetry
The manifold model for space-time
International Nuclear Information System (INIS)
Heller, M.
1981-01-01
Physical processes happen on a space-time arena. It turns out that all contemporary macroscopic physical theories presuppose a common mathematical model for this arena, the so-called manifold model of space-time. The first part of study is an heuristic introduction to the concept of a smooth manifold, starting with the intuitively more clear concepts of a curve and a surface in the Euclidean space. In the second part the definitions of the Csub(infinity) manifold and of certain structures, which arise in a natural way from the manifold concept, are given. The role of the enveloping Euclidean space (i.e. of the Euclidean space appearing in the manifold definition) in these definitions is stressed. The Euclidean character of the enveloping space induces to the manifold local Euclidean (topological and differential) properties. A suggestion is made that replacing the enveloping Euclidean space by a discrete non-Euclidean space would be a correct way towards the quantization of space-time. (author)
Translational spacetime symmetries in gravitational theories
Energy Technology Data Exchange (ETDEWEB)
Petti, R J [MathWorks, Inc., 3 Apple Hill Drive, Natick, MA 01760 (United States)
2006-02-07
How to include spacetime translations in fibre bundle gauge theories has been a subject of controversy, because spacetime symmetries are not internal symmetries of the bundle structure group. The standard method for including affine symmetry in differential geometry is to define a Cartan connection on an affine bundle over spacetime. This is equivalent to (1) defining an affine connection on the affine bundle, (2) defining a zero section on the associated affine vector bundle and (3) using the affine connection and the zero section to define an 'associated solder form', whose lift to a tensorial form on the frame bundle becomes the solder form. The zero section reduces the affine bundle to a linear bundle and splits the affine connection into translational and homogeneous parts; however, it violates translational equivariance/gauge symmetry. This is the natural geometric framework for Einstein-Cartan theory as an affine theory of gravitation. The last section discusses some alternative approaches that claim to preserve translational gauge symmetry.
International Nuclear Information System (INIS)
Manoukian, E.B.
1986-01-01
Generalized conditions (rules) are set up for the existence of the distributional zero-mass limit of renormalized Feynman amplitudes in Minkowski space. These rules are generalizations of rules that have been set up earlier by us and hence are applicable to a larger class of graphs. The study is very general as the vanishing masses are led to vanish at different rates. All subtractions of renormalization are carried out directly in momentum space, about the origin, with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram
Pitts, J. Brian
2016-02-01
What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is algebraic in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities-indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz
The Chevreton tensor and Einstein-Maxwell spacetimes conformal to Einstein spaces
International Nuclear Information System (INIS)
Bergqvist, Goeran; Eriksson, Ingemar
2007-01-01
In this paper, we characterize the source-free Einstein-Maxwell spacetimes which have a trace-free Chevreton tensor. We show that this is equivalent to the Chevreton tensor being of pure radiation type and that it restricts the spacetimes to Petrov type N or O. We prove that the trace of the Chevreton tensor is related to the Bach tensor and use this to find all Einstein-Maxwell spacetimes with a zero cosmological constant that have a vanishing Bach tensor. Among these spacetimes we then look for those which are conformal to Einstein spaces. We find that the electromagnetic field and the Weyl tensor must be aligned, and in the case that the electromagnetic field is null, the spacetime must be conformally Ricci-flat and all such solutions are known. In the non-null case, since the general solution is not known on a closed form, we settle by giving the integrability conditions in the general case, but we do give new explicit examples of Einstein-Maxwell spacetimes that are conformal to Einstein spaces, and we also find examples where the vanishing of the Bach tensor does not imply that the spacetime is conformal to a C-space. The non-aligned Einstein-Maxwell spacetimes with vanishing Bach tensor are conformally C-spaces, but none of them are conformal to Einstein spaces
Quantum field theory in curved space-time
Energy Technology Data Exchange (ETDEWEB)
Davies, P C.W. [King' s Coll., London (UK)
1976-09-30
It is stated that recent theoretical developments indicate that the presence of gravity (curved space-time) can give rise to important new quantum effects, such as cosmological particle production and black-hole evaporation. These processes suggest intriguing new relations between quantum theory, thermodynamics and space-time structure and encourage the hope that a better understanding of a full quantum theory of gravity may emerge from this approach.
Approaching space-time through velocity in doubly special relativity
International Nuclear Information System (INIS)
Aloisio, R.; Galante, A.; Grillo, A.F.; Luzio, E.; Mendez, F.
2004-01-01
We discuss the definition of velocity as dE/d vertical bar p vertical bar, where E, p are the energy and momentum of a particle, in doubly special relativity (DSR). If this definition matches dx/dt appropriate for the space-time sector, then space-time can in principle be built consistently with the existence of an invariant length scale. We show that, within different possible velocity definitions, a space-time compatible with momentum-space DSR principles cannot be derived
Ghost neutrinos as test fields in curved space-time
International Nuclear Information System (INIS)
Audretsch, J.
