WorldWideScience

Sample records for compact noncommutative spaces

  1. Index theory for locally compact noncommutative geometries

    CERN Document Server

    Carey, A L; Rennie, A; Sukochev, F A

    2014-01-01

    Spectral triples for nonunital algebras model locally compact spaces in noncommutative geometry. In the present text, the authors prove the local index formula for spectral triples over nonunital algebras, without the assumption of local units in our algebra. This formula has been successfully used to calculate index pairings in numerous noncommutative examples. The absence of any other effective method of investigating index problems in geometries that are genuinely noncommutative, particularly in the nonunital situation, was a primary motivation for this study and the authors illustrate this point with two examples in the text. In order to understand what is new in their approach in the commutative setting the authors prove an analogue of the Gromov-Lawson relative index formula (for Dirac type operators) for even dimensional manifolds with bounded geometry, without invoking compact supports. For odd dimensional manifolds their index formula appears to be completely new.

  2. Noncommutative products of Euclidean spaces

    Science.gov (United States)

    Dubois-Violette, Michel; Landi, Giovanni

    2018-05-01

    We present natural families of coordinate algebras on noncommutative products of Euclidean spaces R^{N_1} × _R R^{N_2} . These coordinate algebras are quadratic ones associated with an R -matrix which is involutive and satisfies the Yang-Baxter equations. As a consequence, they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces R4 × _R R4 . Among these, particularly well behaved ones have deformation parameter u \\in S^2 . Quotients include seven spheres S7_u as well as noncommutative quaternionic tori TH_u = S^3 × _u S^3 . There is invariance for an action of {{SU}}(2) × {{SU}}(2) on the torus TH_u in parallel with the action of U(1) × U(1) on a `complex' noncommutative torus T^2_θ which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.

  3. Mapping spaces and automorphism groups of toric noncommutative spaces

    Science.gov (United States)

    Barnes, Gwendolyn E.; Schenkel, Alexander; Szabo, Richard J.

    2017-09-01

    We develop a sheaf theory approach to toric noncommutative geometry which allows us to formalize the concept of mapping spaces between two toric noncommutative spaces. As an application, we study the `internalized' automorphism group of a toric noncommutative space and show that its Lie algebra has an elementary description in terms of braided derivations.

  4. Noncommutative induced gauge theories on Moyal spaces

    International Nuclear Information System (INIS)

    Wallet, J-C

    2008-01-01

    Noncommutative field theories on Moyal spaces can be conveniently handled within a framework of noncommutative geometry. Several renormalisable matter field theories that are now identified are briefly reviewed. The construction of renormalisable gauge theories on these noncommutative Moyal spaces, which remains so far a challenging problem, is then closely examined. The computation in 4-D of the one-loop effective gauge theory generated from the integration over a scalar field appearing in a renormalisable theory minimally coupled to an external gauge potential is presented. The gauge invariant effective action is found to involve, beyond the expected noncommutative version of the pure Yang-Mills action, additional terms that may be interpreted as the gauge theory counterpart of the harmonic term, which for the noncommutative ψ 4 -theory on Moyal space ensures renormalisability. A class of possible candidates for renormalisable gauge theory actions defined on Moyal space is presented and discussed

  5. Noncommutative de Sitter and FRW spaces

    International Nuclear Information System (INIS)

    Burić, Maja; Madore, John

    2015-01-01

    Several versions of fuzzy four-dimensional de Sitter space are constructed using the noncommutative frame formalism. Although all noncommutative spacetimes which are found have commutative de Sitter metric as a classical limit, the algebras and the differential calculi which define them have many differences, which we derive and discuss

  6. Spin Hall effect on a noncommutative space

    International Nuclear Information System (INIS)

    Ma Kai; Dulat, Sayipjamal

    2011-01-01

    We study the spin-orbital interaction and the spin Hall effect of an electron moving on a noncommutative space under the influence of a vector potential A(vector sign). On a noncommutative space, we find that the commutator between the vector potential A(vector sign) and the electric potential V 1 (r(vector sign)) of the lattice induces a new term, which can be treated as an effective electric field, and the spin Hall conductivity obtains some correction. On a noncommutative space, the spin current and spin Hall conductivity have distinct values in different directions, and depend explicitly on the noncommutative parameter. Once this spin Hall conductivity in different directions can be measured experimentally with a high level of accuracy, the data can then be used to impose bounds on the value of the space noncommutativity parameter. We have also defined a new parameter, σ=ρθ (ρ is the electron concentration, θ is the noncommutativity parameter), which can be measured experimentally. Our approach is based on the Foldy-Wouthuysen transformation, which gives a general Hamiltonian of a nonrelativistic electron moving on a noncommutative space.

  7. Noncommutative phase spaces on Aristotle group

    Directory of Open Access Journals (Sweden)

    Ancille Ngendakumana

    2012-03-01

    Full Text Available We realize noncommutative phase spaces as coadjoint orbits of extensions of the Aristotle group in a two dimensional space. Through these constructions the momenta of the phase spaces do not commute due to the presence of a naturally introduced magnetic eld. These cases correspond to the minimal coupling of the momentum with a magnetic potential.

  8. Time-space noncommutativity: quantised evolutions

    International Nuclear Information System (INIS)

    Balachandran, Aiyalam P.; Govindarajan, Thupil R.; Teotonio-Sobrinho, Paulo; Martins, Andrey Gomes

    2004-01-01

    In previous work, we developed quantum physics on the Moyal plane with time-space noncommutativity, basing ourselves on the work of Doplicher et al. Here we extend it to certain noncommutative versions of the cylinder, R 3 and Rx S 3 . In all these models, only discrete time translations are possible, a result known before in the first two cases. One striking consequence of quantised time translations is that even though a time independent hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. (In contrast, on a one-dimensional periodic lattice of lattice spacing a and length L = Na, only momentum mod 2π/L is observable (and can be conserved).) Suggestions for further study of this effect are made. Scattering theory is formulated and an approach to quantum field theory is outlined. (author)

  9. Two-dimensional black holes and non-commutative spaces

    International Nuclear Information System (INIS)

    Sadeghi, J.

    2008-01-01

    We study the effects of non-commutative spaces on two-dimensional black hole. The event horizon of two-dimensional black hole is obtained in non-commutative space up to second order of perturbative calculations. A lower limit for the non-commutativity parameter is also obtained. The observer in that limit in contrast to commutative case see two horizon

  10. Discreteness of area in noncommutative space

    Energy Technology Data Exchange (ETDEWEB)

    Amelino-Camelia, Giovanni [Dipartimento di Fisica, Universita di Roma ' La Sapienza' and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)], E-mail: amelino@roma1.infn.it; Gubitosi, Giulia; Mercati, Flavio [Dipartimento di Fisica, Universita di Roma ' La Sapienza' and Sez. Roma1 INFN, P.le A. Moro 2, 00185 Roma (Italy)

    2009-06-08

    We introduce an area operator for the Moyal noncommutative plane. We find that the spectrum is discrete, but, contrary to the expectation formulated by other authors, not characterized by a 'minimum-area principle'. We show that an intuitive analysis of the uncertainty relations obtained from Moyal-plane noncommutativity is fully consistent with our results for the spectrum, and we argue that our area operator should be generalizable to several other noncommutative spaces. We also observe that the properties of distances and areas in the Moyal plane expose some weaknesses in the line of reasoning adopted in some of the heuristic analyses of the measurability of geometric spacetime observables in the quantum-gravity realm.

  11. Discreteness of area in noncommutative space

    International Nuclear Information System (INIS)

    Amelino-Camelia, Giovanni; Gubitosi, Giulia; Mercati, Flavio

    2009-01-01

    We introduce an area operator for the Moyal noncommutative plane. We find that the spectrum is discrete, but, contrary to the expectation formulated by other authors, not characterized by a 'minimum-area principle'. We show that an intuitive analysis of the uncertainty relations obtained from Moyal-plane noncommutativity is fully consistent with our results for the spectrum, and we argue that our area operator should be generalizable to several other noncommutative spaces. We also observe that the properties of distances and areas in the Moyal plane expose some weaknesses in the line of reasoning adopted in some of the heuristic analyses of the measurability of geometric spacetime observables in the quantum-gravity realm.

  12. Noncommutative Phase Spaces by Coadjoint Orbits Method

    Directory of Open Access Journals (Sweden)

    Ancille Ngendakumana

    2011-12-01

    Full Text Available We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing. We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field.

  13. Quantum electrodynamics with arbitrary charge on a noncommutative space

    International Nuclear Information System (INIS)

    Zhou Wanping; Long Zhengwen; Cai Shaohong

    2009-01-01

    Using the Seiberg-Witten map, we obtain a quantum electrodynamics on a noncommutative space, which has arbitrary charge and keep the gauge invariance to at the leading order in theta. The one-loop divergence and Compton scattering are reinvestigated. The noncommutative effects are larger than those in ordinary noncommutative quantum electrodynamics. (authors)

  14. Classical mechanics in non-commutative phase space

    International Nuclear Information System (INIS)

    Wei Gaofeng; Long Chaoyun; Long Zhengwen; Qin Shuijie

    2008-01-01

    In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. (authors)

  15. Construction of non-Abelian gauge theories on noncommutative spaces

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.; Moeller, L.; Wess, J.; Max-Planck-Inst. fuer Physik, Muenchen; Humboldt-Univ., Berlin; Schraml, S.; Humboldt-Univ., Berlin

    2001-01-01

    We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

  16. Construction of non-Abelian gauge theories on noncommutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B.; Schupp, P. [Sektion Physik, Muenchen Univ. (Germany); Moeller, L.; Wess, J. [Sektion Physik, Muenchen Univ. (Germany); Max-Planck-Inst. fuer Physik, Muenchen (Germany); Humboldt-Univ., Berlin (Germany). Inst. fuer Physik; Schraml, S. [Sektion Physik, Muenchen Univ. (Germany)

    2001-06-01

    We present a formalism to explicitly construct non-Abelian gauge theories on noncommutative spaces (induced via a star product with a constant Poisson tensor) from a consistency relation. This results in an expansion of the gauge parameter, the noncommutative gauge potential and fields in the fundamental representation, in powers of a parameter of the noncommutativity. This allows the explicit construction of actions for these gauge theories. (orig.)

  17. Unitary quantum physics with time-space non-commutativity

    International Nuclear Information System (INIS)

    Balachandran, A P; Govindarajan, T R; Martins, A G; Molina, C; Teotonio-Sobrinho, P

    2005-01-01

    In these lectures 4 quantum physics in noncommutative spacetime is developed. It is based on the work of Doplicher et al. which allows for time-space noncommutativity. In the context of noncommutative quantum mechanics, some important points are explored, such as the formal construction of the theory, symmetries, causality, simultaneity and observables. The dynamics generated by a noncommutative Schroedinger equation is studied. The theory is further extended to certain noncommutative versions of the cylinder, R 3 and R x S 3 . In all these models, only discrete time translations are possible. One striking consequence of quantised time translations is that even though a time independent Hamiltonian is an observable, in scattering processes, it is conserved only modulo 2π/θ, where θ is the noncommutative parameter. Scattering theory is formulated and an approach to quantumfield theory is outlined

  18. Noncommutative spaces and Poincaré symmetry

    Energy Technology Data Exchange (ETDEWEB)

    Meljanac, Stjepan, E-mail: meljanac@irb.hr [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia); Meljanac, Daniel [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia); Mercati, Flavio [Perimeter Institute for Theoretical Physics, 31 Caroline St. N., Waterloo, ON, N2L 2Y5 (Canada); Pikutić, Danijel [Division of Theoretical Physics, Rudjer Bošković Institute, Bijenička c. 54, HR-10002 Zagreb (Croatia)

    2017-03-10

    We present a framework which unifies a large class of noncommutative spacetimes that can be described in terms of a deformed Heisenberg algebra. The commutation relations between spacetime coordinates are up to linear order in the coordinates, with structure constants depending on the momenta plus terms depending only on the momenta. The possible implementations of the action of Lorentz transformations on these deformed phase spaces are considered, together with the consistency requirements they introduce. It is found that Lorentz transformations in general act nontrivially on tensor products of momenta. In particular the Lorentz group element which acts on the left and on the right of a composition of two momenta is different, and depends on the momenta involved in the process. We conclude with two representative examples, which illustrate the mentioned effect.

  19. Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups

    CERN Document Server

    2017-01-01

    Providing an introduction to current research topics in functional analysis and its applications to quantum physics, this book presents three lectures surveying recent progress and open problems.  A special focus is given to the role of symmetry in non-commutative probability, in the theory of quantum groups, and in quantum physics. The first lecture presents the close connection between distributional symmetries and independence properties. The second introduces many structures (graphs, C*-algebras, discrete groups) whose quantum symmetries are much richer than their classical symmetry groups, and describes the associated quantum symmetry groups. The last lecture shows how functional analytic and geometric ideas can be used to detect and to quantify entanglement in high dimensions.  The book will allow graduate students and young researchers to gain a better understanding of free probability, the theory of compact quantum groups, and applications of the theory of Banach spaces to quantum information. The l...

  20. Wigner Functions for the Bateman System on Noncommutative Phase Space

    Science.gov (United States)

    Heng, Tai-Hua; Lin, Bing-Sheng; Jing, Si-Cong

    2010-09-01

    We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra.

  1. Wigner Functions for the Bateman System on Noncommutative Phase Space

    International Nuclear Information System (INIS)

    Tai-Hua, Heng; Bing-Sheng, Lin; Si-Cong, Jing

    2010-01-01

    We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra

  2. Dirac equation in noncommutative space for hydrogen atom

    Energy Technology Data Exchange (ETDEWEB)

    Adorno, T.C., E-mail: tadorno@nonada.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Chaichian, M., E-mail: Masud.Chaichian@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318, CEP 05508-090 Sao Paulo, SP (Brazil); Tureanu, A., E-mail: Anca.Tureanu@helsinki.f [Department of Physics, University of Helsinki and Helsinki Institute of Physics, PO Box 64, FIN-00014 Helsinki (Finland)

    2009-11-30

    We consider the energy levels of a hydrogen-like atom in the framework of theta-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S{sub 1/2}, 2P{sub 1/2} and 2P{sub 3/2} is lifted completely, such that new transition channels are allowed.

  3. Dirac equation in noncommutative space for hydrogen atom

    International Nuclear Information System (INIS)

    Adorno, T.C.; Baldiotti, M.C.; Chaichian, M.; Gitman, D.M.; Tureanu, A.

    2009-01-01

    We consider the energy levels of a hydrogen-like atom in the framework of θ-modified, due to space noncommutativity, Dirac equation with Coulomb field. It is shown that on the noncommutative (NC) space the degeneracy of the levels 2S 1/2 , 2P 1/2 and 2P 3/2 is lifted completely, such that new transition channels are allowed.

  4. Deformed two-photon squeezed states in noncommutative space

    International Nuclear Information System (INIS)

    Zhang Jianzu

    2004-01-01

    Recent studies on nonperturbation aspects of noncommutative quantum mechanics explored a new type of boson commutation relations at the deformed level, described by deformed annihilation-creation operators in noncommutative space. This correlated boson commutator correlates different degrees of freedom, and shows an essential influence on dynamics. This Letter devotes to the development of formalism of deformed two-photon squeezed states in noncommutative space. General representations of deformed annihilation-creation operators and the consistency condition for the electromagnetic wave with a single mode of frequency in noncommunicative space are obtained. Two-photon squeezed states are studied. One finds that variances of the dimensionless Hermitian quadratures of the annihilation operator in one degree of freedom include variances in the other degree of freedom. Such correlations show the new feature of spatial noncommutativity and allow a deeper understanding of the correlated boson commutator

  5. Non-commutative geometry on quantum phase-space

    International Nuclear Information System (INIS)

    Reuter, M.

    1995-06-01

    A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)

  6. Klein-Gordon oscillators in noncommutative phase space

    International Nuclear Information System (INIS)

    Wang Jianhua

    2008-01-01

    We study the Klein-Gordon oscillators in non-commutative (NC) phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly. (authors)

  7. 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.)

  8. 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.)

  9. The Event Horizon of The Schwarzschild Black Hole in Noncommutative Spaces

    OpenAIRE

    Nasseri, Forough

    2005-01-01

    The event horizon of Schwarzschild black hole is obtained in noncommutative spaces up to the second order of perturbative calculations. Because this type of black hole is non-rotating, to the first order there is no any effect on the event horizon due to the noncommutativity of space. A lower limit for the noncommutativity parameter is also obtained. As a result, the event horizon in noncommutative spaces is less than the event horizon in commutative spaces.

  10. Non-commutative covering spaces and their symmetries

    DEFF Research Database (Denmark)

    Canlubo, Clarisson

    dened and its corresponding Galois theory. Using this and basic concepts from algebraic geometryand spectral theory, we will give a full description of the general structure of non-centralcoverings. Examples of coverings of the rational and irrational non-commutative tori will alsobe studied. Using...... will explain this and relate it to bi-Galois theory.Using the OZ-transform, we will show that non-commutative covering spaces come in pairs.Several categories of covering spaces will be dened and studied. Appealing to Tannaka duality,we will explain how this lead to a notion of an etale fundamental group...

  11. Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space

    Science.gov (United States)

    Masum, Huseyin; Dulat, Sayipjamal; Tohti, Mutallip

    2017-09-01

    The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2 S 1/2, 2 P 1/2 and 2 P 3/2 were obtained by using the 𝜃 and the \\bar θ modified Dirac Hamiltonian of hydrogen-like atom on a noncommutative phase space. The degeneracy of the energy levels 2 P 1/2 and 2 P 3/2 were removed completely by 𝜃-correction. And the \\bar θ -correction shifts these energy levels.

  12. The standard model on non-commutative space-time

    International Nuclear Information System (INIS)

    Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M.; Wess, J.

    2002-01-01

    We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter θ μν . No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in θ μν we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)

  13. The standard model on non-commutative space-time

    Energy Technology Data Exchange (ETDEWEB)

    Calmet, X.; Jurco, B.; Schupp, P.; Wohlgenannt, M. [Sektion Physik, Universitaet Muenchen (Germany); Wess, J. [Sektion Physik, Universitaet Muenchen (Germany); Max-Planck-Institut fuer Physik, Muenchen (Germany)

    2002-03-01

    We consider the standard model on a non-commutative space and expand the action in the non-commutativity parameter {theta}{sup {mu}}{sup {nu}}. No new particles are introduced; the structure group is SU(3) x SU(2) x U(1). We derive the leading order action. At zeroth order the action coincides with the ordinary standard model. At leading order in {theta}{sup {mu}}{sup {nu}} we find new vertices which are absent in the standard model on commutative space-time. The most striking features are couplings between quarks, gluons and electroweak bosons and many new vertices in the charged and neutral currents. We find that parity is violated in non-commutative QCD. The Higgs mechanism can be applied. QED is not deformed in the minimal version of the NCSM to the order considered. (orig.)

  14. Nonperturbative studies of quantum field theories on noncommutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Volkholz, J.

    2007-11-16

    This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the {lambda}{phi}{sup 4} model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized {lambda}{phi}{sup 4} model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted

  15. Nonperturbative studies of quantum field theories on noncommutative spaces

    International Nuclear Information System (INIS)

    Volkholz, J.

    2007-01-01

    This work deals with three quantum field theories on spaces with noncommuting position operators. Noncommutative models occur in the study of string theories and quantum gravity. They usually elude treatment beyond the perturbative level. Due to the technique of dimensional reduction, however, we are able to investigate these theories nonperturbatively. This entails translating the action functionals into a matrix language, which is suitable for numerical simulations. First we explore the λφ 4 model on a noncommutative plane. We investigate the continuum limit at fixed noncommutativity, which is known as the double scaling limit. Here we focus especially on the fate of the striped phase, a phase peculiar to the noncommutative version of the regularized λφ 4 model. We find no evidence for its existence in the double scaling limit. Next we examine the U(1) gauge theory on a four-dimensional spacetime, where two spatial directions are noncommutative. We examine the phase structure and find a new phase with a spontaneously broken translation symmetry. In addition we demonstrate the existence of a finite double scaling limit which confirms the renormalizability of the theory. Furthermore we investigate the dispersion relation of the photon. In the weak coupling phase our results are consistent with an infrared instability predicted by perturbation theory. If the translational symmetry is broken, however, we find a dispersion relation corresponding to a massless particle. Finally, we investigate a supersymmetric theory on the fuzzy sphere, which features scalar neutral bosons and Majorana fermions. The supersymmetry is exact in the limit of infinitely large matrices. We investigate the phase structure of the model and find three distinct phases. Summarizing, we study noncommutative field theories beyond perturbation theory. Moreover, we simulate a supersymmetric theory on the fuzzy sphere, which might provide an alternative to attempted lattice formulations. (orig.)

  16. Moving mirrors and black hole evaporation in noncommutative space-times

    International Nuclear Information System (INIS)

    Casadio, R.; Cox, P.H.; Harms, B.; Micu, O.

    2006-01-01

    We study the evaporation of black holes in noncommutative space-times. We do this by calculating the correction to the detector's response function for a moving mirror in terms of the noncommutativity parameter Θ and then extracting the number density as modified by this parameter. We find that allowing space and time to be noncommutative increases the decay rate of a black hole

  17. Conformal quantum mechanics and holography in noncommutative space-time

    Science.gov (United States)

    Gupta, Kumar S.; Harikumar, E.; Zuhair, N. S.

    2017-09-01

    We analyze the effects of noncommutativity in conformal quantum mechanics (CQM) using the κ-deformed space-time as a prototype. Up to the first order in the deformation parameter, the symmetry structure of the CQM algebra is preserved but the coupling in a canonical model of the CQM gets deformed. We show that the boundary conditions that ensure a unitary time evolution in the noncommutative CQM can break the scale invariance, leading to a quantum mechanical scaling anomaly. We calculate the scaling dimensions of the two and three point functions in the noncommutative CQM which are shown to be deformed. The AdS2 / CFT1 duality for the CQM suggests that the corresponding correlation functions in the holographic duals are modified. In addition, the Breitenlohner-Freedman bound also picks up a noncommutative correction. The strongly attractive regime of a canonical model of the CQM exhibit quantum instability. We show that the noncommutativity softens this singular behaviour and its implications for the corresponding holographic duals are discussed.

  18. Group theoretical construction of planar noncommutative phase spaces

    Energy Technology Data Exchange (ETDEWEB)

    Ngendakumana, Ancille, E-mail: nancille@yahoo.fr; Todjihoundé, Leonard, E-mail: leonardt@imsp.uac.org [Institut de Mathématiques et des Sciences Physiques (IMSP), Porto-Novo (Benin); Nzotungicimpaye, Joachim, E-mail: kimpaye@kie.ac.rw [Kigali Institute of Education (KIE), Kigali (Rwanda)

    2014-01-15

    Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.