1976-01-01
Without restricting to empty space-times, it is shown that ghost neutrinos (their energy-momentum tensor vanishes) can only be found in algebraically special space-times with a neutrino flux vector parallel to one of the principal null vectors of the conformal tensor. The optical properties are studied. There are no ghost neutrinos in the Kerr-Newman and in spherically symmetric space-times. The example of a non-vacuum gravitational pp-wave accompanied by a ghost neutrino pp-wave is discussed. (Auth.)
The Minkowski and conformal superspaces the classical and quantum descriptions
Fioresi, Rita
2015-01-01
This book is aimed at graduate students and researchers in physics and mathematics who seek to understand the basics of supersymmetry from a mathematical point of view. It provides a bridge between the physical and mathematical approaches to the superworld. The physicist who is devoted to learning the basics of supergeometry can find a friendly approach here, since only the concepts that are strictly necessary are introduced. On the other hand, the mathematician who wants to learn from physics will find that all the mathematical assumptions are firmly rooted in physical concepts. This may open up a channel of communication between the two communities working on different aspects of supersymmetry. Starting from special relativity and Minkowski space, the idea of conformal space and superspace is built step by step in a mathematically rigorous way, and always connecting with the ideas and notation used in physics. While the book is mainly devoted to these important physical examples of superspaces, it can also ...
Geometric extension through Schwarzschild r = 0
International Nuclear Information System (INIS)
Lynden-Bell, D.; Katz, J.; Hebrew Univ., Jerusalem
1990-01-01
Singularities in space-time are not necessarily cancers in the manifold but can herald interesting topological change in the space-time at places where there are several different tangent Minkowski spaces. Most discussions of gravitational collapse cease when space-time becomes singular. In the 'hour-glass' universe we have an example where the singularity develops in empty space; here we give a geometrical extension through the singularity in which geodesics that enter it emerge into a new space. The result extends Schwarzschild space and is periodic in 'extended' Penrose coordinates. There is a topological singularity but no mass at r = 0. The extension is mildly nonanalytic but unique. It is based on the concept that time does not stop and that empty space-times which develop singularities must still have zero Ricci tensors even where the Riemann tensor becomes infinite. (author)
On the architecture of spacetime geometry
International Nuclear Information System (INIS)
Bianchi, Eugenio; Myers, Robert C
2014-01-01
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein–Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity, the AdS/CFT correspondence and loop quantum gravity, as well as Jacobson's ‘thermodynamic’ perspective of gravity. (paper)
Entropy in Spacetime and Topological Hair
Hyun, Young-Hwan; Kim, Yoonbai
2018-01-01
Global topological soliton of the hedgehog ansatz is added to de Sitter spacetime in arbitrary dimensions larger than three, and then thermodynamic law is checked at the cosmological horizon. All geometric and thermodynamic quantities are varied in the presence of a long-range interacting matter distribution with negative pressure, however the entropy-area relation is satisfied in the exact form. Its geometry involves deficit solid angle but maintains a single horizon which allows unique temperature normalization, different from the case of Schwarzschild-de Sitter spacetime.
FLRW cosmology in Weyl-integrable space-time
Energy Technology Data Exchange (ETDEWEB)
Gannouji, Radouane [Department of Physics, Faculty of Science, Tokyo University of Science, 1–3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan); Nandan, Hemwati [Department of Physics, Gurukula Kangri Vishwavidayalaya, Haridwar 249404 (India); Dadhich, Naresh, E-mail: gannouji@rs.kagu.tus.ac.jp, E-mail: hntheory@yahoo.co.in, E-mail: nkd@iucaa.ernet.in [IUCAA, Post Bag 4, Ganeshkhind, Pune 411 007 (India)
2011-11-01
We investigate the Weyl space-time extension of general relativity (GR) for studying the FLRW cosmology through focusing and defocusing of the geodesic congruences. We have derived the equations of evolution for expansion, shear and rotation in the Weyl space-time. In particular, we consider the Starobinsky modification, f(R) = R+βR{sup 2}−2Λ, of gravity in the Einstein-Palatini formalism, which turns out to reduce to the Weyl integrable space-time (WIST) with the Weyl vector being a gradient. The modified Raychaudhuri equation takes the form of the Hill-type equation which is then analysed to study the formation of the caustics. In this model, it is possible to have a Big Bang singularity free cyclic Universe but unfortunately the periodicity turns out to be extremely short.
Presheaves of Superselection Structures in Curved Spacetimes
Vasselli, Ezio
2015-04-01
We show that superselection structures on curved spacetimes that are expected to describe quantum charges affected by the underlying geometry are categories of sections of presheaves of symmetric tensor categories. When an embedding functor is given, the superselection structure is a Tannaka-type dual of a locally constant group bundle, which hence becomes a natural candidate for the role of the gauge group. Indeed, we show that any locally constant group bundle (with suitable structure group) acts on a net of C* algebras fulfilling normal commutation relations on an arbitrary spacetime. We also give examples of gerbes of C* algebras, defined by Wightman fields and constructed using projective representations of the fundamental group of the spacetime, which we propose as solutions for the problem that existence and uniqueness of the embedding functor are not guaranteed.
Diamond's temperature: Unruh effect for bounded trajectories and thermal time hypothesis
International Nuclear Information System (INIS)
Martinetti, Pierre; Rovelli, Carlo
2003-01-01
We study the Unruh effect for an observer with a finite lifetime, using the thermal time hypothesis. The thermal time hypothesis maintains that: (i) time is the physical quantity determined by the flow defined by a state over an observable algebra and (ii) when this flow is proportional to a geometric flow in spacetime, the temperature is the ratio between flow parameter and proper time. An eternal accelerated Unruh observer has access to the local algebra associated with a Rindler wedge. The flow defined by the Minkowski vacuum of a field theory over this algebra is proportional to a flow in spacetime and the associated temperature is the Unruh temperature. An observer with a finite lifetime has access to the local observable algebra associated with a finite spacetime region called a 'diamond'. The flow defined by the Minkowski vacuum of a (four-dimensional, conformally invariant) quantum field theory over this algebra is also proportional to a flow in spacetime. The associated temperature generalizes the Unruh temperature to finite lifetime observers. Furthermore, this temperature does not vanish even in the limit in which the acceleration is zero. The temperature associated with an inertial observer with lifetime Τ which we denote as 'diamond's temperature', is T D = 2 h/ π k b Τ. This temperature is related to the fact that a finite lifetime observer does not have access to all the degrees of freedom of the quantum field theory. However, we do not attempt to provide any physical interpretation of our proposed assignment of a temperature
Stereoscopic visualization in curved spacetime: seeing deep inside a black hole
International Nuclear Information System (INIS)
Hamilton, Andrew J S; Polhemus, Gavin
2010-01-01
Stereoscopic visualization adds an additional dimension to the viewer's experience, giving them a sense of distance. In a general relativistic visualization, distance can be measured in a variety of ways. We argue that the affine distance, which matches the usual notion of distance in flat spacetime, is a natural distance to use in curved spacetime. As an example, we apply affine distance to the visualization of the interior of a black hole. Affine distance is not the distance perceived with normal binocular vision in curved spacetime. However, the failure of binocular vision is simply a limitation of animals that have evolved in flat spacetime, not a fundamental obstacle to depth perception in curved spacetime. Trinocular vision would provide superior depth perception.
Gravitational lensing and ghost images in the regular Bardeen no-horizon spacetimes
International Nuclear Information System (INIS)
Schee, Jan; Stuchlík, Zdeněk
2015-01-01
We study deflection of light rays and gravitational lensing in the regular Bardeen no-horizon spacetimes. Flatness of these spacetimes in the central region implies existence of interesting optical effects related to photons crossing the gravitational field of the no-horizon spacetimes with low impact parameters. These effects occur due to existence of a critical impact parameter giving maximal deflection of light rays in the Bardeen no-horizon spacetimes. We give the critical impact parameter in dependence on the specific charge of the spacetimes, and discuss 'ghost' direct and indirect images of Keplerian discs, generated by photons with low impact parameters. The ghost direct images can occur only for large inclination angles of distant observers, while ghost indirect images can occur also for small inclination angles. We determine the range of the frequency shift of photons generating the ghost images and determine distribution of the frequency shift across these images. We compare them to those of the standard direct images of the Keplerian discs. The difference of the ranges of the frequency shift on the ghost and direct images could serve as a quantitative measure of the Bardeen no-horizon spacetimes. The regions of the Keplerian discs giving the ghost images are determined in dependence on the specific charge of the no-horizon spacetimes. For comparison we construct direct and indirect (ordinary and ghost) images of Keplerian discs around Reissner-Nördström naked singularities demonstrating a clear qualitative difference to the ghost direct images in the regular Bardeen no-horizon spacetimes. The optical effects related to the low impact parameter photons thus give clear signature of the regular Bardeen no-horizon spacetimes, as no similar phenomena could occur in the black hole or naked singularity spacetimes. Similar direct ghost images have to occur in any regular no-horizon spacetimes having nearly flat central region
Elementary particles in curved spaces
International Nuclear Information System (INIS)
Lazanu, I.