  19. Group theoretical construction of planar noncommutative phase spaces

    International Nuclear Information System (INIS)

    Ngendakumana, Ancille; Todjihoundé, Leonard; Nzotungicimpaye, Joachim

    2014-01-01

    Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given

  20. Nucleon structure functions in noncommutative space-time

    Energy Technology Data Exchange (ETDEWEB)

    Rafiei, A.; Rezaei, Z.; Mirjalili, A. [Yazd University, Physics Department, Yazd (Iran, Islamic Republic of)

    2017-05-15

    In the context of noncommutative space-time we investigate the nucleon structure functions which play an important role in identifying the internal structure of nucleons. We use the corrected vertices and employ new vertices that appear in two approaches of noncommutativity and calculate the proton structure functions in terms of the noncommutative tensor θ{sub μν}. To check our results we plot the nucleon structure function (NSF), F{sub 2}(x), and compare it with experimental data and the results from the GRV, GJR and CT10 parametrization models. We show that with the new vertex that arises the noncommutativity correction will lead to a better consistency between theoretical results and experimental data for the NSF. This consistency will be better for small values of the Bjorken variable x. To indicate and confirm the validity of our calculations we also act conversely. We obtain a lower bound for the numerical values of Λ{sub NC} scale which correspond to recent reports. (orig.)

  1. Stringy Fuzziness as the Custodial of Time-Space Noncommutativity

    CERN Document Server

    Barbón, José L F

    2000-01-01

    We study aspects of obtaining field theories with noncommuting time-space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed-string backgrounds, there is an obstruction to decoupling the time-space noncommutativity scale from that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure. We study the moduli space of the obstruction in terms of the open- and closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally by considering complex values of the dilaton and inverting the role of space and time of the light cone. This is reminiscent of a black-hole horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity.

  2. Stringy fuzziness as the custodian of time-space noncommutativity

    CERN Document Server

    Barbón, José L F

    2000-01-01

    We study aspects of obtaining field theories with noncommuting time- space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed- string backgrounds, there is an obstruction to decoupling the time- space noncommutativity scale from that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure. We study the moduli space of the obstruction in terms of the open- and closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally by considering complex values of the dilaton and inverting the role of space and time in the light cone. This is reminiscent of a black-hole horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity. (23 refs).

  3. Noncommutative differential forms on the kappa-deformed space

    International Nuclear Information System (INIS)

    Meljanac, Stjepan; Kresic-Juric, Sasa

    2009-01-01

    We construct a differential algebra of forms on the kappa-deformed space. For a given realization of noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.

  4. Space/time non-commutative field theories and causality

    International Nuclear Information System (INIS)

    Bozkaya, H.; Fischer, P.; Pitschmann, M.; Schweda, M.; Grosse, H.; Putz, V.; Wulkenhaar, R.

    2003-01-01

    As argued previously, amplitudes of quantum field theories on non-commutative space and time cannot be computed using naive path integral Feynman rules. One of the proposals is to use the Gell-Mann-Low formula with time-ordering applied before performing the integrations. We point out that the previously given prescription should rather be regarded as an interaction-point time-ordering. Causality is explicitly violated inside the region of interaction. It is nevertheless a consistent procedure, which seems to be related to the interaction picture of quantum mechanics. In this framework we compute the one-loop self-energy for a space/time non-commutative φ 4 theory. Although in all intermediate steps only three-momenta play a role, the final result is manifestly Lorentz covariant and agrees with the naive calculation. Deriving the Feynman rules for general graphs, we show, however, that such a picture holds for tadpole lines only. (orig.)

  5. Phase transition and entropy inequality of noncommutative black holes in a new extended phase space

    Energy Technology Data Exchange (ETDEWEB)

    Miao, Yan-Gang; Xu, Zhen-Ming, E-mail: miaoyg@nankai.edu.cn, E-mail: xuzhenm@mail.nankai.edu.cn [School of Physics, Nankai University, Tianjin 300071 (China)

    2017-03-01

    We analyze the thermodynamics of the noncommutative high-dimensional Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter distribution by regarding a noncommutative parameter as an independent thermodynamic variable named as the noncommutative pressure . In the new extended phase space that includes this noncommutative pressure and its conjugate variable, we reveal that the noncommutative pressure and the original thermodynamic pressure related to the negative cosmological constant make the opposite effects in the phase transition of the noncommutative black hole, i.e. the former dominates the UV regime while the latter does the IR regime, respectively. In addition, by means of the reverse isoperimetric inequality, we indicate that only the black hole with the Gaussian smeared matter distribution holds the maximum entropy for a given thermodynamic volume among the noncommutative black holes with various matter distributions.

  6. Pair production of Dirac particles in a d + 1-dimensional noncommutative space-time

    Energy Technology Data Exchange (ETDEWEB)

    Ousmane Samary, Dine [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin); N' Dolo, Emanonfi Elias; Hounkonnou, Mahouton Norbert [University of Abomey-Calavi, International Chair in Mathematical Physics and Applications (ICMPA-UNESCO Chair), Cotonou (Benin)

    2014-11-15

    This work addresses the computation of the probability of fermionic particle pair production in d + 1-dimensional noncommutative Moyal space. Using Seiberg-Witten maps, which establish relations between noncommutative and commutative field variables, up to the first order in the noncommutative parameter θ, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent, and space-dependent electric fields are considered and discussed. (orig.)

  7. Small Valdivia compact spaces

    CERN Document Server

    Kubi's, W; Kubi\\'s, Wieslaw; Michalewski, Henryk

    2005-01-01

    We prove a preservation theorem for the class of Valdivia compact spaces, which involves inverse sequences of ``simple'' retractions. Consequently, a compact space of weight $\\loe\\aleph_1$ is Valdivia compact iff it is the limit of an inverse sequence of metric compacta whose bonding maps are retractions. As a corollary, we show that the class of Valdivia compacta of weight at most $\\aleph_1$ is preserved both under retractions and under open 0-dimensional images. Finally, we characterize the class of all Valdivia compacta in the language of category theory, which implies that this class is preserved under all continuous weight preserving functors.

  8. Non-commutative phase space and its space-time symmetry

    International Nuclear Information System (INIS)

    Li Kang; Dulat Sayipjamal

    2010-01-01

    First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space. (authors)

  9. 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.

  10. PURE STATE ENTANGLEMENT ENTROPY IN NONCOMMUTATIVE 2D DE SITTER SPACE TIME

    Directory of Open Access Journals (Sweden)

    M.F Ghiti

    2014-12-01

    Full Text Available Using the general modified field equation, a general noncommutative Klein-Gordon equation up to the second order of the noncommutativity parameter is derived in the context of noncommutative 2D De Sitter space-time. Using Bogoliubov coefficients and a special technics called conformal time; the boson-antiboson pair creation density is determined. The Von Neumann boson-antiboson pair creation quantum entanglement entropy is presented to compute the entanglement between the modes created presented.

  11. Strong limit theorems in noncommutative L2-spaces

    CERN Document Server

    Jajte, Ryszard

    1991-01-01

    The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.

  12. Quantum Field Theory with a Minimal Length Induced from Noncommutative Space

    International Nuclear Information System (INIS)

    Lin Bing-Sheng; Chen Wei; Heng Tai-Hua

    2014-01-01

    From the inspection of noncommutative quantum mechanics, we obtain an approximate equivalent relation for the energy dependence of the Planck constant in the noncommutative space, which means a minimal length of the space. We find that this relation is reasonable and it can inherit the main properties of the noncommutative space. Based on this relation, we derive the modified Klein—Gordon equation and Dirac equation. We investigate the scalar field and ϕ 4 model and then quantum electrodynamics in our theory, and derive the corresponding Feynman rules. These results may be considered as reasonable approximations to those of noncommutative quantum field theory. Our theory also shows a connection between the space with a minimal length and the noncommutative space. (physics of elementary particles and fields)

  13. Realization of Cohen-Glashow very special relativity on noncommutative space-time.

    Science.gov (United States)

    Sheikh-Jabbari, M M; Tureanu, A

    2008-12-31

    We show that the Cohen-Glashow very special relativity (VSR) theory [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. 97, 021601 (2006)] can be realized as the part of the Poincaré symmetry preserved on a noncommutative Moyal plane with lightlike noncommutativity. Moreover, we show that the three subgroups relevant to VSR can also be realized in the noncommutative space-time setting. For all of these three cases, the noncommutativity parameter theta(mu upsilon) should be lightlike (theta(mu upsilon) theta mu upsilon = 0). We discuss some physical implications of this realization of the Cohen-Glashow VSR.

  14. Quadratic algebras and noncommutative integration of Klein-Gordon equations in non-steckel Riemann spaces

    International Nuclear Information System (INIS)

    Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.; Shirokov, I.V.

    1995-01-01

    The method of noncommutative integration of linear partial differential equations is used to solve the Klein-Gordon equations in Riemann space, in the case when the set of noncommutating symmetry operators of this equation for a quadratic algebra consists of one second-order operator and several first-order operators. Solutions that do not permit variable separation are presented

  15. On the Lie symmetry group for classical fields in noncommutative space

    Energy Technology Data Exchange (ETDEWEB)

    Pereira, Ricardo Martinho Lima Santiago [Universidade Federal da Bahia (UFBA), BA (Brazil); Instituto Federal da Bahia (IFBA), BA (Brazil); Ressureicao, Caio G. da [Universidade Federal da Bahia (UFBA), BA (Brazil). Inst. de Fisica; Vianna, Jose David M. [Universidade Federal da Bahia (UFBA), BA (Brazil); Universidade de Brasilia (UnB), DF (Brazil)

    2011-07-01

    Full text: An alternative way to include effects of noncommutative geometries in field theory is based on the concept of noncommutativity among degrees of freedom of the studied system. In this context it is reasonable to consider that, in the multiparticle noncommutative quantum mechanics (NCQM), the noncommutativity among degrees of freedom to discrete system with N particles is also verified. Further, an analysis of the classical limit of the single particle NCQM leads to a deformed Newtonian mechanics where the Newton's second law is modified in order to include the noncommutative parameter {theta}{sub {iota}j} and, for a one-dimensional discrete system with N particles, the dynamical evolution of each particle is given by this modified Newton's second law. Hence, applying the continuous limit to this multiparticle classical system it is possible to obtain a noncommutative extension of two -dimensional field theory in a noncommutative space. In the present communication we consider a noncommutative extension of the scalar field obtained from this approach and we analyze the Lie symmetries in order to compare the Lie group of this field with the usual scalar field in the commutative space. (author)

  16. Remarks on the formulation of quantum mechanics on noncommutative phase spaces

    International Nuclear Information System (INIS)

    Muthukumar, Balasundaram

    2007-01-01

    We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry

  17. 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.)

  18. Statistical mechanics of free particles on space with Lie-type noncommutativity

    Energy Technology Data Exchange (ETDEWEB)

    Shariati, Ahmad; Khorrami, Mohammad; Fatollahi, Amir H, E-mail: shariati@mailaps.or, E-mail: mamwad@mailaps.or, E-mail: ahfatol@gmail.co [Department of Physics, Alzahra University, Tehran 1993891167 (Iran, Islamic Republic of)

    2010-07-16

    Effects of Lie-type noncommutativity on thermodynamic properties of a system of free identical particles are investigated. A definition for finite volume of the configuration space is given, and the grandcanonical partition function in the thermodynamic limit is calculated. Two possible definitions for the pressure are discussed, which are equivalent when the noncommutativity vanishes. The thermodynamic observables are extracted from the partition function. Different limits are discussed where either the noncommutativity or the quantum effects are important. Finally, specific cases are discussed where the group is SU(2) or SO(3), and the partition function of a nondegenerate gas is calculated.

  19. Scalar-graviton interaction in the noncommutative space

    International Nuclear Information System (INIS)

    Brandt, F. T.; Elias-Filho, M. R.

    2006-01-01

    We obtain the leading order interaction between the graviton and the neutral scalar boson in the context of noncommutative field theory. Our approach makes use of the Ward identity associated with the invariance under a subgroup of symplectic diffeomorphisms

  20. LAPLACE-RUNGE-LENZ VECTOR IN QUANTUM MECHANICS IN NONCOMMUTATIVE SPACE

    Directory of Open Access Journals (Sweden)

    Peter Prešnajder

    2014-04-01

    Full Text Available The object under scrutiny is the dynamical symmetry connected with conservation of the Laplace-Runge-Lenz vector (LRL in the hydrogen atom problem solved by means of noncommutative quantum mechanics (NCQM. The considered noncommutative configuration space has such a “fuzzy”structure that the rotational invariance is not spoilt. An analogy with the LRL vector in the NCQM is brought to provide our results and also a comparison with the standard QM predictions.

  1. 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)

  2. On Some Isomorphisms between Bounded Linear Maps and Non-Commutative Lp-Spaces

    Directory of Open Access Journals (Sweden)

    E. J. Atto

    2014-04-01

    Full Text Available We define a particular space of bounded linear maps using a Von Neumann algebra and some operator spaces. By this, we prove some isomorphisms, and using interpolation in some particular cases, we get analogue of non-commutative Lp spaces.

  3. Stabilization of compactification volume in a noncommutative mini-super-phase-space

    International Nuclear Information System (INIS)

    Khosravi, N.; Sepangi, H.R.; Sheikh-Jabbari, M.M.

    2007-01-01

    We consider a class of generalized FRW type metrics in the context of higher dimensional Einstein gravity in which the extra dimensions are allowed to have different scale factors. It is shown that noncommutativity between the momenta conjugate to the internal space scale factors controls the power-law behavior of the scale factors in the extra dimensions, taming it to an oscillatory behavior. Hence noncommutativity among the internal momenta of the mini-super-phase-space can be used to explain stabilization of the compactification volume of the internal space in a higher dimensional gravity theory

  4. Noncommutative spaces and matrix embeddings on flat ℝ{sup 2n+1}

    Energy Technology Data Exchange (ETDEWEB)

    Karczmarek, Joanna L.; Yeh, Ken Huai-Che [Department of Physics and Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver (Canada)

    2015-11-23

    We conjecture an embedding operator which assigns, to any 2n+1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n+1)-dimensional Euclidean space. This corresponds to precisely defining a fuzzy D(2n)-brane corresponding to N D0-branes. Points on the emergent hypersurface correspond to zero eigenstates of the embedding operator, which have an interpretation as coherent states underlying the emergent noncommutative geometry. Using this correspondence, all physical properties of the emergent D(2n)-brane can be computed. We apply our conjecture to noncommutative flat and spherical spaces. As a by-product, we obtain a construction of a rotationally symmetric flat noncommutative space in 4 dimensions.

  5. Newton's second law in a non-commutative space

    International Nuclear Information System (INIS)

    Romero, Juan M.; Santiago, J.A.; Vergara, J. David

    2003-01-01

    In this Letter we show that corrections to Newton's second law appear if we assume a symplectic structure consistent with the commutation rules of the non-commutative quantum mechanics. For central field we find that the correction term breaks the rotational symmetry. For the Kepler problem, this term is similar to a Coriolis force

  6. Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces

    Science.gov (United States)

    Meljanac, Stjepan; Krešić–Jurić, Saša; Martinić, Tea

    2017-07-01

    This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra g0, we construct a Lie superalgebra g =g0⊕g1 containing noncommutative coordinates and one-forms. We show that g can be extended by a set of generators TAB whose action on the enveloping algebra U (g ) gives the commutation relations between monomials in U (g0 ) and one-forms. Realizations of noncommutative coordinates, one-forms, and the generators TAB as formal power series in a semicompleted Weyl superalgebra are found. In the special case dim(g0 ) =dim(g1 ) , we also find a realization of the exterior derivative on U (g0 ) . The realizations of these geometric objects yield a bicovariant differential calculus on U (g0 ) as a deformation of the standard calculus on the Euclidean space.

  7. Quantum theories on noncommutative spaces with nontrivial topology: Aharonov-Bohm and Casimir effects

    International Nuclear Information System (INIS)

    Chaichian, M.; Tureanu, A.; Demichev, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

    2001-02-01

    After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with nontrivial topology and the operator representation of the *-product on them, we consider the Aharonov-Bohm and Casimir effects for such spaces. For the case of the Aharonov-Bohm effect, we have obtained an explicit expression for the shift of the phase, which is gauge invariant in the NC sense. The Casimir energy of a field theory on a NC cylinder is divergent, while it becomes finite on a torus, when the dimensionless parameter of noncommutativity is a rational number. The latter corresponds to a well-defined physical picture. Certain distinctions from other treatments based on a different way of taking the noncommutativity into account are also discussed. (author)

  8. Search of wormholes in different dimensional non-commutative inspired space-times with Lorentzian distribution

    Energy Technology Data Exchange (ETDEWEB)

    Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India)

    2014-12-01

    In this paper we ask whether the wormhole solutions exist in different dimensional noncommutativity-inspired spacetimes. It is well known that the noncommutativity of the space is an outcome of string theory and it replaced the usual point-like object by a smeared object. Here we have chosen the Lorentzian distribution as the density function in the noncommutativity-inspired spacetime. We have observed that the wormhole solutions exist only in four and five dimensions; however, in higher than five dimensions no wormhole exists. For five dimensional spacetime, we get a wormhole for a restricted region. In the usual four dimensional spacetime, we get a stable wormhole which is asymptotically flat. (orig.)

  9. Noncommutative configuration space. Classical and quantum mechanical aspects

    OpenAIRE

    Vanhecke, F. J.; Sigaud, C.; da Silva, A. R.

    2005-01-01

    In this work we examine noncommutativity of position coordinates in classical symplectic mechanics and its quantisation. In coordinates $\\{q^i,p_k\\}$ the canonical symplectic two-form is $\\omega_0=dq^i\\wedge dp_i$. It is well known in symplectic mechanics {\\bf\\cite{Souriau,Abraham,Guillemin}} that the interaction of a charged particle with a magnetic field can be described in a Hamiltonian formalism without a choice of a potential. This is done by means of a modified symplectic two-form $\\ome...

  10. Perturbed nonlinear models from noncommutativity

    International Nuclear Information System (INIS)

    Cabrera-Carnero, I.; Correa-Borbonet, Luis Alejandro; Valadares, G.C.S.

    2007-01-01

    By means of the Ehrenfest's Theorem inside the context of a noncommutative Quantum Mechanics it is obtained the Newton's Second Law in noncommutative space. Considering discrete systems with infinite degrees of freedom whose dynamical evolutions are governed by the noncommutative Newton's Second Law we have constructed some alternative noncommutative generalizations of two-dimensional field theories. (author)

  11. Quantum mechanical systems interacting with different polarizations of gravitational waves in noncommutative phase space

    Science.gov (United States)

    Saha, Anirban; Gangopadhyay, Sunandan; Saha, Swarup

    2018-02-01

    Owing to the extreme smallness of any noncommutative scale that may exist in nature, both in the spatial and momentum sector of the quantum phase space, a credible possibility of their detection lies in the gravitational wave (GW) detection scenario, where one effectively probes the relative length-scale variations ˜O [10-20-10-23] . With this motivation, we have theoretically constructed how a free particle and a harmonic oscillator will respond to linearly and circularly polarized gravitational waves if their quantum mechanical phase space has a noncommutative structure. We critically analyze the formal solutions which show resonance behavior in the responses of both free particle and HO systems to GW with both kind of polarizations. We discuss the possible implications of these solutions in detecting noncommutativity in a GW detection experiment. We use the currently available upper-bound estimates on various noncommutative parameters to anticipate the relative importance of various terms in the solutions. We also argue how the quantum harmonic oscillator system we considered here can be very relevant in the context of the resonant bar detectors of GW which are already operational.

  12. An introduction to noncommutative spaces and their geometries characterization of the shallow subsurface implications for urban infrastructure and environmental assessment

    CERN Document Server

    Landi, Giovanni

    1997-01-01

    These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory. Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topolo...

  13. Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory

    CERN Document Server

    Landau, Olav Arnfinn

    2011-01-01

    This is a monograph about non-commutative algebraic geometry, and its application to physics. The main mathematical inputs are the non-commutative deformation theory, moduli theory of representations of associative algebras, a new non-commutative theory o

  14. On Yang's Noncommutative Space Time Algebra, Holography, Area Quantization and C-space Relativity

    CERN Document Server

    Castro, C

    2004-01-01

    An isomorphism between Yang's Noncommutative space-time algebra (involving two length scales) and the holographic-area-coordinates algebra of C-spaces (Clifford spaces) is constructed via an AdS_5 space-time which is instrumental in explaining the origins of an extra (infrared) scale R in conjunction to the (ultraviolet) Planck scale lambda characteristic of C-spaces. Yang's space-time algebra allowed Tanaka to explain the origins behind the discrete nature of the spectrum for the spatial coordinates and spatial momenta which yields a minimum length-scale lambda (ultraviolet cutoff) and a minimum momentum p = (\\hbar / R) (maximal length R, infrared cutoff). The double-scaling limit of Yang's algebra : lambda goes to 0, and R goes to infinity, in conjunction with the large n infinity limit, leads naturally to the area quantization condition : lambda R = L^2 = n lambda^2 (in Planck area units) given in terms of the discrete angular-momentum eigenvalues n . The generalized Weyl-Heisenberg algebra in C-spaces is ...

  15. 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

  16. Quantum gravity boundary terms from the spectral action of noncommutative space.

    Science.gov (United States)

    Chamseddine, Ali H; Connes, Alain

    2007-08-17

    We study the boundary terms of the spectral action of the noncommutative space, defined by the spectral triple dictated by the physical spectrum of the standard model, unifying gravity with all other fundamental interactions. We prove that the spectral action predicts uniquely the gravitational boundary term required for consistency of quantum gravity with the correct sign and coefficient. This is a remarkable result given the lack of freedom in the spectral action to tune this term.

  17. Scattering theory of space-time non-commutative abelian gauge field theory

    International Nuclear Information System (INIS)

    Rim, Chaiho; Yee, Jaehyung

    2005-01-01

    The unitary S-matrix for space-time non-commutative quantum electrodynamics is constructed using the *-time ordering which is needed in the presence of derivative interactions. Based on this S-matrix, we formulate the perturbation theory and present the Feynman rule. We then apply this perturbation analysis to the Compton scattering process to the lowest order and check the gauge invariance of the scattering amplitude at this order.

  18. Some consequences of a non-commutative space-time structure

    International Nuclear Information System (INIS)

    Vilela Mendes, R.

    2005-01-01

    The existence of a fundamental length (or fundamental time) has been conjectured in many contexts. Here we discuss some consequences of a fundamental constant of this type, which emerges as a consequence of deformation-stability considerations leading to a non-commutative space-time structure. This mathematically well defined structure is sufficiently constrained to allow for unambiguous experimental predictions. In particular we discuss the phase-space volume modifications and their relevance for the calculation of the Greisen-Zatsepin-Kuz'min sphere. The (small) corrections to the spectrum of the Coulomb problem are also computed. (orig.)

  19. Noncommutative baby Skyrmions

    International Nuclear Information System (INIS)

    Ioannidou, Theodora; Lechtenfeld, Olaf

    2009-01-01

    We subject the baby Skyrme model to a Moyal deformation, for unitary or Grassmannian target spaces and without a potential term. In the Abelian case, the radial BPS configurations of the ordinary noncommutative sigma model also solve the baby Skyrme equation of motion. This gives a class of exact analytic noncommutative baby Skyrmions, which have a singular commutative limit but are stable against scaling due to the noncommutativity. We compute their energies, investigate their stability and determine the asymptotic two-Skyrmion interaction.