2004-01-01
The theories in particle physics are developed currently, in Minkowski space-time starting from the Poincare group. A physical theory in flat space can be seen as the limit of a more general physical theory in a curved space. At the present time, a theory of particles in curved space does not exist, and thus the only possibility is to extend the existent theories in these spaces. A formidable obstacle to the extension of physical models is the absence of groups of motion in more general Riemann spaces. A space of constant curvature has a group of motion that, although differs from that of a flat space, has the same number of parameters and could permit some generalisations. In this contribution we try to investigate some physical implications of the presumable existence of elementary particles in curved space. In de Sitter space (dS) the invariant rest mass is a combination of the Poincare rest mass and the generalised angular momentum of a particle and it permits to establish a correlation with the vacuum energy and with the cosmological constant. The consequences are significant because in an experiment the local structure of space-time departs from the Minkowski space and becomes a dS or AdS space-time. Discrete symmetry characteristics of the dS/AdS group suggest some arguments for the possible existence of the 'mirror matter'. (author)
Particle decay in inflationary cosmology
International Nuclear Information System (INIS)
Boyanovsky, D.; Vega, H.J. de
2004-01-01
We investigate the relaxation and decay of a particle during inflation by implementing the dynamical renormalization group. This investigation allows us to give a meaningful definition for the decay rate in an expanding universe. As a prelude to a more general scenario, the method is applied here to study the decay of a particle in de Sitter inflation via a trilinear coupling to massless conformally coupled particles, both for wavelengths much larger and much smaller than the Hubble radius. For superhorizon modes we find that the decay is of the form η Γ 1 with η being conformal time and we give an explicit expression for Γ 1 to leading order in the coupling which has a noteworthy interpretation in terms of the Hawking temperature of de Sitter space-time. We show that if the mass M of the decaying field is << H then the decay rate during inflation is enhanced over the Minkowski space-time result by a factor 2H/πM. For wavelengths much smaller than the Hubble radius we find that the decay law is e with C(η) the scale factor and α determined by the strength of the trilinear coupling. In all cases we find a substantial enhancement in the decay law as compared to Minkowski space-time. These results suggest potential implications for the spectrum of scalar density fluctuations as well as non-Gaussianities
The scalar wave equation in a Schwarzschild spacetime
International Nuclear Information System (INIS)
Stewart, J.M.; Schmidt, B.G.
1978-09-01
This paper studies the asymptotic behaviour of solutions of the zero rest mass scalar wave equation in the Schwarzschild spacetime in a neighbourhood of spatial infinity, which includes parts of future and past null infinity. The behaviour of such fields is essentially different from that which accurs in a flat spacetime. (orig.) [de
Andonov, Zdravko
Complex Time and Quan-tum Wave Cosmology Paradigm for Decision of the Main Problem of Contemporary Physics. 3. R&D of Einstein-Minkowski Geodesies' Paradigm in the 4D-Space-Time Continuum to 6D-6nD Space-Time Continuum Paradigms and 6D S-T Equations. . . 4. R&D of Erwin Schrüdinger 4D S-T Universe' Evolutional Equation; It's David Bohm 4D generalization for anisotropic mediums and innovative 6D -for instantaneously quantum measurement -Bohm-Schrüdinger 6D S-T Universe' Evolutional Equation. 5. R&D of brain new 6D Planning of S-T Experi-ments, brain new 6D Space Technicks and Space Technology Generalizations, especially for 6D RS VHRS Research, Monitoring and 6D Computational Tomography. 6. R&D of "6D Euler-Poisson Equations" and "6D Kolmogorov Turbulence Theory" for GeoDynamics and for Space Dynamics as evolution of Gauss-Riemann Paradigms. 7. R&D of N. Boneff NASA RD for Asteroid "Eros" & Space Science' Laws Evolution. 8. R&D of H. Poincare Paradigm for Nature and Cosmos as 6D Group of Transferences. 9. R&D of K. Popoff N-Body General Problem & General Thermodynamic S-T Theory as Einstein-Prigogine-Landau' Paradigms Development. ü 10. R&D of 1st GUT since 1958 by N. S. Kalitzin (Kalitzin N. S., 1958: Uber eine einheitliche Feldtheorie. ZAHeidelberg-ARI, WZHUmnR-B., 7 (2), 207-215) and "Multitemporal Theory of Relativity" -With special applications to Photon Rockets and all Space-Time R&D. GENERAL CONCLUSION: Multidimensional Space-Time Methodology is advance in space research, corresponding to the IAF-IAA-COSPAR Innovative Strategy and R&D Programs -UNEP, UNDP, GEOSS, GMES, Etc.
Equatorial circular orbits in the Kerr-de Sitter spacetimes
International Nuclear Information System (INIS)
Stuchlik, Zdenek; Slany, Petr
2004-01-01
Equatorial motion of test particles in Kerr-de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both black-hole and naked-singularity spacetimes, and their relevance for thin accretion disks is established. The circular orbits constitute two families that coalesce at the so-called static radius. The orientation of the motion along the circular orbits is, in accordance with case of asymptotically flat Kerr spacetimes, defined by relating the motion to the locally nonrotating frames. The minus-family orbits are all counterrotating, while the plus-family orbits are usually corotating relative to these frames. However, the plus-family orbits become counterrotating in the vicinity of the static radius in all Kerr-de Sitter spacetimes, and they become counterrotating in the vicinity of the ring singularity in Kerr-de Sitter naked-singularity spacetimes with a low enough rotational parameter. In such spacetimes, the efficiency of the conversion of the rest energy into heat energy in the geometrically thin plus-family accretion disks can reach extremely high values exceeding the efficiency of the annihilation process. The transformation of a Kerr-de Sitter naked singularity into an extreme black hole due to accretion in the thin disks is briefly discussed for both the plus-family and minus-family disks. It is shown that such a conversion leads to an abrupt instability of the innermost parts of the plus-family accretion disks that can have strong observational consequences
Charged fluid distribution in higher dimensional spheroidal space-time
Indian Academy of Sciences (India)
A general solution of Einstein field equations corresponding to a charged fluid distribution on the background of higher dimensional spheroidal space-time is obtained. The solution generates several known solutions for superdense star having spheroidal space-time geometry.