  20. Noncommutative solitons: moduli spaces, quantization, finite θ effects and stability

    Science.gov (United States)

    Hadasz, Leszek; Rocek, Martin; Lindström, Ulf; von Unge, Rikard

    2001-06-01

    We find the N-soliton solution at infinite θ, as well as the metric on the moduli space corresponding to spatial displacements of the solitons. We use a perturbative expansion to incorporate the leading θ-1 corrections, and find an effective short range attraction between solitons. We study the stability of various solutions. We discuss the finite θ corrections to scattering, and find metastable orbits. Upon quantization of the two-soliton moduli space, for any finite θ, we find an s-wave bound state.

  1. q-deformed superstatistics of the Schrödinger equation in commutative and noncommutative spaces with magnetic field

    Science.gov (United States)

    Sargolzaeipor, S.; Hassanabadi, H.; Chung, W. S.

    2018-01-01

    We discuss the q-deformed algebra and study the Schrödinger equation in commutative and noncommutative spaces, under an external magnetic field. In this work, we obtain the energy spectrum by an analytical method and the thermodynamic properties of the system by using the q-deformed superstatistics are calculated. Actually, we derive a generalized version of the ordinary superstatistic for the non-equilibrium systems. Also, different effective Boltzmann factor descriptions are derived. In addition, we discuss about the results for various values of θ in commutative and noncommutative spaces and, to illustrate the results, some figures are plotted.

  2. The Gribov problem in noncommutative QED

    Energy Technology Data Exchange (ETDEWEB)

    Canfora, Fabrizio [Centro de Estudios Científicos (CECS),Casilla 1469, Valdivia (Chile); Kurkov, Maxim A. [Dipartimento di Matematica, Università di Napoli Federico II,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); CMCC-Universidade Federal do ABC,Santo André, S.P. (Brazil); INFN, Sezione di Napoli,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); Rosa, Luigi; Vitale, Patrizia [Dipartimento di Fisica, Università di Napoli Federico II,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy); INFN, Sezione di Napoli,Monte S. Angelo, Via Cintia, 80126 Napoli (Italy)

    2016-01-04

    It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.

  3. A short essay on quantum black holes and underlying noncommutative quantized space-time

    International Nuclear Information System (INIS)

    Tanaka, Sho

    2017-01-01

    We emphasize the importance of noncommutative geometry or Lorenz-covariant quantized space-time towards the ultimate theory of quantum gravity and Planck scale physics. We focus our attention on the statistical and substantial understanding of the Bekenstein–Hawking area-entropy law of black holes in terms of the kinematical holographic relation (KHR). KHR manifestly holds in Yang’s quantized space-time as the result of kinematical reduction of spatial degrees of freedom caused by its own nature of noncommutative geometry, and plays an important role in our approach without any recourse to the familiar hypothesis, so-called holographic principle. In the present paper, we find a unified form of KHR applicable to the whole region ranging from macroscopic to microscopic scales in spatial dimension d   =  3. We notice a possibility of nontrivial modification of area-entropy law of black holes which becomes most remarkable in the extremely microscopic system close to Planck scale. (paper)

  4. Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

    Science.gov (United States)

    Jurco, B.; Schraml, S.; Schupp, P.; Wess, J.

    2000-11-01

    An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces.

  5. Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

    International Nuclear Information System (INIS)

    Jurco, B.; Schraml, S.; Wess, J.; Schupp, P.

    2000-01-01

    An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces. (orig.)

  6. Enveloping algebra-valued gauge transformations for non-abelian gauge groups on non-commutative spaces

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B. [Max-Planck-Institut fuer Mathematik, Bonn (Germany); Schraml, S.; Wess, J. [Max-Planck-Institut fuer Physik, Foehringer Ring 6, 80805 Muenchen (Germany); Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany); Schupp, P. [Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)

    2000-11-01

    An enveloping algebra-valued gauge field is constructed, its components are functions of the Lie algebra-valued gauge field and can be constructed with the Seiberg-Witten map. This allows the formulation of a dynamics for a finite number of gauge field components on non-commutative spaces. (orig.)

  7. Compact space-like hypersurfaces in de Sitter space

    OpenAIRE

    Lv, Jinchi

    2005-01-01

    We present some integral formulas for compact space-like hypersurfaces in de Sitter space and some equivalent characterizations for totally umbilical compact space-like hypersurfaces in de Sitter space in terms of mean curvature and higher-order mean curvatures.

  8. Compact variable rate laser for space application

    Data.gov (United States)

    National Aeronautics and Space Administration — We will focus on the development and test of high reliable, radiation tolerant, compact laser for planetary mission.  The laser will be able to operate at variable...

  9. Compactly supported frames for decomposition spaces

    DEFF Research Database (Denmark)

    Nielsen, Morten; Rasmussen, Kenneth Niemann

    2012-01-01

    In this article we study a construction of compactly supported frame expansions for decomposition spaces of Triebel-Lizorkin type and for the associated modulation spaces. This is done by showing that finite linear combinations of shifts and dilates of a single function with sufficient decay in b...

  10. Sobolev Spaces on Locally Compact Abelian Groups: Compact Embeddings and Local Spaces

    Directory of Open Access Journals (Sweden)

    Przemysław Górka

    2014-01-01

    Full Text Available We continue our research on Sobolev spaces on locally compact abelian (LCA groups motivated by our work on equations with infinitely many derivatives of interest for string theory and cosmology. In this paper, we focus on compact embedding results and we prove an analog for LCA groups of the classical Rellich lemma and of the Rellich-Kondrachov compactness theorem. Furthermore, we introduce Sobolev spaces on subsets of LCA groups and study its main properties, including the existence of compact embeddings into Lp-spaces.

  11. Noncommutative field gas driven inflation

    Energy Technology Data Exchange (ETDEWEB)

    Barosi, Luciano; Brito, Francisco A [Departamento de Fisica, Universidade Federal de Campina Grande, Caixa Postal 10071, 58109-970 Campina Grande, Paraiba (Brazil); Queiroz, Amilcar R, E-mail: lbarosi@ufcg.edu.br, E-mail: fabrito@df.ufcg.edu.br, E-mail: amilcarq@gmail.com [Centro Internacional de Fisica da Materia Condensada, Universidade de Brasilia, Caixa Postal 04667, Brasilia, DF (Brazil)

    2008-04-15

    We investigate early time inflationary scenarios in a Universe filled with a dilute noncommutative bosonic gas at high temperature. A noncommutative bosonic gas is a gas composed of a bosonic scalar field with noncommutative field space on a commutative spacetime. Such noncommutative field theories were recently introduced as a generalization of quantum mechanics on a noncommutative spacetime. Key features of these theories are Lorentz invariance violation and CPT violation. In the present study we use a noncommutative bosonic field theory that, besides the noncommutative parameter {theta}, shows up a further parameter {sigma}. This parameter {sigma} controls the range of the noncommutativity and acts as a regulator for the theory. Both parameters play a key role in the modified dispersion relations of the noncommutative bosonic field, leading to possible striking consequences for phenomenology. In this work we obtain an equation of state p = {omega}({sigma},{theta};{beta}){rho} for the noncommutative bosonic gas relating pressure p and energy density {rho}, in the limit of high temperature. We analyse possible behaviours for these gas parameters {sigma}, {theta} and {beta}, so that -1{<=}{omega}<-1/3, which is the region where the Universe enters an accelerated phase.

  12. Time-dependent transitions with time–space noncommutativity and its implications in quantum optics

    International Nuclear Information System (INIS)

    Chandra, Nitin

    2012-01-01

    We study the time-dependent transitions of a quantum-forced harmonic oscillator in noncommutative R 1,1 perturbatively to linear order in the noncommutativity θ. We show that the Poisson distribution gets modified, and that the vacuum state evolves into a ‘squeezed’ state rather than a coherent state. The time evolutions of uncertainties in position and momentum in vacuum are also studied and imply interesting consequences for modeling nonlinear phenomena in quantum optics. (paper)

  13. Einstein-Podolski-Rosen experiment from noncommutative quantum gravity

    International Nuclear Information System (INIS)

    Heller, Michael; Sasin, Wieslaw

    1998-01-01

    It is shown that the Einstein-Podolski-Rosen type experiments are the natural consequence of the groupoid approach to noncommutative unification of general relativity and quantum mechanics. The geometry of this model is determined by the noncommutative algebra A=C c ∞ (G,C) of complex valued, compactly supported, functions (with convolution as multiplication) on the groupoid G=ExΓ. In the model considered in the present paper E is the total space of the frame bundle over space-time and Γ is the Lorentz group. The correlations of the EPR type should be regarded as remnants of the totally non-local physics below the Planck threshold which is modelled by a noncommutative geometry

  14. The moduli space of two U(1) instantons on noncommutative $R^4$ and $R^3\\times S^1$

    OpenAIRE

    Lee, Kimyeong; Tong, David; Yi, Sangheon

    2000-01-01

    We employ the ADHM method to derive the moduli space of two instantons in U(1) gauge theory on a noncommutative space. We show by an explicit hyperK\\"ahler quotient construction that the relative metric of the moduli space of two instantons on $R^4$ is the Eguchi-Hanson metric and find a unique threshold bound state. For two instantons on $R^3\\times S^1$, otherwise known as calorons, we give the asymptotic metric and conjecture a completion. We further discuss the relationship of caloron modu...

  15. Non-commutative representation for quantum systems on Lie groups

    Energy Technology Data Exchange (ETDEWEB)

    Raasakka, Matti Tapio

    2014-01-27

    space path integral with the help of the non-commutative dual variables. In studying the classical limit of the path integral, we show that we recover the correct classical equations of motion for the particle, if we account for the deformation of the phase space in the variational calculus. The non-commutative variables correspond in this limit to the classical momentum variables, further verifying their physical interpretation. We conclude that the non-commutative harmonic analysis facilitates a convenient study of the classical limit of quantum dynamics on a Lie group even if the group is compact, in which case variational calculus cannot easily be applied. As the second physics application, we repeat our above considerations for the case of Ponzano-Regge spin foam model for 3-dimensional quantum gravity. The non-commutative dual variables correspond in this case to discrete metric variables, thus illuminating the geometrical interpretation of the model. Again, we find that a convenient study of the classical limit is made possible through the non-commutative phase space path integral.

  16. Non-commutative representation for quantum systems on Lie groups

    International Nuclear Information System (INIS)

    Raasakka, Matti Tapio

    2014-01-01

    integral with the help of the non-commutative dual variables. In studying the classical limit of the path integral, we show that we recover the correct classical equations of motion for the particle, if we account for the deformation of the phase space in the variational calculus. The non-commutative variables correspond in this limit to the classical momentum variables, further verifying their physical interpretation. We conclude that the non-commutative harmonic analysis facilitates a convenient study of the classical limit of quantum dynamics on a Lie group even if the group is compact, in which case variational calculus cannot easily be applied. As the second physics application, we repeat our above considerations for the case of Ponzano-Regge spin foam model for 3-dimensional quantum gravity. The non-commutative dual variables correspond in this case to discrete metric variables, thus illuminating the geometrical interpretation of the model. Again, we find that a convenient study of the classical limit is made possible through the non-commutative phase space path integral.

  17. Open branes in space-time non-commutative little string theory

    International Nuclear Information System (INIS)

    Harmark, T.

    2001-01-01

    We conjecture the existence of two new non-gravitational six-dimensional string theories, defined as the decoupling limit of NS5-branes in the background of near-critical electrical two- and three-form RR fields. These theories are space-time non-commutative Little String Theories with open branes. The theory with (2,0) supersymmetry has an open membrane in the spectrum and reduces to OM theory at low energies. The theory with (1,1) supersymmetry has an open string in the spectrum and reduces to (5+1)-dimensional NCOS theory for weak NCOS coupling and low energies. The theories are shown to be T-dual with the open membrane being T-dual to the open string. The theories therefore provide a connection between (5+1)-dimensional NCOS theory and OM theory. We study the supergravity duals of these theories and we consider a chain of dualities that shows how the T-duality between the two theories is connected with the S-duality between (4+1)-dimensional NCOS theory and OM theory

  18. Noncommutative QED and anomalous dipole moments

    International Nuclear Information System (INIS)

    Riad, I.F.; Sheikh-Jabbari, M.M.

    2000-09-01

    We study QED on noncommutative spaces, NCQED. In particular we present the detailed calculation for the noncommutative electron-photon vertex and show that the Ward identity is satisfied. We discuss that in the noncommutative case moving electron will show electric dipole effects. In addition, we work out the electric and magnetic dipole moments up to one loop level. For the magnetic moment we show that noncommutative electron has an intrinsic (spin independent) magnetic moment. (author)

  19. Noncommutative Lagrange Mechanics

    Directory of Open Access Journals (Sweden)

    Denis Kochan

    2008-02-01

    Full Text Available It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy, which are extensively applied within noncommutative quantum theories. Newton-Lagrange noncommutative equations of motion are formulated and their properties are analyzed from the pure geometrical point of view. It is argued that the dynamical quintessence of the system consists in its kinetic energy (Riemannian metric specifying Riemann-Levi-Civita connection and thus the inertia geodesics of the free motion. Throughout the paper, ''noncommutativity'' is considered as an internal geometric structure of the configuration space, which can not be ''observed'' per se. Manifestation of the noncommutative phenomena is mediated by the interaction of the system with noncommutative background under the consideration. The simplest model of the interaction (minimal coupling is proposed and it is shown that guiding affine connection is modified by the quadratic analog of the Lorentz electromagnetic force (contortion term.

  20. Arithmetic noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2005-01-01

    Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

  1. Noncommutative gravity

    International Nuclear Information System (INIS)

    Schupp, P.

    2007-01-01

    Heuristic arguments suggest that the classical picture of smooth commutative spacetime should be replaced by some kind of quantum / noncommutative geometry at length scales and energies where quantum as well as gravitational effects are important. Motivated by this idea much research has been devoted to the study of quantum field theory on noncommutative spacetimes. More recently the focus has started to shift back to gravity in this context. We give an introductory overview to the formulation of general relativity in a noncommutative spacetime background and discuss the possibility of exact solutions. (author)

  2. Instantons, quivers and noncommutative Donaldson-Thomas theory

    Science.gov (United States)

    Cirafici, Michele; Sinkovics, Annamaria; Szabo, Richard J.

    2011-12-01

    We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

  3. Instantons, quivers and noncommutative Donaldson-Thomas theory

    Energy Technology Data Exchange (ETDEWEB)

    Cirafici, Michele, E-mail: cirafici@math.ist.utl.pt [Centro de Analise Matematica, Geometria e Sistemas Dinamicos, Departamento de Matematica, Instituto Superior Tecnico, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Sinkovics, Annamaria, E-mail: A.Sinkovics@damtp.cam.ac.uk [Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Szabo, Richard J., E-mail: R.J.Szabo@ma.hw.ac.uk [Department of Mathematics, Heriot-Watt University, Colin Maclaurin Building, Riccarton, Edinburgh EH14 4AS (United Kingdom); Maxwell Institute for Mathematical Sciences, Edinburgh (United Kingdom)

    2011-12-11

    We construct noncommutative Donaldson-Thomas invariants associated with abelian orbifold singularities by analyzing the instanton contributions to a six-dimensional topological gauge theory. The noncommutative deformation of this gauge theory localizes on noncommutative instantons which can be classified in terms of three-dimensional Young diagrams with a colouring of boxes according to the orbifold group. We construct a moduli space for these gauge field configurations which allows us to compute its virtual numbers via the counting of representations of a quiver with relations. The quiver encodes the instanton dynamics of the noncommutative gauge theory, and is associated to the geometry of the singularity via the generalized McKay correspondence. The index of BPS states which compute the noncommutative Donaldson-Thomas invariants is realized via topological quantum mechanics based on the quiver data. We illustrate these constructions with several explicit examples, involving also higher rank Coulomb branch invariants and geometries with compact divisors, and connect our approach with other ones in the literature.

  4. Noncommutative black-body radiation: Implications on cosmic microwave background

    International Nuclear Information System (INIS)

    Fatollahi, A.H.; Hajirahimi, M.

    2006-01-01

    Including loop corrections, black-body radiation in noncommutative space is anisotropic. A direct implication of possible space non-commutativity on the cosmic microwave background map is argued. (authors)

  5. Fock space representation of differential calculus on the noncommutative quantum space

    International Nuclear Information System (INIS)

    Mishra, A.K.; Rajasekaran, G.

    1997-01-01

    A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed. The concept of statistical transmutation between bosons and fermions is introduced. copyright 1997 American Institute of Physics

  6. Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative black hole space-time

    Science.gov (United States)

    Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.

    2018-06-01

    We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

  7. Noncommutativity from spectral flow

    Energy Technology Data Exchange (ETDEWEB)

    Heinzl, Thomas; Ilderton, Anton [School of Mathematics and Statistics, University of Plymouth, Drake Circus, Plymouth PL4 8AA (United Kingdom)

    2007-07-27

    We investigate the transition from second- to first-order systems. Quantum mechanically, this transforms configuration space into phase space and hence introduces noncommutativity in the former. This transition may be described in terms of spectral flow. Gaps in the energy or mass spectrum may become large which effectively truncates the available state space. Using both operator and path integral languages we explicitly discuss examples in quantum mechanics (light-front) quantum field theory and string theory.

  8. Noncommutative quantum electrodynamics in path integral framework

    Energy Technology Data Exchange (ETDEWEB)

    Bourouaine, S; Benslama, A [Departement de Physique, Faculte des Sciences, Universite Mentouri, Constantine (Algeria)

    2005-08-19

    In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative {theta} matrix.

  9. Noncommutative quantum electrodynamics in path integral framework

    International Nuclear Information System (INIS)

    Bourouaine, S; Benslama, A

    2005-01-01

    In this paper, the dynamics of a relativistic particle of spin 1/2, interacting with an external electromagnetic field in noncommutative space, is studied in the path integral framework. By adopting the Fradkin-Gitman formulation, the exact Green's function in noncommutative space (NCGF) for the quadratic case of a constant electromagnetic field is computed, and it is shown that its form is similar to its counterpart given in commutative space. In addition, it is deduced that the effect of noncommutativity has the same effect as an additional constant field depending on a noncommutative θ matrix

  10. The Lω-Compactness in Lω-Spaces

    Directory of Open Access Journals (Sweden)

    Shui-Li Chen

    2013-01-01

    Full Text Available The concepts of αω-remote neighborhood family, γω-cover, and Lω-compactness are defined in Lω-spaces. The characterizations of Lω-compactness are systematically discussed. Some important properties of Lω-compactness such as ω-closed heredity, arbitrarily multiplicative property, and preserving invariance under ω-continuous mappings are obtained. Finally, the Alexander ω-subbase lemma and the Tychonoff product theorem with respect to Lω-compactness are given.

  11. Quantum symmetries of classical spaces

    OpenAIRE

    Bhowmick, Jyotishman; Goswami, Debashish; Roy, Subrata Shyam

    2009-01-01

    We give a general scheme for constructing faithful actions of genuine (noncommutative as $C^*$ algebra) compact quantum groups on classical topological spaces. Using this, we show that: (i) a compact connected classical space can have a faithful action by a genuine compact quantum group, and (ii) there exists a spectral triple on a classical connected compact space for which the quantum group of orientation and volume preserving isometries (in the sense of \\cite{qorient}) is a genuine quantum...

  12. Polarized electron-muon neutrino scattering to electron and neutrino in noncommutative space

    Directory of Open Access Journals (Sweden)

    MM Ettefaghi

    2011-06-01

    Full Text Available For neutrino scattering from polarized electron, the weak interaction term in the cross section is significantly suppressed by the polarized term. The magnetic moment term does not receive any correction from the electron polarization. Hence, the study of the magnetic moment of neutrinos through scattering from the polarized electron leads to a stronger bound on the neutrino magnetic moment compared with the unpolarized case. On the other hand, neutrinos which are electrically neutral can couple directly with photons in Noncommutative (NC QED. In this paper, we calculate the NC QED corrections on this scattering are calculated. The phase difference between the NC term and the polarized weak interaction term is π/2. Therefore, the NC term does not destroy the above suppression.

  13. Strong coupling effects in non-commutative spaces from OM theory and supergravity

    International Nuclear Information System (INIS)

    Russo, J.G.; Sheikh-Jabbari, M.M.

    2000-11-01

    We show that a four-parameter class of 3+1 dimensional NCOS theories can be obtained by dimensional reduction on a general 2-torus from OM theory. Compactifying two spatial directions of NCOS theory on a 2-torus, we study the transformation properties under the SO(2,2; Z) T-duality group. We then discuss non-perturbative configurations of non-commutative super Yang-Mills theory. In particular, we calculate the tension for magnetic monopoles and (p,q) dyons and exhibit their six-dimensional origin, and construct a supergravity solution representing an instanton in the gauge theory. We also compute the potential for a monopole-antimonopole in the supergravity approximation. (author)

  14. Noncommutative time in quantum field theory

    International Nuclear Information System (INIS)

    Salminen, Tapio; Tureanu, Anca

    2011-01-01

    We analyze, starting from first principles, the quantization of field theories, in order to find out to which problems a noncommutative time would possibly lead. We examine the problem in the interaction picture (Tomonaga-Schwinger equation), the Heisenberg picture (Yang-Feldman-Kaellen equation), and the path integral approach. They all indicate inconsistency when time is taken as a noncommutative coordinate. The causality issue appears as the key aspect, while the unitarity problem is subsidiary. These results are consistent with string theory, which does not admit a time-space noncommutative quantum field theory as its low-energy limit, with the exception of lightlike noncommutativity.

  15. Non-commutative analysis

    CERN Document Server

    Jorgensen, Palle

    2017-01-01

    The book features new directions in analysis, with an emphasis on Hilbert space, mathematical physics, and stochastic processes. We interpret 'non-commutative analysis' broadly to include representations of non-Abelian groups, and non-Abelian algebras; emphasis on Lie groups and operator algebras (C* algebras and von Neumann algebras.)A second theme is commutative and non-commutative harmonic analysis, spectral theory, operator theory and their applications. The list of topics includes shift invariant spaces, group action in differential geometry, and frame theory (over-complete bases) and their applications to engineering (signal processing and multiplexing), projective multi-resolutions, and free probability algebras.The book serves as an accessible introduction, offering a timeless presentation, attractive and accessible to students, both in mathematics and in neighboring fields.

  16. Nonabelian noncommutative gauge theory via noncommutative extra dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, Branislav E-mail: jurco@theorie.physik.uni-muenchen.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

    2001-06-18

    The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map). As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric.

  17. Nonabelian noncommutative gauge theory via noncommutative extra dimensions

    International Nuclear Information System (INIS)

    Jurco, Branislav; Schupp, Peter; Wess, Julius

    2001-01-01

    The concept of covariant coordinates on noncommutative spaces leads directly to gauge theories with generalized noncommutative gauge fields of the type that arises in string theory with background B-fields. The theory is naturally expressed in terms of cochains in an appropriate cohomology; we discuss how it fits into the framework of projective modules. The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map). As application we show the exact equality of the Dirac-Born-Infeld action with B-field in the commutative setting and its semi-noncommutative cousin in the intermediate picture. Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; an explicit map between abelian and nonabelian gauge fields is given. All constructions are also valid for non-constant B-field, Poisson structure and metric

  18. Noncommutative field theory

    International Nuclear Information System (INIS)

    Douglas, Michael R.; Nekrasov, Nikita A.

    2001-01-01

    This article reviews the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, on both the classical and the quantum level

  19. Noncommutative solitons

    International Nuclear Information System (INIS)

    Gopakumar, R.

    2002-01-01

    Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect

  20. Noncommutative solitons

    Energy Technology Data Exchange (ETDEWEB)

    Gopakumar, R [Harish-Chandra Research Institute, Jhusi, Allahabad (India)

    2002-05-15

    Though noncommutative field theories have been explored for several years, a resurgence of interest in it was sparked off after it was realised that they arise very naturally as limits of string theory in certain background fields. It became more plausible (at least to string theorists) that these nonlocal deformations of usual quantum field theories are consistent theories in themselves. This led to a detailed exploration of many of their classical and quantum properties. I will elaborate further on the string theory context in the next section. One of the consequences of this exploration was the discovery of novel classical solutions in noncommutative field theories. Since then much work has been done in exploring many of their novel properties. My lectures focussed on some specific aspects of these noncommutative solitons. They primarily reflect the topics that I have worked on and are not intended to be a survey of the large amount of work on this topic. We have tried to give a flavour of the physics that can be captured by the relatively elementary classical solutions of noncommutative field theories. We have seen in different contexts how these solitons are really simple manifestations of D-branes, possessing many of their important features. Though they have been primarily studied in the context of tachyon condensation, we saw that they can also shed some light on the resolution of singularities in spacetime by D-brane probes. In addition to other applications in string theory it is important at this stage to explore their presence in other systems with a strong magnetic field like the quantum hall effect.

  1. Vector fields and differential operators: noncommutative case

    International Nuclear Information System (INIS)

    Borowiec, A.

    1997-01-01

    A notion of Cartan pairs as an analogy of vector fields in the realm of noncommutative geometry has been proposed previously. In this paper an outline is given of the construction of a noncommutative analogy of the algebra of differential operators as well as its (algebraic) Fock space realization. Co-universal vector fields and covariant derivatives will also be discussed

  2. Quantum information aspects of noncommutative quantum mechanics

    Science.gov (United States)

    Bertolami, Orfeu; Bernardini, Alex E.; Leal, Pedro

    2018-01-01

    Some fundamental aspects related with the construction of Robertson-Schrödinger-like uncertainty-principle inequalities are reported in order to provide an overall description of quantumness, separability and nonlocality of quantum systems in the noncommutative phase-space. Some consequences of the deformed noncommutative algebra are also considered in physical systems of interest.

  3. More on θ-compact fuzzy topological spaces

    International Nuclear Information System (INIS)

    Ekici, Erdal

    2006-01-01

    Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum particle physics in connection with string theory and ε ∞ theory. In 2005, Caldas and Jafari have introduced θ-compact fuzzy topological spaces. The purpose of this paper is to investigate further properties of θ-compact fuzzy topological spaces. Moreover, the notion of θ-closed fuzzy topological spaces is introduced and properties of it are obtained

  4. Noncommutative Geometry, Quantum Fields and Motives

    CERN Document Server

    Connes, Alain

    2007-01-01

    The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book dea

  5. Noncommutative geometry

    CERN Document Server

    Connes, Alain

    1994-01-01

    This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields.Key Features* First full treatment of the subject and its applications* Written by the pioneer of this field* Broad applications in mathemat

  6. On the Chabauty space of locally compact abelian groups

    OpenAIRE

    Cornulier, Yves

    2010-01-01

    This paper contains several results about the Chabauty space of a general locally compact abelian group. Notably, we determine its topological dimension, we characterize when it is totally disconnected or connected; we characterize isolated points.

  7. Acceleration radiation in a compact space

    International Nuclear Information System (INIS)

    Copeland, E.J.; Davies, P.C.W.; Hinton, K.

    1984-01-01

    The response is studied of a uniformly accelerated model particle detector in a spacetime with compact spatial sections. The basic thermal character of the response re-emerges, in spite of the fact that the spacetime does not possess event horizons. The model also permits a study of detector response to twisted field states. (author)

  8. Exact multi-line soliton solutions of noncommutative KP equation

    International Nuclear Information System (INIS)

    Wang, Ning; Wadati, Miki

    2003-01-01

    A method of solving noncommutative linear algebraic equations plays a key role in the extension of the ∂-bar -dressing on the noncommutative space-time manifold. In this paper, a solution-generating method of noncommutative linear algebraic equations is proposed. By use of the proposed method, a class of multi-line soliton solutions of noncommutative KP (ncKP) equation is constructed explicitly. The method is expected to be of use for constructions of noncommutative soliton equations. The significance of the noncommutativity of coordinates is investigated. It is found that the noncommutativity of the space-time coordinate has a role to split the spatial waveform of the classical multi-line solitons and reform it to a new configuration. (author)

  9. Noncommutative Gauge Theory with Covariant Star Product

    International Nuclear Information System (INIS)

    Zet, G.

    2010-01-01

    We present a noncommutative gauge theory with covariant star product on a space-time with torsion. In order to obtain the covariant star product one imposes some restrictions on the connection of the space-time. Then, a noncommutative gauge theory is developed applying this product to the case of differential forms. Some comments on the advantages of using a space-time with torsion to describe the gravitational field are also given.

  10. Noncommutative instantons via dressing and splitting approaches

    International Nuclear Information System (INIS)

    Horvath, Zalan; Lechtenfeld, Olaf; Wolf, Martin

    2002-01-01

    Almost all known instanton solutions in noncommutative Yang-Mills theory have been obtained in the modified ADHM scheme. In this paper we employ two alternative methods for the construction of the self-dual U(2) BPST instanton on a noncommutative euclidean four-dimensional space with self-dual noncommutativity tensor. Firstly, we use the method of dressing transformations, an iterative procedure for generating solutions from a given seed solution, and thereby generalize Belavin's and Zakharov's work to the noncommutative setup. Secondly, we relate the dressing approach with Ward's splitting method based on the twistor construction and rederive the solution in this context. It seems feasible to produce nonsingular noncommutative multi-instantons with these techniques. (author)

  11. Weak compactness and sigma-Asplund generated Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Fabian, Marián; Montesinos, V.; Zizler, Václav

    2007-01-01

    Roč. 181, č. 2 (2007), s. 125-152 ISSN 0039-3223 R&D Projects: GA AV ČR IAA1019301; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : epsilon-Asplund set * epsilon-weakly compact set * weakly compactly generated Banach space Subject RIV: BA - General Mathematics Impact factor: 0.568, year: 2007

  12. Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

    Czech Academy of Sciences Publication Activity Database

    Caetano, A.M.; Gogatishvili, Amiran; Opic, B.

    2016-01-01

    Roč. 146, č. 5 (2016), s. 905-927 ISSN 0308-2105 R&D Projects: GA ČR GA13-14743S Institutional support: RVO:67985840 Keywords : quasi-Banach function space * compactness * compact embedding Subject RIV: BA - General Mathematics Impact factor: 1.158, year: 2016 http:// journals .cambridge.org/action/displayAbstract?fromPage=online&aid=10379393&fileId=S0308210515000761

  13. Emergent Abelian Gauge Fields from Noncommutative Gravity

    Directory of Open Access Journals (Sweden)

    Allen Stern

    2010-02-01

    Full Text Available We construct exact solutions to noncommutative gravity following the formulation of Chamseddine and show that they are in general accompanied by Abelian gauge fields which are first order in the noncommutative scale. This provides a mechanism for generating cosmological electromagnetic fields in an expanding space-time background, and also leads to multipole-like fields surrounding black holes. Exact solutions to noncommutative Einstein-Maxwell theory can give rise to first order corrections to the metric tensor, as well as to the electromagnetic fields. This leads to first order shifts in the horizons of charged black holes.

  14. Noncommutative quantum scattering in a central field

    International Nuclear Information System (INIS)

    Bellucci, Stefano; Yeranyan, Armen

    2005-01-01

    In this Letter the problem of noncommutative elastic scattering in a central field is considered. General formulas for the differential cross-section for two cases are obtained. For the case of high energy of an incident wave it is shown that the differential cross-section coincides with that on the commutative space. For the case in which noncommutativity yields only a small correction to the central potential it is shown that the noncommutativity leads to the redistribution of particles along the azimuthal angle, although the whole cross-section coincides with the commutative case

  15. The locally connected compact metric spaces embeddable in the plane

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2004-01-01

    We prove that a 2-connected, locally connected, compact topological space M is homeomorphic to a subset of the 2-sphere if and only if M is metrizable and contains none of the Kuratowski graphs K-5 and K-3,K-3.......We prove that a 2-connected, locally connected, compact topological space M is homeomorphic to a subset of the 2-sphere if and only if M is metrizable and contains none of the Kuratowski graphs K-5 and K-3,K-3....

  16. Classification of locally 2-connected compact metric spaces

    DEFF Research Database (Denmark)

    Thomassen, Carsten

    2005-01-01

    The aim of this paper is to prove that, for compact metric spaces which do not contain infinite complete graphs, the (strong) property of being "locally 2-dimensional" is guaranteed just by a (weak) local connectivity condition. Specifically, we prove that a locally 2-connected, compact metric sp...... space M either contains an infinite complete graph or is surface like in the following sense: There exists a unique surface S such that S and M. contain the same finite graphs. Moreover, M is embeddable in S, that is, M is homeomorphic to a subset of S....

  17. Fermions in noncommutative emergent gravity

    International Nuclear Information System (INIS)

    Klammer, D.

    2010-01-01

    Noncommutative emergent gravity is a novel framework disclosing how gravity is contained naturally in noncommutative gauge theory formulated as a matrix model. It describes a dynamical space-time which itself is a four-dimensional brane embedded in a higher-dimensional space. In noncommutative emergent gravity, the metric is not a fundamental object of the model; rather it is determined by the Poisson structure and by the induced metric of the embedding. In this work the coupling of fermions to these matrix models is studied from the point of view of noncommutative emergent gravity. The matrix Dirac operator as given by the IKKT matrix model defines an appropriate coupling for fermions to an effective gravitational metric of noncommutative four-dimensional spaces that are embedded into a ten-dimensional ambient space. As it turns out this coupling is non-standard due to a spin connection that vanishes in the preferred but unobservable coordinates defined by the model. The purpose of this work is to study the one-loop effective action of this approach. Standard results of the literature cannot be applied due to this special coupling of the fermions. However, integrating out these fields in a nontrivial geometrical background induces indeed the Einstein-Hilbert action of the effective metric, as well as additional terms which couple the noncommutative structure to the Riemann tensor, and a dilaton-like term. It remains to be understood what the effects of these terms are and whether they can be avoided. In a second step, the existence of a duality between noncommutative gauge theory and gravity which explains the phenomenon of UV/IR mixing as a gravitational effect is discussed. We show how the gravitational coupling of fermions can be interpreted as a coupling of fermions to gauge fields, which suffers then from UV/IR mixing. This explanation does not render the model finite but it reveals why some UV/IR mixing remains even in supersymmetric models, except in the N

  18. A View on Optimal Transport from Noncommutative Geometry

    Directory of Open Access Journals (Sweden)

    Francesco D'Andrea

    2010-07-01

    Full Text Available We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry. Starting from a remark of Rieffel on compact manifolds, we first show that on any - i.e. non-necessary compact - complete Riemannian spin manifolds, the two distances coincide. Then, on convex manifolds in the sense of Nash embedding, we provide some natural upper and lower bounds to the distance between any two probability distributions. Specializing to the Euclidean space R^n, we explicitly compute the distance for a particular class of distributions generalizing Gaussian wave packet. Finally we explore the analogy between the spectral and the Wasserstein distances in the noncommutative case, focusing on the standard model and the Moyal plane. In particular we point out that in the two-sheet space of the standard model, an optimal-transport interpretation of the metric requires a cost function that does not vanish on the diagonal. The latest is similar to the cost function occurring in the relativistic heat equation.

  19. Foundations of free noncommutative function theory

    CERN Document Server

    Kaliuzhnyi-Verbovetskyi, Dmitry S

    2014-01-01

    In this book the authors develop a theory of free noncommutative functions, in both algebraic and analytic settings. Such functions are defined as mappings from square matrices of all sizes over a module (in particular, a vector space) to square matrices over another module, which respect the size, direct sums, and similarities of matrices. Examples include, but are not limited to, noncommutative polynomials, power series, and rational expressions. Motivation and inspiration for using the theory of free noncommutative functions often comes from free probability. An important application area is "dimensionless" matrix inequalities; these arise, e.g., in various optimization problems of system engineering. Among other related areas are those of polynomial identities in rings, formal languages and finite automata, quasideterminants, noncommutative symmetric functions, operator spaces and operator algebras, and quantum control.

  20. {theta}-Compactness in L-topological spaces

    Energy Technology Data Exchange (ETDEWEB)

    Hanafy, I.M. [Department of Mathematics, Faculty of Education, Suez Canal University, El-Arish (Egypt)], E-mail: ihanafy@hotmail.com

    2009-12-15

    Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum particle physics in connection with string theory and e{sup {infinity}} theory. In 2005, Caldas and Jafari have introduced {theta}-compact fuzzy topological spaces. In this paper, the concepts of{theta}-compactness, countable{theta}-compactness and the{theta}-Lindeloef property are introduced and studied in L-topological spaces, where L is a complete de Morgan algebra. They are defined by means of{theta}-openL-sets and their inequalities. They does not rely on the structure of basis lattice L and no distributivity in L is required. They can also be characterized by{theta}-closedL-sets and their inequalities. When L is a completely de Morgan algebra, their many characterizations are presented.

  1. Discrete symmetries (C,P,T) in noncommutative field theories

    International Nuclear Information System (INIS)

    Sheikh-Jabbari, M.M.

    2000-01-01

    In this paper we study the invariance of the noncommutative gauge theories tinder C, P and T transformations. For the noncommutative space (when only the spatial part of θ is non-zero) we show that NCQED is Parity invariant. In addition, we show that under charge conjugation the theory on noncommutative R θ 4 is transformed to the theory on R -θ 4 , so NCQED is a CP violating theory. The theory remains invariant under time reversal if, together with proper changes in fields, we also change θ by -θ. Hence altogether NCQED is CPT invariant. Moreover we show that the CPT invariance holds for general noncommutative space-time. (author)

  2. Non-Supramenable Groups Acting on Locally Compact Spaces

    DEFF Research Database (Denmark)

    Kellerhals, Julian; Monod, Nicolas; Rørdam, Mikael

    2013-01-01

    Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product $C^*$-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UCT class are constructed using crossed ...

  3. On planarity of compact, locally connected, metric spaces

    DEFF Research Database (Denmark)

    Richter, R. Bruce; Rooney, Brendan; Thomassen, Carsten

    2011-01-01

    Independently, Claytor [Ann. Math. 35 (1934), 809–835] and Thomassen [Combinatorica 24 (2004), 699–718] proved that a 2-connected, compact, locally connected metric space is homeomorphic to a subset of the sphere if and only if it does not contain K 5 or K 3;3. The “thumbtack space” consisting of...

  4. On Fock Space Representations of quantized Enveloping Algebras related to Non-Commutative Differential Geometry

    CERN Document Server

    Jurco, B; Jurco, B; Schlieker, M

    1995-01-01

    In this paper we construct explicitly natural (from the geometrical point of view) Fock space representations (contragradient Verma modules) of the quantized enveloping algebras. In order to do so, we start from the Gauss decomposition of the quantum group and introduce the differential operators on the corresponding q-deformed flag manifold (asuumed as a left comodule for the quantum group) by a projection to it of the right action of the quantized enveloping algebra on the quantum group. Finally, we express the representatives of the elements of the quantized enveloping algebra corresponding to the left-invariant vector fields on the quantum group as first-order differential operators on the q-deformed flag manifold.

  5. Quantum group of isometries in classical and noncommutative geometry

    International Nuclear Information System (INIS)

    Goswami, D.

    2007-04-01

    We formulate a quantum generalization of the notion of the group of Riemannian isometries for a compact Riemannian manifold, by introducing a natural notion of smooth and isometric action by a compact quantum group on a classical or noncommutative manifold described by spectral triples, and then proving the existence of a universal object (called the quantum isometry group) in the category of compact quantum groups acting smoothly and isometrically on a given (possibly noncommutative) manifold. Our formulation accommodates spectral triples which are not of type II. We give an explicit description of quantum isometry groups of commutative and noncommutative tori, and in this context, obtain the quantum double torus defined in [7] as the universal quantum group of holomorphic isometries of the noncommutative torus. (author)

  6. Black-body radiation of noncommutative gauge fields

    International Nuclear Information System (INIS)

    Fatollahi, Amir H.; Hajirahimi, Maryam

    2006-01-01

    The black-body radiation is considered in a theory with noncommutative electRomegnetic fields; that is noncommutativity is introduced in field space, rather than in real space. A direct implication of the result on cosmic microwave background map is argued

  7. Hydrogen atom spectrum and the Lamb shift in noncommutative QED

    International Nuclear Information System (INIS)

    Chaichian, M. . Helsinki Institute of Physics, Helsinki; Tureanu, A. . Helsinki Institute of Physics, Helsinki; FI)

    2000-10-01

    We have calculated the energy levels of the hydrogen atom and as well the Lamb shift within the noncommutative quantum electrodynamics theory. The results show deviations from the usual QED both on the classical and on the quantum levels. On both levels, the deviations depend on the parameter of space/space noncommutativity. (author)

  8. Photon defects in noncommutative standard model candidates

    International Nuclear Information System (INIS)

    Abel, S.A.; Khoze, V.V.

    2006-06-01

    Restrictions imposed by gauge invariance in noncommutative spaces together with the effects of ultraviolet/infrared mixing lead to strong constraints on possible candidates for a noncommutative extension of the Standard Model. We study a general class of noncommutative models consistent with these restrictions. Specifically we consider models based upon a gauge theory with the gauge group U(N 1 ) x U(N 2 ) x.. x U(N m ) coupled to matter fields transforming in the (anti)-fundamental, bi-fundamental and adjoint representations. We pay particular attention to overall trace-U(1) factors of the gauge group which are affected by the ultraviolet/infrared mixing. Typically, these trace-U(1) gauge fields do not decouple sufficiently fast in the infrared, and lead to sizable Lorentz symmetry violating effects in the low-energy effective theory. In a 4-dimensional theory on a continuous space-time making these effects unobservable would require making the effects of noncommutativity tiny, M NC >> M P . This severely limits the phenomenological prospects of such models. However, adding additional universal extra dimensions the trace-U(1) factors decouple with a power law and the constraint on the noncommutativity scale is weakened considerably. Finally, we briefly mention some interesting properties of the photon that could arise if the noncommutative theory is modified at a high energy scale. (Orig.)

  9. Noncommutative black holes

    Energy Technology Data Exchange (ETDEWEB)

    Lopez-DomInguez, J C [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico); RamIrez, C [Facultad de Ciencias FIsico Matematicas, Universidad Autonoma de Puebla, PO Box 1364, 72000 Puebla (Mexico); Sabido, M [Instituto de Fisica de la Universidad de Guanajuato PO Box E-143, 37150 Leoen Gto. (Mexico)

    2007-11-15

    We study noncommutative black holes, by using a diffeomorphism between the Schwarzschild black hole and the Kantowski-Sachs cosmological model, which is generalized to noncommutative minisuperspace. Through the use of the Feynman-Hibbs procedure we are able to study the thermodynamics of the black hole, in particular, we calculate Hawking's temperature and entropy for the 'noncommutative' Schwarzschild black hole.

  10. Noncommutative Valuation of Options

    Science.gov (United States)

    Herscovich, Estanislao

    2016-12-01

    The aim of this note is to show that the classical results in finance theory for pricing of derivatives, given by making use of the replication principle, can be extended to the noncommutative world. We believe that this could be of interest in quantum probability. The main result called the First fundamental theorem of asset pricing, states that a noncommutative stock market admits no-arbitrage if and only if it admits a noncommutative equivalent martingale probability.

  11. Pair production by a constant external field in noncommutative QED

    International Nuclear Information System (INIS)

    Chair, N.; Sheikh-Jabbari, M.M.

    2000-09-01

    In this paper we study QED on the noncommutative space in the constant electro-magnetic field background. Using the explicit solutions of the noncommutative version of Dirac equation in such background, we show that there are well-defined in and out-going asymptotic states and also there is a causal Green's function. We calculate the pair production rate in this case. We show that at tree level noncommutativity will not change the pair production and the threshold electric field. We also calculate the pair production rate considering the first loop corrections. In this case we show that the threshold electric field is decreased by the noncommutativity effects. (author)

  12. Noncommutative instantons: a new approach

    International Nuclear Information System (INIS)

    Schwarz, A.

    2001-01-01

    We discuss instantons on noncommutative four-dimensional Euclidean space. In the commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the trivial field at infinity. However, technically it is more convenient to work on the four-dimensional sphere. We will show that the situation in the noncommutative case is quite similar. One can analyze instantons taking as a starting point the algebra of smooth functions vanishing at infinity, but it is convenient to add a unit element to this algebra (this corresponds to a transition to a sphere at the level of topology). Our approach is more rigorous than previous considerations; it seems that it is also simpler and more transparent. In particular, we obtain the ADHM equations in a very simple way. (orig.)

  13. Non-commutative Nash inequalities

    International Nuclear Information System (INIS)

    Kastoryano, Michael; Temme, Kristan

    2016-01-01

    A set of functional inequalities—called Nash inequalities—are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative L p spaces, where their relationship to Poincaré and log-Sobolev inequalities is fleshed out. We prove Nash inequalities for a number of unital reversible semigroups

  14. Gul'ko, descriptive, and Gruenhage compact spaces

    Czech Academy of Sciences Publication Activity Database

    Fabian, Marián; Montesinos, V.; Zizler, Václav

    2010-01-01

    Roč. 104, č. 2 (2010), s. 201-220 ISSN 1578-7303 R&D Projects: GA AV ČR IAA100190901; GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : Gul'ko * descriptive * fragmentable compact spaces * network Subject RIV: BA - General Mathematics Impact factor: 0.400, year: 2010 http://link.springer.com/article/10.5052%2FRACSAM.2010.14

  15. Complementation in spaces of continuous functions on compact lines

    Czech Academy of Sciences Publication Activity Database

    Kalenda, O.F.K.; Kubiś, Wieslaw

    2012-01-01

    Roč. 386, č. 1 (2012), s. 241-257 ISSN 0022-247X R&D Projects: GA AV ČR IAA100190901 Institutional research plan: CEZ:AV0Z10190503 Keywords : compact linearly ordered space * averagign operator * continuous separable complementation property * projectional skeleton Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11007128

  16. Classification of compact homogeneous spaces with invariant G(2)-structures

    Czech Academy of Sciences Publication Activity Database

    Le, Hong-Van; Munir, M.