Constant scalar curvature hypersurfaces in extended Schwarzschild space-time
International Nuclear Information System (INIS)
Pareja, M. J.; Frauendiener, J.
2006-01-01
We present a class of spherically symmetric hypersurfaces in the Kruskal extension of the Schwarzschild space-time. The hypersurfaces have constant negative scalar curvature, so they are hyperboloidal in the regions of space-time which are asymptotically flat
Differential Space-Time Block Code Modulation for DS-CDMA Systems
Directory of Open Access Journals (Sweden)
Liu Jianhua
2002-01-01
Full Text Available A differential space-time block code (DSTBC modulation scheme is used to improve the performance of DS-CDMA systems in fast time-dispersive fading channels. The resulting scheme is referred to as the differential space-time block code modulation for DS-CDMA (DSTBC-CDMA systems. The new modulation and demodulation schemes are especially studied for the down-link transmission of DS-CDMA systems. We present three demodulation schemes, referred to as the differential space-time block code Rake (D-Rake receiver, differential space-time block code deterministic (D-Det receiver, and differential space-time block code deterministic de-prefix (D-Det-DP receiver, respectively. The D-Det receiver exploits the known information of the spreading sequences and their delayed paths deterministically besides the Rake type combination; consequently, it can outperform the D-Rake receiver, which employs the Rake type combination only. The D-Det-DP receiver avoids the effect of intersymbol interference and hence can offer better performance than the D-Det receiver.
Metric space construction for the boundary of space-time
International Nuclear Information System (INIS)
Meyer, D.A.
1986-01-01
A distance function between points in space-time is defined and used to consider the manifold as a topological metric space. The properties of the distance function are investigated: conditions under which the metric and manifold topologies agree, the relationship with the causal structure of the space-time and with the maximum lifetime function of Wald and Yip, and in terms of the space of causal curves. The space-time is then completed as a topological metric space; the resultant boundary is compared with the causal boundary and is also calculated for some pertinent examples
Photon motion in Kerr-de Sitter spacetimes
Energy Technology Data Exchange (ETDEWEB)
Charbulak, Daniel; Stuchlik, Zdenek [Silesian University in Opava, Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Opava (Czech Republic)
2017-12-15
We study the general motion of photons in the Kerr-de Sitter black-hole and naked singularity spacetimes. The motion is governed by the impact parameters X, related to the axial symmetry of the spacetime, and q, related to its hidden symmetry. Appropriate 'effective potentials' governing the latitudinal and radial motion are introduced and their behavior is examined by the 'Chinese boxes' technique giving regions allowed for the motion in terms of the impact parameters. Restrictions on the impact parameters X and q are established in dependence on the spacetime parameters M, Λ, a. The motion can be of orbital type (crossing the equatorial plane, q > 0) and vortical type (tied above or below the equatorial plane, q < 0). It is shown that for negative values of q, the reality conditions imposed on the latitudinal motion yield stronger constraints on the parameter X than that following from the reality condition of the radial motion, excluding the existence of vortical motion of constant radius. The properties of the spherical photon orbits of the orbital type are determined and used along with the properties of the effective potentials as criteria of classification of the KdS spacetimes according to the properties of the motion of the photon. (orig.)
Thin shells joining local cosmic string geometries
Energy Technology Data Exchange (ETDEWEB)
Eiroa, Ernesto F. [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Rubin de Celis, Emilio; Simeone, Claudio [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Ciudad Universitaria Pabellon I, IFIBA-CONICET, Buenos Aires (Argentina)
2016-10-15
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)
Thin shells joining local cosmic string geometries
International Nuclear Information System (INIS)
Eiroa, Ernesto F.; Rubin de Celis, Emilio; Simeone, Claudio
2016-01-01
In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)
Black Holes with Anisotropic Fluid in Lyra Scalar-Tensor Theory
Directory of Open Access Journals (Sweden)
Melis ULU DOĞRU
2018-02-01
Full Text Available In this paper, we investigate distribution of anisotropic fluid which is a resource of black holes in regard to Lyra scalar-tensor theory. As part of the theory, we obtain field equations of spherically symmetric space-time with anisotropic fluid. By using field equations, we suggest distribution of anisotropic fluid, responsible for space-time geometries such as Schwarzschild, Reissner-Nordström, Minkowski type, de Sitter type, Anti-de Sitter type, BTZ and charged BTZ black holes. Finally, we discuss obtained pressures and density of the fluid for different values of arbitrary constants, geometrically and physically.
Entropy of space-time outcome in a movement speed-accuracy task.