    2012-01-01

    Roč. 12, č. 2 (2012), s. 303-328 ISSN 1615-715X R&D Projects: GA AV ČR IAA100190701 Institutional support: RVO:67985840 Keywords : compact homogeneous space * G(2)-structure Subject RIV: BA - General Mathematics Impact factor: 0.371, year: 2012 http://www.degruyter.com/view/j/advg.2012.12.issue-2/advgeom.2011.054/advgeom.2011.054. xml

  17. Non-commutative and commutative vacua effects in a scalar torsion scenario

    Energy Technology Data Exchange (ETDEWEB)

    Sheikhahmadi, Haidar, E-mail: h.sh.ahmadi@gmail.com [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of); Aghamohammadi, Ali, E-mail: a.aghamohamadi@iausdj.ac.ir [Sanandaj Branch, Islamic Azad University, Sanandaj (Iran, Islamic Republic of); Saaidi, Khaled, E-mail: ksaaidi@uok.ac.ir [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

    2015-10-07

    In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  18. Non-commutative and commutative vacua effects in a scalar torsion scenario

    International Nuclear Information System (INIS)

    Sheikhahmadi, Haidar; Aghamohammadi, Ali; Saaidi, Khaled

    2015-01-01

    In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  19. Non-commutative and commutative vacua effects in a scalar torsion scenario

    Directory of Open Access Journals (Sweden)

    Haidar Sheikhahmadi

    2015-10-01

    Full Text Available In this work, the effects of non-commutative and commutative vacua on the phase space generated by a scalar field in a scalar torsion scenario are investigated. For both classical and quantum regimes, the commutative and non-commutative cases are compared. To take account the effects of non-commutativity, two well known non-commutative parameters, θ and β, are introduced. It should be emphasized, the effects of β which is related to momentum sector has more key role in comparison to θ which is related to space sector. Also the different boundary conditions and mathematical interpretations of non-commutativity are explored.

  20. Minimal length uncertainty and generalized non-commutative geometry

    International Nuclear Information System (INIS)

    Farmany, A.; Abbasi, S.; Darvishi, M.T.; Khani, F.; Naghipour, A.

    2009-01-01

    A generalized formulation of non-commutative geometry for the Bargmann-Fock space of quantum field theory is presented. The analysis is related to the symmetry of the simplistic space and a minimal length uncertainty.

  1. A Cp-theory problem book compactness in function spaces

    CERN Document Server

    Tkachuk, Vladimir V

    2015-01-01

    This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level.  The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained...

  2. Noncommutative Geometry in M-Theory and Conformal Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Morariu, Bogdan [Univ. of California, Berkeley, CA (United States)

    1999-05-01

    In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of Uq(SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Funq (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models.

  3. Noncommutative Geometry in M-Theory and Conformal Field Theory

    International Nuclear Information System (INIS)

    Morariu, Bogdan

    1999-01-01

    In the first part of the thesis I will investigate in the Matrix theory framework, the subgroup of dualities of the Discrete Light Cone Quantization of M-theory compactified on tori, which corresponds to T-duality in the auxiliary Type II string theory. After a review of matrix theory compactification leading to noncommutative supersymmetric Yang-Mills gauge theory, I will present solutions for the fundamental and adjoint sections on a two-dimensional twisted quantum torus and generalize to three-dimensional twisted quantum tori. After showing how M-theory T-duality is realized in supersymmetric Yang-Mills gauge theories on dual noncommutative tori I will relate this to the mathematical concept of Morita equivalence of C*-algebras. As a further generalization, I consider arbitrary Ramond-Ramond backgrounds. I will also discuss the spectrum of the toroidally compactified Matrix theory corresponding to quantized electric fluxes on two and three tori. In the second part of the thesis I will present an application to conformal field theory involving quantum groups, another important example of a noncommutative space. First, I will give an introduction to Poisson-Lie groups and arrive at quantum groups using the Feynman path integral. I will quantize the symplectic leaves of the Poisson-Lie group SU(2)*. In this way we obtain the unitary representations of U q (SU(2)). I discuss the X-structure of SU(2)* and give a detailed description of its leaves using various parametrizations. Then, I will introduce a new reality structure on the Heisenberg double of Fun q (SL(N,C)) for q phase, which can be interpreted as the quantum phase space of a particle on the q-deformed mass-hyperboloid. I also present evidence that the above real form describes zero modes of certain non-compact WZNW-models

  4. Non-commutativity in polar coordinates

    Energy Technology Data Exchange (ETDEWEB)

    Edwards, James P. [Universidad Michoacana de San Nicolas de Hidalgo, Ciudad Universitaria, Instituto de Fisica y Matematicas, Morelia, Michoacan (Mexico)

    2017-05-15

    We reconsider the fundamental commutation relations for non-commutative R{sup 2} described in polar coordinates with non-commutativity parameter θ. Previous analysis found that the natural transition from Cartesian coordinates to the traditional polar system led to a representation of [r, φ] as an everywhere diverging series. In this article we compute the Borel resummation of this series, showing that it can subsequently be extended throughout parameter space and hence provide an interpretation of this commutator. Our analysis provides a complete solution for arbitrary r and θ that reproduces the earlier calculations at lowest order and benefits from being generally applicable to problems in a two-dimensional non-commutative space. We compare our results to previous literature in the (pseudo-)commuting limit, finding a surprising spatial dependence for the coordinate commutator when θ >> r{sup 2}. Finally, we raise some questions for future study in light of this progress. (orig.)

  5. A compact frequency stabilized telecom laser diode for space applications

    Science.gov (United States)

    Philippe, C.; Holleville, D.; Le Targat, R.; Wolf, P.; Leveque, T.; Le Goff, R.; Martaud, E.; Acef, O.

    2017-09-01

    We report on a Telecom laser diode (LD) frequency stabilization to a narrow iodine hyperfine line in the green range, after frequency tripling process using fibered nonlinear waveguide PPLN crystals. We have generated up to 300 mW optical power in the green range ( 514 nm) from 800 mW of infrared power ( 1542 nm), corresponding to a nonlinear conversion efficiency h = P3?/P? 36%. Less than 10 mW of the generated green power are used for Doppler-free spectroscopy of 127I2 molecular iodine, and -therefore- for the frequency stabilization purpose. The frequency tripling optical setup is very compact (test the potential of this new frequency standard based on the couple "1.5 ?m laser / iodine molecule". We have already demonstrated a preliminary frequency stability of 4.8 x 10-14 ? -1/2 with a minimum value of 6 x 10-15 reached after 50 s of integration time, conferred to a laser diode operating at 1542.1 nm. We focus now our efforts to expand the frequency stability to a longer integration time in order to meet requirements of many space experiments, such earth gravity missions, inters satellites links or space to ground communications. Furthermore, we investigate the potential of a new approach based on frequency modulation technique (FM), associated to a 3rd harmonic detection of iodine lines to increase the compactness of the optical setup.

  6. Nonlinear sigma models with compact hyperbolic target spaces

    International Nuclear Information System (INIS)

    Gubser, Steven; Saleem, Zain H.; Schoenholz, Samuel S.; Stoica, Bogdan; Stokes, James

    2016-01-01

    We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.

  7. Nonlinear sigma models with compact hyperbolic target spaces

    Energy Technology Data Exchange (ETDEWEB)

    Gubser, Steven [Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (United States); Saleem, Zain H. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); National Center for Physics, Quaid-e-Azam University Campus,Islamabad 4400 (Pakistan); Schoenholz, Samuel S. [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States); Stoica, Bogdan [Walter Burke Institute for Theoretical Physics, California Institute of Technology,452-48, Pasadena, CA 91125 (United States); Stokes, James [Department of Physics and Astronomy, University of Pennsylvania,Philadelphia, PA 19104 (United States)

    2016-06-23

    We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be approximated by a lattice spin system which we simulate using Monte Carlo methods. The target space possesses interesting geometric and topological properties which are reflected in novel features of the sigma model. In particular, we observe a topological phase transition at a critical temperature, above which vortices proliferate, reminiscent of the Kosterlitz-Thouless phase transition in the O(2) model V.L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group II. Quantum systems, Sov. Phys. JETP 34 (1972) 610. J.M. Kosterlitz and D.J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [http://inspirehep.net/search?p=find+J+%22J.Phys.,C6,1181%22]. . Unlike in the O(2) case, there are many different types of vortices, suggesting a possible analogy to the Hagedorn treatment of statistical mechanics of a proliferating number of hadron species. Below the critical temperature the spins cluster around six special points in the target space known as Weierstrass points. The diversity of compact hyperbolic manifolds suggests that our model is only the simplest example of a broad class of statistical mechanical models whose main features can be understood essentially in geometric terms.

  8. Covariant Noncommutative Field Theory

    Energy Technology Data Exchange (ETDEWEB)

    Estrada-Jimenez, S [Licenciaturas en Fisica y en Matematicas, Facultad de Ingenieria, Universidad Autonoma de Chiapas Calle 4a Ote. Nte. 1428, Tuxtla Gutierrez, Chiapas (Mexico); Garcia-Compean, H [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN P.O. Box 14-740, 07000 Mexico D.F., Mexico and Centro de Investigacion y de Estudios Avanzados del IPN, Unidad Monterrey Via del Conocimiento 201, Parque de Investigacion e Innovacion Tecnologica (PIIT) Autopista nueva al Aeropuerto km 9.5, Lote 1, Manzana 29, cp. 66600 Apodaca Nuevo Leon (Mexico); Obregon, O [Instituto de Fisica de la Universidad de Guanajuato P.O. Box E-143, 37150 Leon Gto. (Mexico); Ramirez, C [Facultad de Ciencias Fisico Matematicas, Universidad Autonoma de Puebla, P.O. Box 1364, 72000 Puebla (Mexico)

    2008-07-02

    The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced.

  9. Noncommutative calculi of probabilty

    Directory of Open Access Journals (Sweden)

    Michał Heller

    2010-12-01

    Full Text Available The paper can be regarded as a short and informal introduction to noncommutative calculi of probability. The standard theory of probability is reformulated in the algebraic language. In this form it is readily generalized to that its version which is virtually present in quantum mechanics, and then generalized to the so-called free theory of probability. Noncommutative theory of probability is a pair (M, φ where M is a von Neumann algebra, and φ a normal state on M which plays the role of a noncommutative probability measure. In the standard (commutative theory of probability, there is, in principle, one mathematically interesting probability measure, namely the Lebesgue measure, whereas in the noncommutative theories there are many nonequivalent probability measures. Philosophical implications of this fact are briefly discussed.

  10. Covariant Noncommutative Field Theory

    International Nuclear Information System (INIS)

    Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

    2008-01-01

    The covariant approach to noncommutative field and gauge theories is revisited. In the process the formalism is applied to field theories invariant under diffeomorphisms. Local differentiable forms are defined in this context. The lagrangian and hamiltonian formalism is consistently introduced

  11. The boosts in the noncommutative special relativity

    International Nuclear Information System (INIS)

    Lagraa, M.

    2001-01-01

    From the quantum analogue of the Iwasawa decomposition of SL(2, C) group and the correspondence between quantum SL(2, C) and Lorentz groups we deduce the different properties of the Hopf algebra representing the boost of particles in noncommutative special relativity. The representation of the boost in the Hilbert space states is investigated and the addition rules of the velocities are established from the coaction. The q-deformed Clebsch-Gordon coefficients describing the transformed states of the evolution of particles in noncommutative special relativity are introduced and their explicit calculation are given. (author)

  12. On total noncommutativity in quantum mechanics

    Science.gov (United States)

    Lahti, Pekka J.; Ylinen, Kari

    1987-11-01

    It is shown within the Hilbert space formulation of quantum mechanics that the total noncommutativity of any two physical quantities is necessary for their satisfying the uncertainty relation or for their being complementary. The importance of these results is illustrated with the canonically conjugate position and momentum of a free particle and of a particle closed in a box.

  13. Non-commutative geometry and supersymmetry 2

    International Nuclear Information System (INIS)

    Hussain, F.; Thompson, G.

    1991-05-01

    Following the general construction of supersymmetric models, the model based on the idea of non-commutative geometry is formulated as a Yang-Mills theory of the graded Lie algebra U(2/1) over a graded space-time manifold. 4 refs

  14. Electromagnetic radiation in a semi-compact space

    Science.gov (United States)

    Iso, Satoshi; Kitazawa, Noriaki; Yokoo, Sumito

    2018-02-01

    In this note, we investigate the electromagnetic radiation emitted from a revolving point charge in a compact space. If the point charge is circulating with an angular frequency ω0 on the (x , y)-plane at z = 0 with boundary conditions, x ∼ x + 2 πR and y ∼ y + 2 πR, it emits radiation into the z-direction of z ∈ [ - ∞ , + ∞ ]. We find that the radiation shows discontinuities as a function of ω0 R at which a new propagating mode with a different Fourier component appears. For a small radius limit ω0 R ≪ 1, all the Fourier modes except the zero mode on (x , y)-plane are killed, but an effect of squeezing the electric field totally enhances the radiation. In the large volume limit ω0 R → ∞, the energy flux of the radiation reduces to the expected Larmor formula.

  15. Efficient and compact hyperspectral imager for space-borne applications

    Science.gov (United States)

    Pisani, Marco; Zucco, Massimo

    2017-11-01

    In the last decades Hyperspectral Imager (HI) have become irreplaceable space-borne instruments for an increasing number of applications. A number of HIs are now operative onboard (e.g. CHRIS on PROBA), others are going to be launched (e.g. PRISMA, EnMAP, HyspIRI), many others are at the breadboard level. The researchers goal is to realize HI with high spatial and spectral resolution, having low weight and contained dimensions. The most common HI technique is based on the use of a dispersive mean (a grating or a prism) or on the use of band pass filters (tunable or linear variable). These approaches have the advantages of allowing compact devices. Another approach is based on the use of interferometer based spectrometers (Michelson or Sagnac type). The advantage of the latter is a very high efficiency in light collection because of the well-known Felgett and Jaquinot principles.

  16. Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

    Energy Technology Data Exchange (ETDEWEB)

    Gitman, D.M. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Kupriyanov, V.G. [Universidade de Sao Paulo, Instituto de Fisica, Sao Paulo, SP (Brazil); Tomsk State University, Physics Department, Tomsk (Russian Federation)

    2008-03-15

    It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them {theta}-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing {theta}-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract {theta}-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as {theta}-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The {theta}-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case. (orig.)

  17. CIRiS: Compact Infrared Radiometer in Space

    Science.gov (United States)

    Osterman, D. P.; Collins, S.; Ferguson, J.; Good, W.; Kampe, T.; Rohrschneider, R.; Warden, R.

    2016-09-01

    The Compact Infrared Radiometer in Space (CIRiS) is a thermal infrared radiometric imaging instrument under development by Ball Aerospace for a Low Earth Orbit mission on a CubeSat spacecraft. Funded by the NASA Earth Science Technology Office's In-Space Validation of Earth Science Technology (InVEST) program, the mission objective is technology demonstration for improved on-orbit radiometric calibration. The CIRiS calibration approach uses a scene select mirror to direct three calibration views to the focal plane array and to transfer the resulting calibrated response to earth images. The views to deep space and two blackbody sources, including one at a selectable temperature, provide multiple options for calibration optimization. Two new technologies, carbon nanotube blackbody sources and microbolometer focal plane arrays with reduced pixel sizes, enable improved radiometric performance within the constrained 6U CubeSat volume. The CIRiS instrument's modular design facilitates subsystem modifications as required by future mission requirements. CubeSat constellations of CIRiS and derivative instruments offer an affordable approach to achieving revisit times as short as one day for diverse applications including water resource and drought management, cloud, aerosol, and dust studies, and land use and vegetation monitoring. Launch is planned for 2018.

  18. Non-Commutative Mechanics in Mathematical & in Condensed Matter Physics

    Directory of Open Access Journals (Sweden)

    Peter A. Horváthy

    2006-12-01

    Full Text Available Non-commutative structures were introduced, independently and around the same time, in mathematical and in condensed matter physics (see Table 1. Souriau's construction applied to the two-parameter central extension of the planar Galilei group leads to the ''exotic'' particle, which has non-commuting position coordinates. A Berry-phase argument applied to the Bloch electron yields in turn a semiclassical model that has been used to explain the anomalous/spin/optical Hall effects. The non-commutative parameter is momentum-dependent in this case, and can take the form of a monopole in momentum space.

  19. The application of *-products to noncommutative geometry and gauge theory

    International Nuclear Information System (INIS)

    Sykora, A.

    2004-06-01

    Due to the singularities arising in quantum field theory and the difficulties in quantizing gravity it is often believed that the description of spacetime by a smooth manifold should be given up at small length scales or high energies. In this work we will replace spacetime by noncommutative structures arising within the framework of deformation quantization. The ordinary product between functions will be replaced by a *-product, an associative product for the space of functions on a manifold. We develop a formalism to realize algebras defined by relations on function spaces. For this purpose we construct the Weyl-ordered *-product and present a method how to calculate *-products with the help of commuting vector fields. Concepts developed in noncommutative differential geometry will be applied to this type of algebras and we construct actions for noncommutative field theories. In the classical limit these noncommutative theories become field theories on manifolds with nonvanishing curvature. It becomes clear that the application of *-products is very fruitful to the solution of noncommutative problems. In the semiclassical limit every *-product is related to a Poisson structure, every derivation of the algebra to a vector field on the manifold. Since in this limit many problems are reduced to a couple of differential equations the *-product representation makes it possible to construct noncommutative spaces corresponding to interesting Riemannian manifolds. Derivations of *-products makes it further possible to extend noncommutative gauge theory in the Seiberg-Witten formalism with covariant derivatives. The resulting noncommutative gauge fields may be interpreted as one forms of a generalization of the exterior algebra of a manifold. For the Formality *-product we prove the existence of the abelian Seiberg-Witten map for derivations of these *-products. We calculate the enveloping algebra valued non abelian Seiberg-Witten map pertubatively up to second order for

  20. Strings from position-dependent noncommutativity

    International Nuclear Information System (INIS)

    Fring, Andreas; Gouba, Laure; Scholtz, Frederik G

    2010-01-01

    We introduce a new set of noncommutative spacetime commutation relations in two space dimensions. The space-space commutation relations are deformations of the standard flat noncommutative spacetime relations taken here to have position-dependent structure constants. Some of the new variables are non-Hermitian in the most natural choice. We construct their Hermitian counterparts by means of a Dyson map, which also serves to introduce a new metric operator. We propose PT-like symmetries, i.e. antilinear involutory maps, respected by these deformations. We compute minimal lengths and momenta arising in this space from generalized versions of Heisenberg's uncertainty relations and find that any object in this two-dimensional space is string like, i.e. having a fundamental length in one direction beyond which a resolution is impossible. Subsequently, we formulate and partly solve some simple models in these new variables, the free particle, its PT-symmetric deformations and the harmonic oscillator.

  1. A noncommutative catenoid

    Science.gov (United States)

    Arnlind, Joakim; Holm, Christoffer

    2018-01-01

    A noncommutative algebra corresponding to the classical catenoid is introduced together with a differential calculus of derivations. We prove that there exists a unique metric and torsion-free connection that is compatible with the complex structure, and the curvature is explicitly calculated. A noncommutative analogue of the fact that the catenoid is a minimal surface is studied by constructing a Laplace operator from the connection and showing that the embedding coordinates are harmonic. Furthermore, an integral is defined and the total curvature is computed. Finally, classes of left and right modules are introduced together with constant curvature connections, and bimodule compatibility conditions are discussed in detail.

  2. Probabilistic n-normed spaces, D-n-compact sets and D-n-bounded sets

    International Nuclear Information System (INIS)

    Pourmoslemi, A.; Salimi, M.

    2009-01-01

    In this paper, first we define and study the probabilistic n-normed spaces and D-n-compactness, also we prove some theorems and inequalities. In the next section we define D-n-boundedness and prove some results in relation between D-n-compact and D-n-bounded sets in these spaces.

  3. Noncommutative geometry and fluid dynamics

    International Nuclear Information System (INIS)

    Das, Praloy; Ghosh, Subir

    2016-01-01

    In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)

  4. Noncommutative geometry and fluid dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Das, Praloy; Ghosh, Subir [Indian Statistical Institute, Physics and Applied Mathematics Unit, Kolkata (India)

    2016-11-15

    In the present paper we have developed a Non-Commutative (NC) generalization of perfect fluid model from first principles, in a Hamiltonian framework. The noncommutativity is introduced at the Lagrangian (particle) coordinate space brackets and the induced NC fluid bracket algebra for the Eulerian (fluid) field variables is derived. Together with a Hamiltonian this NC algebra generates the generalized fluid dynamics that satisfies exact local conservation laws for mass and energy, thereby maintaining mass and energy conservation. However, nontrivial NC correction terms appear in the charge and energy fluxes. Other non-relativistic spacetime symmetries of the NC fluid are also discussed in detail. This constitutes the study of kinematics and dynamics of NC fluid. In the second part we construct an extension of the Friedmann-Robertson-Walker (FRW) cosmological model based on the NC fluid dynamics presented here. We outline the way in which NC effects generate cosmological perturbations bringing about anisotropy and inhomogeneity in the model. We also derive a NC extended Friedmann equation. (orig.)

  5. Finite quantum physics and noncommutative geometry

    International Nuclear Information System (INIS)

    Balachandran, A.P.; Ercolessi, E.; Landi, G.; Teotonio-Sobrinho, P.; Lizzi, F.; Sparano, G.

    1994-04-01

    Conventional discrete approximations of a manifold do not preserve its nontrivial topological features. In this article we describe an approximation scheme due to Sorkin which reproduces physically important aspects of manifold topology with striking fidelity. The approximating topological spaces in this scheme are partially ordered sets (posets). Now, in ordinary quantum physics on a manifold M, continuous probability densities generate the commutative C * -algebra C(M) of continuous functions on M. It has a fundamental physical significance, containing the information to reconstruct the topology of M, and serving to specify the domains of observables like the Hamiltonian. For a poset, the role of this algebra is assumed by a noncommutative C * -algebra A. As noncommutative geometries are based on noncommutative C * -algebra, we therefore have a remarkable connection between finite approximations to quantum physics and noncommutative geometries. Varies methods for doing quantum physics using A are explored. Particular attention is paid to developing numerically viable approximation schemes which at the same time preserve important topological features of continuum physics. (author). 21 refs, 13 figs

  6. Principal noncommutative torus bundles

    DEFF Research Database (Denmark)

    Echterhoff, Siegfried; Nest, Ryszard; Oyono-Oyono, Herve

    2008-01-01

    of bivariant K-theory (denoted RKK-theory) due to Kasparov. Using earlier results of Echterhoff and Williams, we shall give a complete classification of principal non-commutative torus bundles up to equivariant Morita equivalence. We then study these bundles as topological fibrations (forgetting the group...

  7. One-loop beta functions for the orientable non-commutative Gross Neveu model TH1"-->

    Science.gov (United States)

    Lakhoua, A.; Vignes-Tourneret, F.; Wallet, J.-C.

    2007-11-01

    We compute at the one-loop order the β-functions for a renormalisable non-commutative analog of the Gross Neveu model defined on the Moyal plane. The calculation is performed within the so called x-space formalism. We find that this non-commutative field theory exhibits asymptotic freedom for any number of colors. The β-function for the non-commutative counterpart of the Thirring model is found to be non vanishing.

  8. Some aspects of noncommutative integrable systems a la Moyal

    International Nuclear Information System (INIS)

    Dafounansou, O.; El Boukili, A.; Sedra, M.B.

    2005-12-01

    Besides its various applications in string and D-brane physics, the non commutativity of space (-time) coordinates, based on the *-product, behaves as a more general framework providing more mathematical and physical information about the associated system. Similar to the Gelfand-Dickey framework of pseudo differential operators, the non commutativity a la Moyal applied to physical problems makes the study more systematic. Using these facts, as well as the backgrounds of Moyal momentum algebra introduced in previous works, we look for the important task of studying integrability in the noncommutativity framework. The main focus is on the noncommutative version of the Lax representation of two principal examples: the noncommutative sl 2 KdV equation and the noncommutative version of Burgers systems. Important properties are presented. (author)

  9. 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

  10. Trace Dynamics and a non-commutative special relativity

    International Nuclear Information System (INIS)

    Lochan, Kinjalk; Singh, T.P.

    2011-01-01

    Trace Dynamics is a classical dynamical theory of non-commuting matrices in which cyclic permutation inside a trace is used to define the derivative with respect to an operator. We use the methods of Trace Dynamics to construct a non-commutative special relativity. We define a line-element using the Trace over space-time coordinates which are assumed to be operators. The line-element is shown to be invariant under standard Lorentz transformations, and is used to construct a non-commutative relativistic dynamics. The eventual motivation for constructing such a non-commutative relativity is to relate the statistical thermodynamics of this classical theory to quantum mechanics. -- Highlights: → Classical time is external to quantum mechanics. → This implies need for a formulation of quantum theory without classical time. → A starting point could be a non-commutative special relativity. → Such a relativity is developed here using the theory of Trace Dynamics. → A line-element is defined using the Trace over non-commuting space-time operators.

  11. Vacuum energy from noncommutative models

    Science.gov (United States)

    Mignemi, S.; Samsarov, A.

    2018-04-01

    The vacuum energy is computed for a scalar field in a noncommutative background in several models of noncommutative geometry. One may expect that the noncommutativity introduces a natural cutoff on the ultraviolet divergences of field theory. Our calculations show however that this depends on the particular model considered: in some cases the divergences are suppressed and the vacuum energy is only logarithmically divergent, in other cases they are stronger than in the commutative theory.

  12. Noncommutative duality of Gelfand-Naimark and applications in gauge theory and spinc structure

    International Nuclear Information System (INIS)

    RATSIMBARISON, H.M.

    2004-01-01

    We use the GN (Gelfand-Naimark) duality and its generalizations in order to describe some physical constructions, our main tool is the categorical formalism. We start with the first GN theorem, a duality between a category of commutative unital C*-algebras and a category of compact Hausdorff spaces, which we interpret as equivalence between classical observables and classical states. Then, we give the GNS construction providing the 'Fock space' in Quantum Field Theory, and which is the constructive proof of the second GN theorem. A particular formulation of this latter, the Serre-Swan theorem introduces vector bundle structure, a new kind of classical states space. And this lead to K-theory, which we show compatible with a noncommutative concept : the Morita equivalence. From these ideas of Noncommutative geometry, we meet two important applications in QFT : Gauge theory and Spin c structure.The first application begin with the origin of gauge theory: it permit to obtain the interaction lagrangian term from the gauge non invariance of the free lagrangian of matter. Thanks to theories of principal bundles, the gauge potential and the gauge transformation are represented by connection and bundle G-automorphism on the identity of a principal bundle over the spacetime manifold. Finally, the Serre-Swan theorem gives the step of Connes's generalization to noncommutative case. In the second application, we show that the construction of Dirac operator lead to the definitions of Clifford algebra and spinor space. A categorical equivalent definition, similar to those of the Grothendieck group, is done. At the end, we make use of the structure of Clifford algebra and the Morita equivalence to reconstruct Plymen's definition of the spin c structure [fr

  13. An invitation to noncommutative geometry

    CERN Document Server

    Marcolli, Matilde

    2008-01-01

    This is the first existing volume that collects lectures on this important and fast developing subject in mathematics. The lectures are given by leading experts in the field and the range of topics is kept as broad as possible by including both the algebraic and the differential aspects of noncommutative geometry as well as recent applications to theoretical physics and number theory. Sample Chapter(s). A Walk in the Noncommutative Garden (1,639 KB). Contents: A Walk in the Noncommutative Garden (A Connes & M Marcolli); Renormalization of Noncommutative Quantum Field Theory (H Grosse & R Wulke

  14. Phenomenology of noncommutative field theories

    International Nuclear Information System (INIS)

    Carone, C D

    2006-01-01

    Experimental limits on the violation of four-dimensional Lorentz invariance imply that noncommutativity among ordinary spacetime dimensions must be small. In this talk, I review the most stringent bounds on noncommutative field theories and suggest a possible means of evading them: noncommutativity may be restricted to extra, compactified spatial dimensions. Such theories have a number of interesting features, including Abelian gauge fields whose Kaluza-Klein excitations have self couplings. We consider six-dimensional QED in a noncommutative bulk, and discuss the collider signatures of the model

  15. Gravity and the structure of noncommutative algebras

    International Nuclear Information System (INIS)

    Buric, Maja; Madore, John; Grammatikopoulos, Theodoros; Zoupanos, George

    2006-01-01

    A gravitational field can be defined in terms of a moving frame, which when made noncommutative yields a preferred basis for a differential calculus. It is conjectured that to a linear perturbation of the commutation relations which define the algebra there corresponds a linear perturbation of the gravitational field. This is shown to be true in the case of a perturbation of Minkowski space-time

  16. Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces

    Directory of Open Access Journals (Sweden)

    Muhammad Shabir

    2017-06-01

    Full Text Available Bipolar soft topological spaces are mathematical expressions to estimate interpretation of data frameworks. Bipolar soft theory considers the core features of data granules. Bipolarity is important to distinguish between positive information which is guaranteed to be possible and negative information which is forbidden or surely false. Connectedness and compactness are the most important fundamental topological properties. These properties highlight the main features of topological spaces and distinguish one topology from another. Taking this into account, we explore the bipolar soft connectedness, bipolar soft disconnectedness and bipolar soft compactness properties for bipolar soft topological spaces. Moreover, we introduce the notion of bipolar soft disjoint sets, bipolar soft separation, and bipolar soft hereditary property and study on bipolar soft connected and disconnected spaces. By giving the detailed picture of bipolar soft connected and disconnected spaces we investigate bipolar soft compact spaces and derive some results related to this concept.

  17. Noncommutative vector bundles over fuzzy CPN and their covariant derivatives

    International Nuclear Information System (INIS)

    Dolan, Brian P.; Huet, Idrish; Murray, Sean; O'Connor, Denjoe

    2007-01-01

    We generalise the construction of fuzzy CP N in a manner that allows us to access all noncommutative equivariant complex vector bundles over this space. We give a simplified construction of polarization tensors on S 2 that generalizes to complex projective space, identify Laplacians and natural noncommutative covariant derivative operators that map between the modules that describe noncommuative sections. In the process we find a natural generalization of the Schwinger-Jordan construction to su(n) and identify composite oscillators that obey a Heisenberg algebra on an appropriate Fock space

  18. Quantum theory of noncommutative fields

    International Nuclear Information System (INIS)

    Carmona, J.M.; Cortes, J.L.; Gamboa, J.; Mendez, F.

    2003-01-01

    Generalizing the noncommutative harmonic oscillator construction, we propose a new extension of quantum field theory based on the concept of 'noncommutative fields'. Our description permits to break the usual particle-antiparticle degeneracy at the dispersion relation level and introduces naturally an ultraviolet and an infrared cutoff. Phenomenological bounds for these new energy scales are given. (author)

  19. Worldline approach to noncommutative field theory

    International Nuclear Information System (INIS)

    Bonezzi, R; Corradini, O; Viñas, S A Franchino; Pisani, P A G

    2012-01-01

    The study of the heat-trace expansion in non-commutative field theory has shown the existence of Moyal non-local Seeley–DeWitt coefficients which are related to the UV/IR mixing and manifest, in some cases, the non-renormalizability of the theory. We show that these models can be studied in a worldline approach implemented in phase space and arrive at a master formula for the n-point contribution to the heat-trace expansion. This formulation could be useful in understanding some open problems in this area, as the heat-trace expansion for the non-commutative torus or the introduction of renormalizing terms in the action, as well as for generalizations to other non-local operators. (paper)

  20. Hall effect in noncommutative coordinates

    International Nuclear Information System (INIS)

    Dayi, Oemer F.; Jellal, Ahmed

    2002-01-01

    We consider electrons in uniform external magnetic and electric fields which move on a plane whose coordinates are noncommuting. Spectrum and eigenfunctions of the related Hamiltonian are obtained. We derive the electric current whose expectation value gives the Hall effect in terms of an effective magnetic field. We present a receipt to find the action which can be utilized in path integrals for noncommuting coordinates. In terms of this action we calculate the related Aharonov-Bohm phase and show that it also yields the same effective magnetic field. When magnetic field is strong enough this phase becomes independent of magnetic field. Measurement of it may give some hints on spatial noncommutativity. The noncommutativity parameter θ can be tuned such that electrons moving in noncommutative coordinates are interpreted as either leading to the fractional quantum Hall effect or composite fermions in the usual coordinates

  1. Strong consistency of nonparametric Bayes density estimation on compact metric spaces with applications to specific manifolds.

    Science.gov (United States)

    Bhattacharya, Abhishek; Dunson, David B

    2012-08-01

    This article considers a broad class of kernel mixture density models on compact metric spaces and manifolds. Following a Bayesian approach with a nonparametric prior on the location mixing distribution, sufficient conditions are obtained on the kernel, prior and the underlying space for strong posterior consistency at any continuous density. The prior is also allowed to depend on the sample size n and sufficient conditions are obtained for weak and strong consistency. These conditions are verified on compact Euclidean spaces using multivariate Gaussian kernels, on the hypersphere using a von Mises-Fisher kernel and on the planar shape space using complex Watson kernels.

  2. Coherent states for quantum compact groups

    International Nuclear Information System (INIS)

    Jurco, B.; Stovicek, P.; CTU, Prague

    1996-01-01

    Coherent states are introduced and their properties are discussed for simple quantum compact groups A l , B l , C l and D l . The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)

  3. Coherent states for quantum compact groups

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B. [European Organization for Nuclear Research, Geneva (Switzerland). Theory Div.; Stovicek, P. [Ceske Vysoke Uceni Technicke, Prague (Czech Republic). Dept. of Mathematics]|[CTU, Prague (Czech Republic). Doppler Inst.

    1996-12-01

    Coherent states are introduced and their properties are discussed for simple quantum compact groups A{sub l}, B{sub l}, C{sub l} and D{sub l}. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit. The coherent state is interpreted as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R-matrix formulation (generalizing this way the q-deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel-Weil construction) is described using the concept of coherent state. The relation between representation theory and non-commutative differential geometry is suggested. (orig.)

  4. Coherent states for quantum compact groups

    CERN Document Server

    Jurco, B

    1996-01-01

    Coherent states are introduced and their properties are discussed for all simple quantum compact groups. The multiplicative form of the canonical element for the quantum double is used to introduce the holomorphic coordinates on a general quantum dressing orbit and interpret the coherent state as a holomorphic function on this orbit with values in the carrier Hilbert space of an irreducible representation of the corresponding quantized enveloping algebra. Using Gauss decomposition, the commutation relations for the holomorphic coordinates on the dressing orbit are derived explicitly and given in a compact R--matrix formulation (generalizing this way the q--deformed Grassmann and flag manifolds). The antiholomorphic realization of the irreducible representations of a compact quantum group (the analogue of the Borel--Weil construction) are described using the concept of coherent state. The relation between representation theory and non--commutative differential geometry is suggested.}

  5. Boundedness and compactness of a new product-type operator from a general space to Bloch-type spaces

    Directory of Open Access Journals (Sweden)

    Stevo Stević

    2016-09-01

    Full Text Available Abstract We characterize the boundedness and compactness of a product-type operator, which, among others, includes all the products of the single composition, multiplication, and differentiation operators, from a general space to Bloch-type spaces. We also give some upper and lower bounds for the norm of the operator.

  6. Noncommutative quantum mechanics

    Science.gov (United States)

    Gamboa, J.; Loewe, M.; Rojas, J. C.

    2001-09-01

    A general noncommutative quantum mechanical system in a central potential V=V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter θ, we find an explicit expression for the eigenvalues. In fact, any quantum mechanical system with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V=V(HHO,Lz), where HHO is the Hamiltonian of the two-dimensional harmonic oscillator and Lz is the z component of the angular momentum. For other finite values of θ the model can be solved by using perturbation theory.

  7. Can noncommutativity resolve the Big-Bang singularity?

    CERN Document Server

    Maceda, M; Manousselis, P; Zoupanos, George

    2004-01-01

    A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has noncommutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a noncommutative version of the Kasner metric is constructed which is nonsingular at all scales and becomes commutative at large length scales.

  8. Compact and continuous embeddings of logarithmic Bessel potential spaces

    Czech Academy of Sciences Publication Activity Database

    Edmunds, D. E.; Gurka, P.; Opic, Bohumír

    2005-01-01

    Roč. 168, č. 3 (2005), s. 229-250 ISSN 0039-3223 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : Bessel potential spaces * spaces of Hölder-continuous functions * Lorentz-Zygmund spaces Subject RIV: BA - General Mathematics Impact factor: 0.538, year: 2005

  9. Seiberg–Witten map and quantum phase effects for neutral Dirac particle on noncommutative plane

    Directory of Open Access Journals (Sweden)

    Kai Ma

    2016-05-01

    Full Text Available We provide a new approach to study the noncommutative effects on the neutral Dirac particle with anomalous magnetic or electric dipole moment on the noncommutative plane. The advantages of this approach are demonstrated by investigating the noncommutative corrections on the Aharonov–Casher and He–McKellar–Wilkens effects. This approach is based on the effective U(1 gauge symmetry for the electrodynamics of spin on the two dimensional space. The Seiberg–Witten map for this symmetry is then employed when we study the noncommutative corrections. Because the Seiberg–Witten map preserves the gauge symmetry, the noncommutative corrections can be defined consistently with the ordinary phases. Based on this approach we find the noncommutative corrections on the Aharonov–Casher and He–McKellar–Wilkens phases consist of two terms. The first one depends on the beam particle velocity and consistence with the previous results. However the second term is velocity-independent and then completely new. Therefore our results indicate it is possible to investigate the noncommutative space by using ultra-cold neutron interferometer in which the velocity-dependent term is negligible. Furthermore, both these two terms are proportional to the ratio between the noncommutative parameter θ and the cross section Ae/m of the electrical/magnetic charged line enclosed by the trajectory of beam particles. Therefore the experimental sensitivity can be significantly enhanced by reducing the cross section of the charge line Ae/m.

  10. Environmental education excursions and proximity to urban green space : Densification in a ‘compact city’

    NARCIS (Netherlands)

    Wolsink, M.

    2016-01-01

    The value of urban green space for environmental education fieldwork is empirically investigated in a study among all secondary schools in Amsterdam. The article describes how the proximity of schools to green spaces emerges as a new factor in the ‘sustainable city’ and the ‘compact city’ debate.

  11. An integrable noncommutative version of the sine-Gordon system

    International Nuclear Information System (INIS)

    Grisaru, Marcus T.; Penati, Silvia

    2003-01-01

    Using the bicomplex approach we discuss an integrable noncommutative system in two-dimensional Euclidean space. It is described by an equation of motion which reduces to the ordinary sine-Gordon equation when the noncommutation parameter is removed, plus a constraint equation which is nontrivial only in the noncommutative case. The implications of this constraint, which is required by integrability but seems to reduce the space of classical solutions, remain to be understood. We show that the system has an infinite number of conserved currents and we give the general recursive relation for constructing them. For the particular cases of lower spin nontrivial currents we work out the explicit expressions and perform a direct check of their conservation. These currents reduce to the usual sine-Gordon currents in the commutative limit. We find classical 'localized' solutions to first order in the noncommutativity parameter and describe the Backlund transformations for our system. Finally, we comment on the relation of our noncommutative system to the commutative sine-Gordon system

  12. Non-commutative flux representation for loop quantum gravity

    Science.gov (United States)

    Baratin, A.; Dittrich, B.; Oriti, D.; Tambornino, J.

    2011-09-01

    The Hilbert space of loop quantum gravity is usually described in terms of cylindrical functionals of the gauge connection, the electric fluxes acting as non-commuting derivation operators. It has long been believed that this non-commutativity prevents a dual flux (or triad) representation of loop quantum gravity to exist. We show here, instead, that such a representation can be explicitly defined, by means of a non-commutative Fourier transform defined on the loop gravity state space. In this dual representation, flux operators act by sstarf-multiplication and holonomy operators act by translation. We describe the gauge invariant dual states and discuss their geometrical meaning. Finally, we apply the construction to the simpler case of a U(1) gauge group and compare the resulting flux representation with the triad representation used in loop quantum cosmology.

  13. Supersymmetry on the noncommutative lattice

    International Nuclear Information System (INIS)

    Nishimura, Jun; Rey, Soo-Jong; Sugino, Fumihiko

    2003-01-01

    Built upon the proposal of Kaplan et al. (heplat{0206109}), we construct noncommutative lattice gauge theory with manifest supersymmetry. We show that such theory is naturally implementable via orbifold conditions generalizing those used by Kaplan et al. We present the prescription in detail and illustrate it for noncommutative gauge theories latticized partially in two dimensions. We point out a deformation freedom in the defining theory by a complex-parameter, reminiscent of discrete torsion in string theory. We show that, in the continuum limit, the supersymmetry is enhanced only at a particular value of the deformation parameter, determined solely by the size of the noncommutativity. (author)

  14. Testing Non-commutative QED, Constructing Non-commutative MHD

    OpenAIRE

    Guralnik, Z.; Jackiw, R.; Pi, S. Y.; Polychronakos, A. P.

    2001-01-01

    The effect of non-commutativity on electromagnetic waves violates Lorentz invariance: in the presence of a background magnetic induction field b, the velocity for propagation transverse to b differs from c, while propagation along b is unchanged. In principle, this allows a test by the Michelson-Morley interference method. We also study non-commutativity in another context, by constructing the theory describing a charged fluid in a strong magnetic field, which forces the fluid particles into ...

  15. Paired quantum Hall states on noncommutative two-tori

    Energy Technology Data Exchange (ETDEWEB)

    Marotta, Vincenzo [Dipartimento di Scienze Fisiche, Universita di Napoli ' Federico II' and INFN, Sezione di Napoli, Compl. universitario M. Sant' Angelo, Via Cinthia, 80126 Napoli (Italy); Naddeo, Adele, E-mail: naddeo@sa.infn.i [CNISM, Unita di Ricerca di Salerno and Dipartimento di Fisica ' E. R. Caianiello' , Universita degli Studi di Salerno, Via Salvador Allende, 84081 Baronissi (Italy)

    2010-08-01

    By exploiting the notion of Morita equivalence for field theories on noncommutative tori and choosing rational values of the noncommutativity parameter theta (in appropriate units), a one-to-one correspondence between an Abelian noncommutative field theory (NCFT) and a non-Abelian theory of twisted fields on ordinary space can be established. Starting from this general result, we focus on the conformal field theory (CFT) describing a quantum Hall fluid (QHF) at paired states fillings nu=m/(pm+2) Cristofano et al. (2000) , recently obtained by means of m-reduction procedure, and show that it is the Morita equivalent of a NCFT. In this way we extend the construction proposed in Marotta and Naddeo (2008) for the Jain series nu=m/(2pm+1) . The case m=2 is explicitly discussed and the role of noncommutativity in the physics of quantum Hall bilayers is emphasized. Our results represent a step forward the construction of a new effective low energy description of certain condensed matter phenomena and help to clarify the relationship between noncommutativity and quantum Hall fluids.

  16. Noncommutative quantum field theory: attempts on renormalization

    International Nuclear Information System (INIS)

    Popp, L.

    2002-05-01

    Quantum field theory is the art of dealing with problems at small distances or, equivalently, large momenta. Although there are different approaches (string theory, for example), it is generally accepted that these principles cannot be extrapolated to arbitrarily small distances as can be shown by applying simple, heuristic arguments. Therefore, the concept of space-time as a differential manifold has to be replaced by something else at such scales, the road we have chosen to follow is noncommutative geometry. We start from the basic relation [ x μ , x ν ] = i θ { μν}, where θ is a (usually) constant, antisymmetric matrix. This relation amounts to a noncommutativity of position measurements, or, put differently, the points are somehow 'smeared' out, which should have a positive effect on field theory since infinities arise from point-like interactions. However, it was shown that the effects of the commutation relation (leading to the so-called Moyal product) do not necessarily cure the divergences but introduce a new kind of problem: whereas UV-divergent integrals are rendered finite by phase factors (that arise as a consequence of the Moyal product), this same kind of 'regularization' introduces IR-divergences which led to the name 'UV/IR-mixing' for this problem. In order to overcome this peculiarity, one expands the action in θ which is immediate for the phase factors but requires the so-called Seiberg-Witten map for the fields. In this thesis, we emphasize the derivation of the Seiberg-Witten map by using noncommutative Lorentz symmetries, which is more general than the original derivation. After that, we concentrate on a treatment of θ-expanded theories and their renormalization, where it can be shown that the photon self-energy of noncommutative Maxwell theory can be renormalized to all orders in hbar and θ when the freedom in the Seiberg-Witten map (there are ambiguities in the map) is exploited. Although this is very promising, it cannot be

  17. On the classical dynamics of charges in non-commutative QED

    International Nuclear Information System (INIS)

    Fatollahi, A.H.; Mohammadzadeh, H.

    2004-01-01

    Following Wong's approach to formulating the classical dynamics of charged particles in non-Abelian gauge theories, we derive the classical equations of motion of a charged particle in U(1) gauge theory on non-commutative space, the so-called non-commutative QED. In the present use of the procedure, it is observed that the definition of the mechanical momenta should be modified. The derived equations of motion manifest the previous statement about the dipole behavior of the charges in non-commutative space. (orig.)