Hsieh, Tsung-Yu; Pacheco, Matheus Maia; Newell, Karl M
2015-12-01
The experiment reported was set-up to investigate the space-time entropy of movement outcome as a function of a range of spatial (10, 20 and 30 cm) and temporal (250-2500 ms) criteria in a discrete aiming task. The variability and information entropy of the movement spatial and temporal errors considered separately increased and decreased on the respective dimension as a function of an increment of movement velocity. However, the joint space-time entropy was lowest when the relative contribution of spatial and temporal task criteria was comparable (i.e., mid-range of space-time constraints), and it increased with a greater trade-off between spatial or temporal task demands, revealing a U-shaped function across space-time task criteria. The traditional speed-accuracy functions of spatial error and temporal error considered independently mapped to this joint space-time U-shaped entropy function. The trade-off in movement tasks with joint space-time criteria is between spatial error and timing error, rather than movement speed and accuracy. Copyright © 2015 Elsevier B.V. All rights reserved.
Towards a theory of spacetime theories
Schiemann, Gregor; Scholz, Erhard
2017-01-01
This contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the “best” theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the “space of spaceti...
International Nuclear Information System (INIS)
Banai, M.
1983-11-01
A quantum relativity theory formulated in terms of Davis' quantum relativity principle is outlined. The first task in this theory as in classical relativity theory is to model space-time, the arena of natural processes. It is argued that the quantum space-time models of Banai introduced in an earlier paper is formulated in terms of Davis' quantum relativity. Then it is shown that the recently proposed classical relativistic quantum theory of Prugovecki and his corresponding classical relativistic quantum model of space-time open the way to introduce in a consistent way the quantum space-time model (the 'canonically quantized Minkowski space') proposed by Banai earlier. The main new aspect of the quantum mechanics of the quantum relativistic particles is, in this model of space-time, that it provides a true mass eigenvalue problem and, that the excited mass states of such particles can be interpreted as classifically relativistic (massive) quantum particles ('elementary particles'). The question of field theory over quantum relativistic models of space-time is also discussed. Finally, it is suggested that 'quarks' should be considered as quantum relativistic particles. (author)
A space-time lattice version of scalar electrodynamics
International Nuclear Information System (INIS)
Kijowski, J.; Thielmann, A.
1993-10-01
A Minkowski-lattice version of quantum scalar electrodynamics is constructed. Quantum field is consequently described in a gauge-independent way, i.e. the algebra of quantum observables of the theory is generated by gauge-invariant operators assigned to zero-, one-, and two-dimensional elements of the lattice. The operators satisfy canonical commutation relations. Field dynamics is formulated in terms of difference equations imposed on the field operators. The dynamics is obtained from a discrete version of the path-integral. (author). 19 refs
Space-time algebra for the generalization of gravitational field
Indian Academy of Sciences (India)
The Maxwell–Proca-like field equations of gravitolectromagnetism are formulated using space-time algebra (STA). The gravitational wave equation with massive gravitons and gravitomagnetic monopoles has been derived in terms of this algebra. Using space-time algebra, the most generalized form of ...
Minkowski space pion model inspired by lattice QCD running quark mass
Energy Technology Data Exchange (ETDEWEB)
Mello, Clayton S. [Instituto Tecnológico de Aeronáutica, DCTA, 12.228-900 São José dos Campos, SP (Brazil); Melo, J.P.B.C. de [Laboratório de Física Teórica e Computacional – LFTC, Universidade Cruzeiro do Sul, 01506-000 São Paulo, SP (Brazil); Frederico, T., E-mail: tobias@ita.br [Instituto Tecnológico de Aeronáutica, DCTA, 12.228-900 São José dos Campos, SP (Brazil)
2017-03-10
The pion structure in Minkowski space is described in terms of an analytic model of the Bethe–Salpeter amplitude combined with Euclidean Lattice QCD results. The model is physically motivated to take into account the running quark mass, which is fitted to Lattice QCD data. The pion pseudoscalar vertex is associated to the quark mass function, as dictated by dynamical chiral symmetry breaking requirements in the limit of vanishing current quark mass. The quark propagator is analyzed in terms of a spectral representation, and it shows a violation of the positivity constraints. The integral representation of the pion Bethe–Salpeter amplitude is also built. The pion space-like electromagnetic form factor is calculated with a quark electromagnetic current, which satisfies the Ward–Takahashi identity to ensure current conservation. The results for the form factor and weak decay constant are found to be consistent with the experimental data.
Minkowski space pion model inspired by lattice QCD running quark mass
Directory of Open Access Journals (Sweden)
Clayton S. Mello
2017-03-01
Full Text Available The pion structure in Minkowski space is described in terms of an analytic model of the Bethe–Salpeter amplitude combined with Euclidean Lattice QCD results. The model is physically motivated to take into account the running quark mass, which is fitted to Lattice QCD data. The pion pseudoscalar vertex is associated to the quark mass function, as dictated by dynamical chiral symmetry breaking requirements in the limit of vanishing current quark mass. The quark propagator is analyzed in terms of a spectral representation, and it shows a violation of the positivity constraints. The integral representation of the pion Bethe–Salpeter amplitude is also built. The pion space-like electromagnetic form factor is calculated with a quark electromagnetic current, which satisfies the Ward–Takahashi identity to ensure current conservation. The results for the form factor and weak decay constant are found to be consistent with the experimental data.