  18. Duality and noncommutative planes

    DEFF Research Database (Denmark)

    Jøndrup, Søren

    2015-01-01

    We study extensions of simple modules over an associative ring A   and we prove that for twosided ideals mm and nn with artinian factors the condition ExtA1(A/m,A/n)≠0 holds for the left A  -modules A/mA/m and A/nA/n if and only if it holds for the right modules A/nA/n and A/mA/m. The methods pro...... proving this are applied to show that noncommutative models of the plane, i.e. algebras of the form k〈x,y〉/(f)k〈x,y〉/(f), where f∈([x,y])f∈([x,y]) are noetherian only in case (f)=([x,y])...

  19. On the energy crisis in noncommutative CP(1) model

    International Nuclear Information System (INIS)

    Sourrouille, Lucas

    2010-01-01

    We study the CP(1) system in (2+1)-dimensional noncommutative space with and without Chern-Simons term. Using the Seiberg-Witten map we convert the noncommutative CP(1) system to an action written in terms of the commutative fields. We find that this system presents the same infinite size instanton solution as the commutative Chern-Simons-CP(1) model without a potential term. Based on this result we argue that the BPS equations are compatible with the full variational equations of motion, rejecting the hypothesis of an 'energy crisis'. In addition we examine the noncommutative CP(1) system with a Chern-Simons interaction. In this case we find that when the theory is transformed by the Seiberg-Witten map it also presents the same instanton solution as the commutative Chern-Simons-CP(1) model.

  20. A deformation quantization theory for noncommutative quantum mechanics

    International Nuclear Information System (INIS)

    Costa Dias, Nuno; Prata, Joao Nuno; Gosson, Maurice de; Luef, Franz

    2010-01-01

    We show that the deformation quantization of noncommutative quantum mechanics previously considered by Dias and Prata ['Weyl-Wigner formulation of noncommutative quantum mechanics', J. Math. Phys. 49, 072101 (2008)] and Bastos, Dias, and Prata ['Wigner measures in non-commutative quantum mechanics', e-print arXiv:math-ph/0907.4438v1; Commun. Math. Phys. (to appear)] can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined and prove a spectral theorem for the star-genvalue equation using an extension of the methods recently initiated by de Gosson and Luef ['A new approach to the *-genvalue equation', Lett. Math. Phys. 85, 173-183 (2008)].

  1. Spectral theorem in noncommutative field theories: Jacobi dynamics

    International Nuclear Information System (INIS)

    Géré, Antoine; Wallet, Jean-Christophe

    2015-01-01

    Jacobi operators appear as kinetic operators of several classes of noncommutative field theories (NCFT) considered recently. This paper deals with the case of bounded Jacobi operators. A set of tools mainly issued from operator and spectral theory is given in a way applicable to the study of NCFT. As an illustration, this is applied to a gauge-fixed version of the induced gauge theory on the Moyal plane expanded around a symmetric vacuum. The characterization of the spectrum of the kinetic operator is given, showing a behavior somewhat similar to a massless theory. An attempt to characterize the noncommutative geometry related to the gauge fixed action is presented. Using a Dirac operator obtained from the kinetic operator, it is shown that one can construct an even, regular, weakly real spectral triple. This spectral triple does not define a noncommutative metric space for the Connes spectral distance. (paper)

  2. Batman flies: a compact spectro-imager for space observation

    Science.gov (United States)

    Zamkotsian, Frederic; Ilbert, Olivier; Zoubian, Julien; Delsanti, Audrey; Boissier, Samuel; Lancon, Ariane

    2017-11-01

    Multi-object spectroscopy (MOS) is a key technique for large field of view surveys. MOEMS programmable slit masks could be next-generation devices for selecting objects in future infrared astronomical instrumentation for space telescopes. MOS is used extensively to investigate astronomical objects by optimizing the Signal-to-Noise Ratio (SNR): high precision spectra are obtained and the problem of spectral confusion and background level occurring in slitless spectroscopy is cancelled. Fainter limiting fluxes are reached and the scientific return is maximized both in cosmology and in legacy science. Major telescopes around the world are equipped with MOS in order to simultaneously record several hundred spectra in a single observation run. Next generation MOS for space like the Near Infrared Multi-Object Spectrograph (NIRSpec) for the James Webb Space Telescope (JWST) require a programmable multi-slit mask. Conventional masks or complex fiber-optics-based mechanisms are not attractive for space. The programmable multi-slit mask requires remote control of the multislit configuration in real time. During the early-phase studies of the European Space Agency (ESA) EUCLID mission, a MOS instrument based on a MOEMS device has been assessed. Due to complexity and cost reasons, slitless spectroscopy was chosen for EUCLID, despite a much higher efficiency with slit spectroscopy. A promising possible solution is the use of MOEMS devices such as micromirror arrays (MMA) [1,2,3] or micro-shutter arrays (MSA) [4]. MMAs are designed for generating reflecting slits, while MSAs generate transmissive slits. In Europe an effort is currently under way to develop single-crystalline silicon micromirror arrays for future generation infrared multi-object spectroscopy (collaboration LAM / EPFL-CSEM) [5,6]. By placing the programmable slit mask in the focal plane of the telescope, the light from selected objects is directed toward the spectrograph, while the light from other objects and

  3. Noncommutative geometry-inspired rotating black hole in three ...

    Indian Academy of Sciences (India)

    We find a new rotating black hole in three-dimensional anti-de Sitter space using an anisotropic perfect fluid inspired by the noncommutative black hole. We deduce the thermodynamical quantities of this black hole and compare them with those of a rotating BTZ solution and give corrections to the area law to get the exact ...

  4. S-duality and noncommutative gauge theory

    International Nuclear Information System (INIS)

    Gopakumar, R.; Maldacena, J.; Minwalla, S.; Strominger, A.

    2000-01-01

    It is conjectured that strongly coupled, spatially noncommutative CN=4 Yang-Mills theory has a dual description as a weakly coupled open string theory in a near critical electric field, and that this dual theory is fully decoupled from closed strings. Evidence for this conjecture is given by the absence of physical closed string poles in the non-planar one-loop open string diagram. The open string theory can be viewed as living in a geometry in which space and time coordinates do not commute. (author)

  5. Noncommuting fields and non-Abelian fluids

    International Nuclear Information System (INIS)

    Jackiw, R.

    2004-01-01

    The original ideas about noncommuting coordinates are recalled. The connection between U(1) gauge fields defined on noncommuting coordinates and fluid mechanics is explained. Non-Abelian fluid mechanics is described

  6. Noncommutative Blackwell-Ross martingale inequality

    Science.gov (United States)

    Talebi, Ali; Moslehian, Mohammad Sal; Sadeghi, Ghadir

    We establish a noncommutative Blackwell-Ross inequality for supermartingales under a suitable condition which generalizes Khan’s work to the noncommutative setting. We then employ it to deduce an Azuma-type inequality.

  7. Large parallel volumes of finite and compact sets in d-dimensional Euclidean space

    DEFF Research Database (Denmark)

    Kampf, Jürgen; Kiderlen, Markus

    The r-parallel volume V (Cr) of a compact subset C in d-dimensional Euclidean space is the volume of the set Cr of all points of Euclidean distance at most r > 0 from C. According to Steiner’s formula, V (Cr) is a polynomial in r when C is convex. For finite sets C satisfying a certain geometric...

  8. A note on biorthogonal systems in weakly compactly generated Banach spaces

    Czech Academy of Sciences Publication Activity Database

    Fabian, Marián; Gonzáles, A.; Montesinos, V.

    2009-01-01

    Roč. 34, č. 2 (2009), s. 555-564 ISSN 1239-629X R&D Projects: GA AV ČR(CZ) IAA100190610 Institutional research plan: CEZ:AV0Z10190503 Keywords : weakly compactly generated (sub)space * projectional resolution * fundamental biorthogonal system Subject RIV: BA - General Mathematics Impact factor: 0.539, year: 2009

  9. A new non-commutative representation of the Wiener and Poisson processes

    International Nuclear Information System (INIS)

    Privault, N.

    1996-01-01

    Using two different constructions of the chaotic and variational calculus on Poisson space, we show that the Wiener and Poisson processes have a non-commutative representation which is different from the one obtained by transfer of the Fock space creation and annihilation operators. We obtain in this way an extension of the non-commutative It calculus. The associated commutation relations show a link between the geometric and exponential distributions. (author). 11 refs

  10. Development and verification of a compact TDC-based data acquisition system for space applications

    Energy Technology Data Exchange (ETDEWEB)

    Losekamm, Martin [Physics Department E18, Technische Universitaet Muenchen (Germany); Institute of Astronautics, Technische Universitaet Muenchen (Germany); Gaisbauer, Dominic; Konorov, Igor; Paul, Stephan; Poeschl, Thomas [Physics Department E18, Technische Universitaet Muenchen (Germany)

    2015-07-01

    The advances of solid-state detectors and in particular those for the detection of photons have made their application in space systems increasingly attractive in recent years. The use of, for example, silicon photomultipliers (SiPM) paired with a suitable scintillating material allows the development of compact and lightweight particle detectors. The Antiproton Flux in Space experiment (AFIS) intends to measure the flux of antiprotons trapped in Earth's magnetosphere aboard a nanosatellite using an active target tracking detector, consisting of plastic scintillating fibers read out by SiPMs. In order to implement a large number of detector channels while adhering to the given space, mass and power constraints, the development of a compact TDC-based data acquisition system was proposed. This talk presents a current prototype featuring 900 channels, real-time multi-channel temperature measurement and bias regulation. Possible alternative applications as well as the next steps in the development are also discussed.

  11. Loop calculations for the non-commutative U*(1) gauge field model with oscillator term

    International Nuclear Information System (INIS)

    Blaschke, Daniel N.; Grosse, Harald; Kronberger, Erwin; Schweda, Manfred; Wohlgenannt, Michael

    2010-01-01

    Motivated by the success of the non-commutative scalar Grosse-Wulkenhaar model, a non-commutative U * (1) gauge field theory including an oscillator-like term in the action has been put forward in (Blaschke et al. in Europhys. Lett. 79:61002, 2007). The aim of the current work is to analyze whether that action can lead to a fully renormalizable gauge model on non-commutative Euclidean space. In a first step, explicit one-loop graph computations are hence presented, and their results as well as necessary modifications of the action are successively discussed. (orig.)

  12. Supersymmetry and cotangent bundle over non-compact exceptional Hermitian symmetric space

    International Nuclear Information System (INIS)

    Arai, Masato; Baba, Kurando

    2015-01-01

    We construct N=2 supersymmetric nonlinear sigma models on the cotangent bundles over the non-compact exceptional Hermitian symmetric spaces M=E 6(−14) /SO(10)×U(1) and E 7(−25) /E 6 ×U(1). In order to construct them we use the projective superspace formalism which is an N=2 off-shell superfield formulation in four-dimensional space-time. This formalism allows us to obtain the explicit expression of N=2 supersymmetric nonlinear sigma models on the cotangent bundles over any Hermitian symmetric spaces in terms of the N=1 superfields, once the Kähler potentials of the base manifolds are obtained. We derive the N=1 supersymmetric nonlinear sigma models on the Kähler manifolds M. Then we extend them into the N=2 supersymmetric models with the use of the result in arXiv:1211.1537 developed in the projective superspace formalism. The resultant models are the N=2 supersymmetric nonlinear sigma models on the cotangent bundles over the Hermitian symmetric spaces M. In this work we complete constructing the cotangent bundles over all the compact and non-compact Hermitian symmetric spaces.

  13. Noncommutative QFT and renormalization

    International Nuclear Information System (INIS)

    Grosse, H.; Wulkenhaar, R.

    2006-01-01

    It was a great pleasure for me (Harald Grosse) to be invited to talk at the meeting celebrating the 70th birthday of Prof. Julius Wess. I remember various interactions with Julius during the last years: At the time of my studies at Vienna with Walter Thirring, Julius left already Vienna, I learned from his work on effective chiral Lagrangians. Next we met at various conferences and places like CERN (were I worked with Andre Martin, an old friend of Julius), and we all learned from Julius' and Bruno's creation of supersymmetry, next we realized our common interests in noncommutative quantum field theory and did have an intensive exchange. Julius influenced our perturbative approach to gauge field theories were we used the Seiberg-Witten map after his advice. And finally I lively remember the sad days when during my invitation to Vienna Julius did have the serious heart attack. So we are very happy, that you recovered so well, and we wish you all the best for the forthcoming years. Many happy recurrences. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  14. Noncommutative CPN and CHN and their physics

    International Nuclear Information System (INIS)

    Sako, Akifumi; Suzuki, Toshiya; Umetsu, Hiroshi

    2013-01-01

    We study noncommutative deformation of manifolds by constructing star products. We start from a noncommutative R d and discuss more genaral noncommutative manifolds. In general, star products can not be described in concrete expressions without some exceptions. In this article we introduce new examples of noncommutative manifolds with explicit star products. Karabegov's deformation quantization of CP N and CH N with separation of variables gives explicit calulable star products represented by gamma functions. Using the results of star products between inhomogeneous coordinates, we find creation and anihilation operators and obtain the Fock representation of the noncommutative CP N and CH N .

  15. Noncommutative mathematics for quantum systems

    CERN Document Server

    Franz, Uwe

    2016-01-01

    Noncommutative mathematics is a significant new trend of mathematics. Initially motivated by the development of quantum physics, the idea of 'making theory noncommutative' has been extended to many areas of pure and applied mathematics. This book is divided into two parts. The first part provides an introduction to quantum probability, focusing on the notion of independence in quantum probability and on the theory of quantum stochastic processes with independent and stationary increments. The second part provides an introduction to quantum dynamical systems, discussing analogies with fundamental problems studied in classical dynamics. The desire to build an extension of the classical theory provides new, original ways to understand well-known 'commutative' results. On the other hand the richness of the quantum mathematical world presents completely novel phenomena, never encountered in the classical setting. This book will be useful to students and researchers in noncommutative probability, mathematical physi...

  16. On noncommutative open string theories

    International Nuclear Information System (INIS)

    Russo, J.G.; Sheikh-Jabbari, M.M.

    2000-08-01

    We investigate new compactifications of OM theory giving rise to a 3+1 dimensional open string theory with noncommutative x 0 -x 1 and x 2 -x 3 coordinates. The theory can be directly obtained by starting with a D3 brane with parallel (near critical) electric and magnetic field components, in the presence of a RR scalar field. The magnetic parameter permits to interpolate continuously between the x 0 -x 1 noncommutative open string theory and the x 2 -x 3 spatial noncommutative U(N) super Yang-Mills theory. We discuss SL(2, Z) transformations of this theory. Using the supergravity description of the large N limit, we also compute corrections to the quark-antiquark Coulomb potential arising in the NCOS theory. (author)

  17. Connecting dissipation and noncommutativity: A Bateman system case study

    Science.gov (United States)

    Pal, Sayan Kumar; Nandi, Partha; Chakraborty, Biswajit

    2018-06-01

    We present an approach to the problem of quantization of the damped harmonic oscillator. To start with, we adopt the standard method of doubling the degrees of freedom of the system (Bateman form) and then, by introducing some new parameters, we get a generalized coupled set of equations from the Bateman form. Using the corresponding time-independent Lagrangian, quantum effects on a pair of Bateman oscillators embedded in an ambient noncommutative space (Moyal plane) are analyzed by using both path integral and canonical quantization schemes within the framework of the Hilbert-Schmidt operator formulation. Our method is distinct from those existing in the literature and where the ambient space was taken to be commutative. Our quantization shows that we end up again with a Bateman system except that the damping factor undergoes renormalization. Strikingly, the corresponding expression shows that the renormalized damping factor can be nonzero even if "bare" one is zero to begin with. In other words, noncommutativity can act as a source of dissipation. Conversely, the noncommutative parameter θ , taken to be a free one now, can be fine tuned to get a vanishing renormalized damping factor. This indicates in some sense a "duality" between dissipation and noncommutativity. Our results match the existing results in the commutative limit.

  18. On noncommutativity with bifermionic parameter

    International Nuclear Information System (INIS)

    Acatrinei, Ciprian Sorin

    2008-01-01

    Recently Gitman and Vassilevich proposed an interesting model of noncommutative (NC) scalar field theory, with a noncommutativity parameter assumed to be the product of two Grassmann variables. They showed in particular that the model possesses a local energy-momentum tensor. Since such a property is quite unusual for a NC model, we provide here an alternative picture, based on an operatorial formulation of NC field theory. It leads to complete locality of the degrees of freedom of the theory, a property in agreement with the termination of the star-product at the second term in its series. (author)

  19. Late time acceleration in a non-commutative model of modified cosmology

    Energy Technology Data Exchange (ETDEWEB)

    Malekolkalami, B., E-mail: b.malakolkalami@uok.ac.ir [Department of Physics, University of Kurdistan, Pasdaran St., Sanandaj (Iran, Islamic Republic of); Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir [Department of Physics, Azarbaijan Shahid Madani University, 53714-161, Tabriz (Iran, Islamic Republic of); Vakili, B., E-mail: b-vakili@iauc.ac.ir [Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)

    2014-12-12

    We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution.

  20. Late time acceleration in a non-commutative model of modified cosmology

    International Nuclear Information System (INIS)

    Malekolkalami, B.; Atazadeh, K.; Vakili, B.

    2014-01-01

    We investigate the effects of non-commutativity between the position–position, position–momentum and momentum–momentum of a phase space corresponding to a modified cosmological model. We show that the existence of such non-commutativity results in a Moyal Poisson algebra between the phase space variables in which the product law between the functions is of the kind of an α-deformed product. We then transform the variables in such a way that the Poisson brackets between the dynamical variables take the form of a usual Poisson bracket but this time with a noncommutative structure. For a power law expression for the function of the Ricci scalar with which the action of the gravity model is modified, the exact solutions in the commutative and noncommutative cases are presented and compared. In terms of these solutions we address the issue of the late time acceleration in cosmic evolution

  1. On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

    Science.gov (United States)

    Arnlind, Joakim; Wilson, Mitsuru

    2017-01-01

    We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.

  2. Noncommutativity into Dirac Equation with mass dependent on the position

    International Nuclear Information System (INIS)

    Bastos, Samuel Batista; Almeida, Carlos Alberto Santos; Nunes, Luciana Angelica da Silva

    2013-01-01

    Full text: In recent years, there is growing interest in the study of theories in non-commutative spaces. Non-commutative fields theories are related with compactifications of M theory, string theory and the quantum Hall effect. Moreover, the role of the non-commutativity of theories of a particle finds large applications when analyzed in scenarios of quantum mechanics and relativistic quantum mechanics. In these contexts investigations on the Schrodinger and Dirac equations with mass depending on the position (MDP) has attracted much attention in the literature. Systems endowed with MDP models are useful for the study of many physical problems. In particular, they are used to study the energy density in problems of many bodies, determining the electronic properties of semiconductor heterostructures and also to describe the properties of heterojunctions and quantum dots. In particular, the investigation of relativistic effects it is important for systems containing heavy atoms or doping by heavy ions. For these types of materials, the study of the properties of the Dirac equation, in the case where the mass becomes variable is of great interest. In this paper, we seek for the non-relativistic limit of the Dirac Hamiltonian in the context of a theory of effective mass, through a Foldy-Wouthuysen transformation. We analyse the Dirac equation with mass dependent on the position, in a smooth step shape mass distribution, in non-commutative space (NC). This potential type kink was recently discussed by several authors in the commutative context and now we present our results in the non-commutative context. (author)

  3. Compactness of the automorphism group of a topological parallelism on real projective 3-space: The disconnected case

    OpenAIRE

    Rainer, Löwen

    2017-01-01

    We prove that the automorphism group of a topological parallelism on real projective 3-space is compact. In a preceding article it was proved that at least the connected component of the identity is compact. The present proof does not depend on that earlier result.

  4. Ob the Froissart-Martin bound in spaces with compact dimensions

    CERN Document Server

    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

  5. Development of space heating and domestic hot water systems with compact thermal energy storage. Compact thermal energy storage: Material development for System Integration

    NARCIS (Netherlands)

    Davidson, J.H.; Quinnell, J.; Burch, J.; Zondag, H.A.; Boer, R. de; Finck, C.J.; Cuypers, R.; Cabeza, L.F.; Heinz, A.; Jahnig, D.; Furbo, S.; Bertsch, F.

    2013-01-01

    Long-term, compact thermal energy storage (TES) is essential to the development of cost-effective solar and passive building-integrated space heating systems and may enhance the annual technical and economic performance of solar domestic hot water (DHW) systems. Systems should provide high energy

  6. Topological and homological properties of the orbit space of a compact linear Lie group with commutative connected component

    OpenAIRE

    Styrt, O. G.

    2016-01-01

    The problem in question is whether the quotient space of a compact linear group is a topological manifold and whether it is a homological manifold. In the paper, the case of an infinite group with commutative connected component is considered.

  7. A note on the Königs domain of compact composition operators on the Bloch space

    Directory of Open Access Journals (Sweden)

    Jones Matthew

    2011-01-01

    Full Text Available Abstract Let be the unit disk in the complex plane. We define to be the little Bloch space of functions f analytic in which satisfy lim|z|→1 (1 - |z|2|f'(z| = 0. If is analytic then the composition operator Cφ : f ↦ f ∘ φ is a continuous operator that maps into itself. In this paper, we show that the compactness of Cφ , as an operator on , can be modelled geometrically by its principal eigenfunction. In particular, under certain necessary conditions, we relate the compactness of Cφ to the geometry of , where σ satisfies Schöder's functional equation σ ∘ φ = φ'(0σ. 2000 Mathematics Subject Classification: Primary 30D05; 47B33 Secondary 30D45.

  8. Twisted covariant noncommutative self-dual gravity

    International Nuclear Information System (INIS)

    Estrada-Jimenez, S.; Garcia-Compean, H.; Obregon, O.; Ramirez, C.

    2008-01-01

    A twisted covariant formulation of noncommutative self-dual gravity is presented. The formulation for constructing twisted noncommutative Yang-Mills theories is used. It is shown that the noncommutative torsion is solved at any order of the θ expansion in terms of the tetrad and some extra fields of the theory. In the process the first order expansion in θ for the Plebanski action is explicitly obtained.

  9. Canonical noncommutativity in special and general relativity

    Energy Technology Data Exchange (ETDEWEB)

    Chryssomalakos, C; Hernandez, H; Okon, E; Vazquez Montejo, P [Instituto de Ciencias Nucleares, Universidad National Autonoma de Mexico, 04510 Mexico, D.F. (Mexico)

    2007-05-15

    There are two main points that concern us in this short contribution. The first one is the conceptual distinction between a intrinsically noncommuting spacetime, i.e., one where the coordinate functions fail to commute among themselves, on the one hand, and the proposal of noncommuting position operators, on the other. The second point concerns a particular form of position operator noncommutativity, involving the spin of the particle, to which several approaches seem to converge. We also suggest an analysis of the effects of spacetime curvature on position operator noncommutativity.