Asymptotic structure of space-time with a positive cosmological constant
Kesavan, Aruna
detail. i) We show explicitly that conformal flatness of the boundary removes half the degrees of freedom of the gravitational field by hand and is not justified by physical considerations; ii) We obtain gauge invariant expressions of energy-momentum and angular momentum fluxes carried by gravitational waves in terms of fields defined at [special character omitted]+; iii) We demonstrate that the flux formulas reduce to the familiar ones in Minkowski spacetime in spite of the fact that the limit Lambda → 0 is discontinuous (since, in particular, [special character omitted]+ changes its space-like character to null in the limit); iv) We obtain a generalization of Einstein's 1918 quadrupole formula for power emission by a linearized source to include a positive Lambda; and, finally v) We show that, although energy of linearized gravitational waves can be arbitrarily negative in general, gravitational waves emitted by physically reasonable sources carry positive energy.
Naked singularity in the global structure of critical collapse spacetimes
International Nuclear Information System (INIS)
Frolov, Andrei V.; Pen, U.-L.
2003-01-01
We examine the global structure of scalar field critical collapse spacetimes using a characteristic double-null code. It can integrate past the horizon without any coordinate problems, due to the careful choice of constraint equations used in the evolution. The limiting sequence of sub- and supercritical spacetimes presents an apparent paradox in the expected Penrose diagrams, which we address in this paper. We argue that the limiting spacetime converges pointwise to a unique limit for all r>0, but not uniformly. The r=0 line is different in the two limits. We interpret that the two different Penrose diagrams differ by a discontinuous gauge transformation. We conclude that the limiting spacetime possesses a singular event, with a future removable naked singularity
Energy in the Kantowski–Sachs space-time using teleparallel ...
Indian Academy of Sciences (India)
Energy in the Kantowski–Sachs space-time using teleparallel geometry ... Kantowski–Sachs metric; teleparallelism; gravitational energy. Abstract. The purpose of this paper is to examine the energy content of the inflationary Universe described by Kantowski–Sachs space-time in quasilocal approach of teleparallel gravity ...
Black holes in loop quantum gravity: the complete space-time.
Gambini, Rodolfo; Pullin, Jorge
2008-10-17
We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.
Gonzalez-Mestres, Luis
2014-04-01
Planck and other recent data in Cosmology and Particle Physics can open the way to controversial analyses concerning the early Universe and its possible ultimate origin. Alternatives to standard cosmology include pre-Big Bang approaches, new space-time geometries and new ultimate constituents of matter. Basic issues related to a possible new cosmology along these lines clearly deserve further exploration. The Planck collaboration reports an age of the Universe t close to 13.8 Gyr and a present ratio H between relative speeds and distances at cosmic scale around 67.3 km/s/Mpc. The product of these two measured quantities is then slightly below 1 (about 0.95), while it can be exactly 1 in the absence of matter and cosmological constant in patterns based on the spinorial space-time we have considered in previous papers. In this description of space-time we first suggested in 1996-97, the cosmic time t is given by the modulus of a SU(2) spinor and the Lundmark-Lemaître-Hubble (LLH) expansion law turns out to be of purely geometric origin previous to any introduction of standard matter and relativity. Such a fundamental geometry, inspired by the role of half-integer spin in Particle Physics, may reflect an equilibrium between the dynamics of the ultimate constituents of matter and the deep structure of space and time. Taking into account the observed cosmic acceleration, the present situation suggests that the value of 1 can be a natural asymptotic limit for the product H t in the long-term evolution of our Universe up to possible small corrections. In the presence of a spinorial space-time geometry, no ad hoc combination of dark matter and dark energy would in any case be needed to get an acceptable value of H and an evolution of the Universe compatible with observation. The use of a spinorial space-time naturally leads to unconventional properties for the space curvature term in Friedmann-like equations. It therefore suggests a major modification of the standard
Space-Time Geometry of Quark and Strange Quark Matter
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We study quark and strange quark matter in the context of general relativity. For this purpose, we solve Einstein's field equations for quark and strange quark matter in spherical symmetric space-times. We analyze strange quark matter for the different equations of state (EOS) in the spherical symmetric space-times, thus we are able to obtain the space-time geometries of quark and strange quark matter. Also, we discuss die features of the obtained solutions. The obtained solutions are consistent with the results of Brookhaven Laboratory, i.e. the quark-gluon plasma has a vanishing shear (i.e. quark-gluon plasma is perfect).
Dynamics in stationary, non-globally hyperbolic spacetimes
Energy Technology Data Exchange (ETDEWEB)
Seggev, Itai [Enrico Fermi Institute and Department of Physics, University of Chicago, 5640 S Ellis Avenue, Chicago, IL 60637 (United States)
2004-06-07
Classically, the dynamics of a scalar field in a non-globally hyperbolic spacetime is ill-posed. Previously, a prescription was given for defining dynamics in static spacetimes in terms of a second-order operator acting on a Hilbert space defined on static slices. The present work extends this result by giving a similar prescription for defining dynamics in stationary spacetimes obeying certain mild assumptions. The prescription is defined in terms of a first-order operator acting on a different Hilbert space from that used in the static prescription. It preserves the important properties of the earlier prescription: the formal solution agrees with the Cauchy evolution within the domain of dependence, and smooth data of compact support always give rise to smooth solutions. In the static case, the first-order formalism agrees with the second-order formalism (using specifically the Friedrichs extension). Applications to field quantization are also discussed.
Holography and Entanglement in Flat Spacetime
International Nuclear Information System (INIS)
Li Wei; Takayanagi, Tadashi
2011-01-01
We propose a holographic correspondence of the flat spacetime based on the behavior of the entanglement entropy and the correlation functions. The holographic dual theory turns out to be highly nonlocal. We argue that after most part of the space is traced out, the reduced density matrix gives the maximal entropy and the correlation functions become trivial. We present a toy model for this holographic dual using a nonlocal scalar field theory that reproduces the same property of the entanglement entropy. Our conjecture is consistent with the entropy of Schwarzschild black holes in asymptotically flat spacetimes.
Global properties of physically interesting Lorentzian spacetimes
Nawarajan, Deloshan; Visser, Matt
Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric tensor. When combined with the classical Einstein field equations this gives an extremely successful empirical model of classical gravity and classical matter — at least as long as one does not ask too many awkward questions about global issues, (such as global topology and global causal structure). We feel however that this is a tactical error — even without invoking full-fledged “quantum gravity” we know that the standard model of particle physics is also an extremely good representation of some parts of empirical reality; and we had better be able to carry over all the good features of the standard model of particle physics — at least into the realm of semi-classical quantum gravity. Doing so gives us some interesting global features that spacetime should possess: On physical grounds spacetime should be space-orientable, time-orientable, and spacetime-orientable, and it should possess a globally defined tetrad (vierbein, or in general a globally defined vielbein/n-bein). So on physical grounds spacetime should be parallelizable. This strongly suggests that the metric is not the fundamental physical quantity; a very good case can be made for the tetrad being more fundamental than the metric. Furthermore, a globally-defined “almost complex structure” is almost unavoidable. Ideas along these lines have previously been mooted, but much is buried in the pre-arXiv literature and is either forgotten or inaccessible. We shall revisit these ideas taking a perspective very much based on empirical physical observation.
A new derivation of the conformally flat stationary cyclic non-circular spacetimes
International Nuclear Information System (INIS)
Ayon-Beato, Eloy; Campuzano, Cuauhtemoc; GarcIa, Alberto
2007-01-01
We present an alternative way to derive the conformally flat stationary cyclic non-circular spacetimes. We show that there is no room for stationary axisymmetric non-circular axisymmetric spacetimes. We reproduce the well know results for this sort of spacetimes recently reported in [1
A new derivation of the conformally flat stationary cyclic non-circular spacetimes
Energy Technology Data Exchange (ETDEWEB)
Ayon-Beato, Eloy [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico); Campuzano, Cuauhtemoc [Departamento de Fisica, Facultad de Fisica e Inteligencia Artificial, Universidad Veracruzana, 91000 Xalapa, Veracruz (Mexico); GarcIa, Alberto [Department of Physics, University of California, Davis, CA 95616 (United States)
2007-11-15
We present an alternative way to derive the conformally flat stationary cyclic non-circular spacetimes. We show that there is no room for stationary axisymmetric non-circular axisymmetric spacetimes. We reproduce the well know results for this sort of spacetimes recently reported in [1].
On electric field in anti-de Sitter spacetime
Energy Technology Data Exchange (ETDEWEB)
Cheong, Lee Yen, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my; Yan, Chew Xiao, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my; Ching, Dennis Ling Chuan, E-mail: lee-yencheong@petronas.com.my, E-mail: chewxy01813@gmail.com, E-mail: dennis.ling@petronas.com.my [Department of Fundamental and Applied Sciences, Universiti Teknologi Petronas, Bandar Seri Iskandar, Tronoh 31750, Perak (Malaysia)
2014-10-24
In this paper we calculate the electromagnetic field produced using retarded Green's function in Anti-de Sitter spacetime (AdS). Since this spacetime is non-globally hyperbolic and has no Cauchy surface, we only consider the field originated from a charge moving along its geodesic in the region consists of points covered by future null geodesic of the charge.
Schrödinger, Erwin
1985-01-01
In response to repeated requests this classic book on space-time structure by Professor Erwin Schrödinger is now available in the Cambridge Science Classics series. First published in 1950, and reprinted in 1954 and 1960, this lucid and profound exposition of Einstein's 1915 theory of gravitation still provides valuable reading for students and research workers in the field.
Is there a relation between the 2D Causal Set action and the Lorentzian Gauss-Bonnet theorem?
Benincasa, Dionigi M. T.
2011-07-01
We investigate the relation between the two dimensional Causal Set action, Script S, and the Lorentzian Gauss-Bonnet theorem (LGBT). We give compelling reasons why the answer to the title's question is no. In support of this point of view we calculate the causal set inspired action of causal intervals in some two dimensional spacetimes: Minkowski, the flat cylinder and the flat trousers.