  10. Noncommutative geometry and twisted conformal symmetry

    International Nuclear Information System (INIS)

    Matlock, Peter

    2005-01-01

    The twist-deformed conformal algebra is constructed as a Hopf algebra with twisted coproduct. This allows for the definition of conformal symmetry in a noncommutative background geometry. The twisted coproduct is reviewed for the Poincare algebra and the construction is then extended to the full conformal algebra. The case of Moyal-type noncommutativity of the coordinates is considered. It is demonstrated that conformal invariance need not be viewed as incompatible with noncommutative geometry; the noncommutativity of the coordinates appears as a consequence of the twisting, as has been shown in the literature in the case of the twisted Poincare algebra

  11. Embeddings of model subspaces of the Hardy space: compactness and Schatten-von Neumann ideals

    International Nuclear Information System (INIS)

    Baranov, Anton D

    2009-01-01

    We study properties of the embedding operators of model subspaces K p Θ (defined by inner functions) in the Hardy space H p (coinvariant subspaces of the shift operator). We find a criterion for the embedding of K p Θ in L p (μ) to be compact similar to the Volberg-Treil theorem on bounded embeddings, and give a positive answer to a question of Cima and Matheson. The proof is based on Bernstein-type inequalities for functions in K p Θ . We investigate measures μ such that the embedding operator belongs to some Schatten-von Neumann ideal.

  12. Foliated Structure of The Kuranishi Space and Isomorphisms of Deformation Families of Compact Complex Manifolds

    OpenAIRE

    Meersseman, Laurent

    2009-01-01

    Consider the following uniformization problem. Take two holomorphic (parametrized by some analytic set defined on a neighborhood of $0$ in $\\Bbb C^p$, for some $p>0$) or differentiable (parametrized by an open neighborhood of $0$ in $\\Bbb R^p$, for some $p>0$) deformation families of compact complex manifolds. Assume they are pointwise isomorphic, that is for each point $t$ of the parameter space, the fiber over $t$ of the first family is biholomorphic to the fiber over $t$ of the second fami...

  13. Quantum thetas on noncommutative Td with general embeddings

    International Nuclear Information System (INIS)

    Chang-Young, Ee; Kim, Hoil

    2008-01-01

    In this paper, we construct quantum theta functions over noncommutative T d with general embeddings. Manin has constructed quantum theta functions from the lattice embedding into vector space x finite group. We extend Manin's construction of quantum thetas to the case of general embedding of vector space x lattice x torus. It turns out that only for the vector space part of the embedding there exists the holomorphic theta vector, while for the lattice part there does not. Furthermore, the so-called quantum translations from embedding into the lattice part become non-additive, while those from the vector space part are additive

  14. Quantum gravity from noncommutative spacetime

    International Nuclear Information System (INIS)

    Lee, Jungjai; Yang, Hyunseok

    2014-01-01

    We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.

  15. Quantum gravity from noncommutative spacetime

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)

    2014-12-15

    We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.

  16. Effects of space-dependent cross sections on core physics parameters for compact fast spectrum space power reactors

    International Nuclear Information System (INIS)

    Lell, R.M.; Hanan, N.A.

    1987-01-01

    Effects of multigroup neutron cross section generation procedures on core physics parameters for compact fast spectrum reactors have been examined. Homogeneous and space-dependent multigroup cross section sets were generated in 11 and 27 groups for a representative fast reactor core. These cross sections were used to compute various reactor physics parameters for the reference core. Coarse group structure and neglect of space-dependence in the generation procedure resulted in inaccurate computations of reactor flux and power distributions and in significant errors regarding estimates of core reactivity and control system worth. Delayed neutron fraction was insensitive to cross section treatment, and computed reactivity coefficients were only slightly sensitive. However, neutron lifetime was found to be very sensitive to cross section treatment. Deficiencies in multigroup cross sections are reflected in core nuclear design and, consequently, in system mechanical design

  17. Calculating the jet quenching parameter in the plasma of noncommutative Yang-Mills theory from gauge/gravity duality

    Science.gov (United States)

    Chakraborty, Somdeb; Roy, Shibaji

    2012-02-01

    A particular decoupling limit of the nonextremal (D1, D3) brane bound state system of type IIB string theory is known to give the gravity dual of space-space noncommutative Yang-Mills theory at finite temperature. We use a string probe in this background to compute the jet quenching parameter in a strongly coupled plasma of hot noncommutative Yang-Mills theory in (3+1) dimensions from gauge/gravity duality. We give expressions for the jet quenching parameter for both small and large noncommutativity. For small noncommutativity, we find that the value of the jet quenching parameter gets reduced from its commutative value. The reduction is enhanced with temperature as T7 for fixed noncommutativity and fixed ’t Hooft coupling. We also give an estimate of the correction due to noncommutativity at the present collider energies like in RHIC or in LHC and find it too small to be detected. We further generalize the results for noncommutative Yang-Mills theories in diverse dimensions.

  18. The noncommutative standard model. Construction beyond leading order in θ and collider phenomenology

    International Nuclear Information System (INIS)

    Alboteanu, A.M.

    2007-01-01

    Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time. In the first part we performed a phenomenological analysis of the hadronic process pp → Z γ → l + l - γ at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl *-product of functions on ordinary space-time and the Seiberg-Witten maps. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale NC. By studying pp→Z γ →l + l - γ to first order in the noncommutative parameter θ, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of Λ NC >or similar 1.2 TeV. By means of e + e - → Z γ → l + l - γ to O(θ) we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on Λ NC derived from the ILC are significantly higher and reach Λ NC >or similar 6 TeV. In the second part of this work we expand the neutral current sector of the noncommutative SM to second order in θ. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by homogeneous solutions of the gauge equivalence equations. The expectation was that the ambiguities correspond to field redefinitions and therefore should

  19. The noncommutative standard model. Construction beyond leading order in {theta} and collider phenomenology

    Energy Technology Data Exchange (ETDEWEB)

    Alboteanu, A.M.

    2007-07-01

    Within this work we study the phenomenological consequences of a possible realization of QFT on noncommutative space-time. In the first part we performed a phenomenological analysis of the hadronic process pp {yields} Z{sub {gamma}} {yields} l{sup +}l{sup -}{gamma} at the LHC and of electron-positron pair annihilation into a Z boson and a photon at the International Linear Collider (ILC). The noncommutative extension of the SM considered within this work relies on two building blocks: the Moyal-Weyl *-product of functions on ordinary space-time and the Seiberg-Witten maps. A consequence of the noncommutativity of space-time is the violation of rotational invariance with respect to the beam axis. This effect shows up in the azimuthal dependence of cross sections, which is absent in the SM as well as in other models beyond the SM. We have found this dependence to be best suited for deriving the sensitivity bounds on the noncommutative scale NC. By studying pp{yields}Z{sub {gamma}} {yields}l{sup +}l{sup -}{gamma} to first order in the noncommutative parameter {theta}, we show in the first part of this work that measurements at the LHC are sensitive to noncommutative effects only in certain cases, giving bounds on the noncommutative scale of {lambda}{sub NC} >or similar 1.2 TeV. By means of e{sup +}e{sup -} {yields} Z{sub {gamma}} {yields} l{sup +}l{sup -}{gamma} to O({theta}) we have shown that ILC measurements are complementary to LHC measurements of the noncommutative parameters. In addition, the bounds on {lambda}{sub NC} derived from the ILC are significantly higher and reach {lambda}{sub NC} >or similar 6 TeV. In the second part of this work we expand the neutral current sector of the noncommutative SM to second order in {theta}. We found that, against the general expectation, the theory must be enlarged by additional parameters. The new parameters enter the theory as ambiguities of the Seiberg-Witten maps. The latter are not uniquely determined and differ by

  20. Non-orthogonal internally contracted multi-configurational perturbation theory (NICPT): Dynamic electron correlation for large, compact active spaces

    Science.gov (United States)

    Kähler, Sven; Olsen, Jeppe

    2017-11-01

    A computational method is presented for systems that require high-level treatments of static and dynamic electron correlation but cannot be treated using conventional complete active space self-consistent field-based methods due to the required size of the active space. Our method introduces an efficient algorithm for perturbative dynamic correlation corrections for compact non-orthogonal MCSCF calculations. In the algorithm, biorthonormal expansions of orbitals and CI-wave functions are used to reduce the scaling of the performance determining step from quadratic to linear in the number of configurations. We describe a hierarchy of configuration spaces that can be chosen for the active space. Potential curves for the nitrogen molecule and the chromium dimer are compared for different configuration spaces. Already the most compact spaces yield qualitatively correct potentials that with increasing size of configuration spaces systematically approach complete active space results.

  1. Absolutely continuous measures and compact composition operator on spaces of Cauchy transforms

    Directory of Open Access Journals (Sweden)

    Yusuf Abu Muhanna

    2004-01-01

    Full Text Available The analytic self-map of the unit disk D, φ is said to induce a composition operator Cφ from the Banach space X to the Banach space Y if Cφ(f=f∘φ∈Y for all f∈X. For z∈D and α>0, the families of weighted Cauchy transforms Fα are defined by f(z=∫TKxα(zdμ(x, where μ(x is complex Borel measure, x belongs to the unit circle T, and the kernel Kx(z=(1−x¯z−1. In this paper, we will explore the relationship between the compactness of the composition operator Cφ acting on Fα and the complex Borel measures μ(x.

  2. Efficiently enclosing the compact binary parameter space by singular-value decomposition

    International Nuclear Information System (INIS)

    Cannon, Kipp; Hanna, Chad; Keppel, Drew

    2011-01-01

    Gravitational-wave searches for the merger of compact binaries use matched filtering as the method of detecting signals and estimating parameters. Such searches construct a fine mesh of filters covering a signal parameter space at high density. Previously it has been shown that singular-value decomposition can reduce the effective number of filters required to search the data. Here we study how the basis provided by the singular-value decomposition changes dimension as a function of template-bank density. We will demonstrate that it is sufficient to use the basis provided by the singular-value decomposition of a low-density bank to accurately reconstruct arbitrary points within the boundaries of the template bank. Since this technique is purely numerical, it may have applications to interpolating the space of numerical relativity waveforms.

  3. Space potential fluctuations during MHD activities in the Compact Helical System (CHS)

    International Nuclear Information System (INIS)

    Iguchi, H.; Fujisawa, A.; Crowley, T.P.

    1998-02-01

    Local space potential fluctuations have been measured during MHD activities in a low-beta NBI heated plasma in the Compact Helical System (CHS) by the use of a heavy ion beam probe (HIBP). Two types of MHD modes with accompanying potential oscillations are observed. One appears in periodic bursts with relatively low frequency (< 40 kHz) and large amplitude (20-40 volts), and is localized around the q=2 surface (average minor radius ρ ∼ 0.7). The other appears in continuous and coherent oscillation with higher frequency (105-125 kHz) and smaller amplitude (∼5 volts). This oscillation also has spatial structure. Possible interpretation for the space potential oscillations is presented. (author)

  4. Black Hole Complementary Principle and Noncommutative Membrane

    International Nuclear Information System (INIS)

    Wei Ren

    2006-01-01

    In the spirit of black hole complementary principle, we have found the noncommutative membrane of Scharzchild black holes. In this paper we extend our results to Kerr black hole and see the same story. Also we make a conjecture that spacetimes are noncommutative on the stretched membrane of the more general Kerr-Newman black hole.

  5. Dolan Grady relations and noncommutative quasi-exactly solvable systems

    Science.gov (United States)

    Klishevich, Sergey M.; Plyushchay, Mikhail S.

    2003-11-01

    We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the {\\mathfrak{su}}(2) and {\\mathfrak{sl}}(2,{\\bb {R}}) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems.

  6. The shear viscosity of the non-commutative plasma

    International Nuclear Information System (INIS)

    Landsteiner, Karl; Mas, Javier

    2007-01-01

    We compute the shear viscosity of the non-commutative N = 4 super Yang-Mills quantum field theory at strong coupling using the dual supergravity background. Special interest derives from the fact that the background presents an intrinsic anisotropy in space through the distinction of commutative and non-commutative directions. Despite this anisotropy the analysis exhibits the ubiquitous result η/s = 1/4π for two different shear channels. In order to derive this result, we show that the boundary energy momentum tensor must couple to the open string metric. As a byproduct we compute the renormalised holographic energy momentum tensor and show that it coincides with one in the commutative theory

  7. Can non-commutativity resolve the big-bang singularity?

    Energy Technology Data Exchange (ETDEWEB)

    Maceda, M.; Madore, J. [Laboratoire de Physique Theorique, Universite de Paris-Sud, Batiment 211, 91405, Orsay (France); Manousselis, P. [Department of Engineering Sciences, University of Patras, 26110, Patras (Greece); Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Zoupanos, G. [Physics Department, National Technical University, Zografou Campus, 157 80, Zografou, Athens (Greece); Theory Division, CERN, 1211, Geneva 23 (Switzerland)

    2004-08-01

    A possible way to resolve the singularities of general relativity is proposed based on the assumption that the description of space-time using commuting coordinates is not valid above a certain fundamental scale. Beyond that scale it is assumed that the space-time has non-commutative structure leading in turn to a resolution of the singularity. As a first attempt towards realizing the above programme a modification of the Kasner metric is constructed which is commutative only at large time scales. At small time scales, near the singularity, the commutation relations among the space coordinates diverge. We interpret this result as meaning that the singularity has been completely delocalized. (orig.)

  8. Quantum Thetas on Noncommutative T^d with General Embeddings

    OpenAIRE

    Chang-Young, Ee; Kim, Hoil

    2007-01-01

    In this paper we construct quantum theta functions over noncommutative T^d with general embeddings. Manin has constructed quantum theta functions from the lattice embedding into vector space x finite group. We extend Manin's construction of quantum thetas to the case of general embedding of vector space x lattice x torus. It turns out that only for the vector space part of the embedding there exists the holomorphic theta vector, while for the lattice part there does not. Furthermore, the so-c...

  9. String states, loops and effective actions in noncommutative field theory and matrix models

    Directory of Open Access Journals (Sweden)

    Harold C. Steinacker

    2016-09-01

    Full Text Available Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.

  10. String states, loops and effective actions in noncommutative field theory and matrix models

    Energy Technology Data Exchange (ETDEWEB)

    Steinacker, Harold C., E-mail: harold.steinacker@univie.ac.at

    2016-09-15

    Refining previous work by Iso, Kawai and Kitazawa, we discuss bi-local string states as a tool for loop computations in noncommutative field theory and matrix models. Defined in terms of coherent states, they exhibit the stringy features of noncommutative field theory. This leads to a closed form for the 1-loop effective action in position space, capturing the long-range non-local UV/IR mixing for scalar fields. The formalism applies to generic fuzzy spaces. The non-locality is tamed in the maximally supersymmetric IKKT or IIB model, where it gives rise to supergravity. The linearized supergravity interactions are obtained directly in position space at one loop using string states on generic noncommutative branes.

  11. An introduction to quantum groups and non-commutative differential calculus

    International Nuclear Information System (INIS)

    Azcarraga, J.A. de; Rodenas, F.

    1995-01-01

    An introduction to quantum groups and quantum spaces is presented, and the non-commutative calculus on them is discussed. The case of q-Minkowski space is presented as an illustrative example. A set of useful expressions and formulae are collected in an appendix. 45 refs

  12. Non-topological non-commutativity in string theory

    International Nuclear Information System (INIS)

    Guttenberg, S.; Herbst, M.; Kreuzer, M.; Rashkov, R.

    2008-01-01

    Quantization of coordinates leads to the non-commutative product of deformation quantization, but is also at the roots of string theory, for which space-time coordinates become the dynamical fields of a two-dimensional conformal quantum field theory. Appositely, open string diagrams provided the inspiration for Kontsevich's solution of the long-standing problem of quantization of Poisson geometry by virtue of his formality theorem. In the context of D-brane physics non-commutativity is not limited, however, to the topological sector. We show that non-commutative effective actions still make sense when associativity is lost and establish a generalized Connes-Flato-Sternheimer condition through second order in a derivative expansion. The measure in general curved backgrounds is naturally provided by the Born-Infeld action and reduces to the symplectic measure in the topological limit, but remains non-singular even for degenerate Poisson structures. Analogous superspace deformations by RR-fields are also discussed. (Abstract Copyright [2008], Wiley Periodicals, Inc.)

  13. The theory of pseudo-differential operators on the noncommutative n-torus

    Science.gov (United States)

    Tao, J.

    2018-02-01

    The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct analogy with the theory of pseudo-differential operators on finite-dimensional real vector spaces, one may derive a similar pseudo-differential calculus on noncommutative n-tori, and with the development of this calculus came many results concerning the local differential geometry of noncommutative tori for n=2,4, as shown in the groundbreaking paper in which the Gauss-Bonnet theorem on the noncommutative two-torus is proved and later papers. Certain details of the proofs in the original derivation of the calculus were omitted, such as the evaluation of oscillatory integrals, so we make it the objective of this paper to fill in all the details. After reproving in more detail the formula for the symbol of the adjoint of a pseudo-differential operator and the formula for the symbol of a product of two pseudo-differential operators, we extend these results to finitely generated projective right modules over the noncommutative n-torus. Then we define the corresponding analog of Sobolev spaces and prove equivalents of the Sobolev and Rellich lemmas.

  14. Hopf algebras in noncommutative geometry

    International Nuclear Information System (INIS)

    Varilly, Joseph C.

    2001-10-01

    We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)

  15. Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics

    Science.gov (United States)

    Rodriguez R., Miguel E.

    2018-01-01

    Quantum mechanics in noncommutative space modifies the standard result of the Aharonov-Bohm effect for electrons and other recent quantum effects. Here we obtain the phase in noncommutative space for the Spavieri effect, a generalization of Aharonov-Bohm effect which involves a coherent superposition of particles with opposite charges moving along a single open interferometric path. By means of the experimental considerations a limit √{θ }≃(0.13TeV)-1 is achieved, improving by 10 orders of magnitude the results derived by Chaichian et al. [Phys. Lett. B 527, 149 (2002), 10.1016/S0370-2693(02)01176-0] for the Aharonov-Bohm effect. It is also shown that the noncommutative phases of the Aharonov-Casher and He-McKellar-Willkens effects are nullified in the current experimental tests.

  16. Towards Noncommutative Topological Quantum Field Theory: New invariants for 3-manifolds

    International Nuclear Information System (INIS)

    Zois, I.P.

    2016-01-01

    We present some ideas for a possible Noncommutative Topological Quantum Field Theory (NCTQFT for short) and Noncommutative Floer Homology (NCFH for short). Our motivation is two-fold and it comes both from physics and mathematics: On the one hand we argue that NCTQFT is the correct mathematical framework for a quantum field theory of all known interactions in nature (including gravity). On the other hand we hope that a possible NCFH will apply to practically every 3-manifold (and not only to homology 3-spheres as ordinary Floer Homology currently does). The two motivations are closely related since, at least in the commutative case, Floer Homology Groups constitute the space of quantum observables of (3+1)-dim Topological Quantum Field Theory. Towards this goal we define some new invariants for 3-manifolds using the space of taut codim-1 foliations modulo coarse isotopy along with various techniques from noncommutative geometry. (paper)

  17. Noncommutative gauge theories and Kontsevich's formality theorem

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.; Wess, J.

    2001-01-01

    The equivalence of star products that arise from the background field with and without fluctuations and Kontsevich's formality theorem allow an explicitly construction of a map that relates ordinary gauge theory and noncommutative gauge theory (Seiberg-Witten map.) Using noncommutative extra dimensions the construction is extended to noncommutative nonabelian gauge theory for arbitrary gauge groups; as a byproduct we obtain a 'Mini Seiberg-Witten map' that explicitly relates ordinary abelian and nonabelian gauge fields. All constructions are also valid for non-constant B-field, and even more generally for any Poisson tensor

  18. Noncommutative quantum mechanics and Bohm's ontological interpretation

    International Nuclear Information System (INIS)

    Barbosa, G.D.; Pinto-Neto, N.

    2004-01-01

    We carry out an investigation into the possibility of developing a Bohmian interpretation based on the continuous motion of point particles for noncommutative quantum mechanics. The conditions for such an interpretation to be consistent are determined, and the implications of its adoption for noncommutativity are discussed. A Bohmian analysis of the noncommutative harmonic oscillator is carried out in detail. By studying the particle motion in the oscillator orbits, we show that small-scale physics can have influence at large scales, something similar to the IR-UV mixing

  19. Noncommuting observables and local realism

    International Nuclear Information System (INIS)

    Malley, James D.; Fine, Arthur

    2005-01-01

    A standard approach in the foundations of quantum mechanics studies local realism and hidden variables models exclusively in terms of violations of Bell-like inequalities. Thus quantum nonlocality is tied to the celebrated no-go theorems, and these comprise a long list that includes the Kochen-Specker and Bell theorems, as well as elegant refinements by Mermin, Peres, Hardy, GHZ, and many others. Typically entanglement or carefully prepared multipartite systems have been considered essential for violations of local realism and for understanding quantum nonlocality. Here we show, to the contrary, that sharp violations of local realism arise almost everywhere without entanglement. The pivotal fact driving these violations is just the noncommutativity of quantum observables. We demonstrate how violations of local realism occur for arbitrary noncommuting projectors, and for arbitrary quantum pure states. Finally, we point to elementary tests for local realism, using single particles and without reference to entanglement, thus avoiding experimental loopholes and efficiency issues that continue to bedevil the Bell inequality related tests

  20. Compact composition operators on real Banach spaces of complex-valued bounded Lipschitz functions

    Directory of Open Access Journals (Sweden)

    Davood Alimohammadi

    2014-10-01

    Full Text Available We characterize compact composition operators on real Banachspaces of complex-valued bounded Lipschitz functions on metricspaces, not necessarily compact, with Lipschitz involutions anddetermine their spectra.

  1. Holographic entanglement in a noncommutative gauge theory

    International Nuclear Information System (INIS)

    Fischler, Willy; Kundu, Arnab; Kundu, Sandipan

    2014-01-01

    In this article we investigate aspects of entanglement entropy and mutual information in a large-N strongly coupled noncommutative gauge theory, both at zero and at finite temperature. Using the gauge-gravity duality and the Ryu-Takayanagi (RT) prescription, we adopt a scheme for defining spatial regions on such noncommutative geometries and subsequently compute the corresponding entanglement entropy. We observe that for regions which do not lie entirely in the noncommutative plane, the RT-prescription yields sensible results. In order to make sense of the divergence structure of the corresponding entanglement entropy, it is essential to introduce an additional cut-off in the theory. For regions which lie entirely in the noncommutative plane, the corresponding minimal area surfaces can only be defined at this cut-off and they have distinctly peculiar properties

  2. The local index formula in noncommutative geometry

    International Nuclear Information System (INIS)

    Higson, N.

    2003-01-01

    These notes present a partial account of the local index theorem in non-commutative geometry discovered by Alain Connes and Henri Moscovici. It includes Elliptic partial differential operators, cyclic homology theory, Chern characters, homotopy invariants and the index formulas

  3. Note on the extended noncommutativity of coordinates

    International Nuclear Information System (INIS)

    Boulahoual, Amina; Sedra, My. Brahim

    2001-04-01

    We present in this short note an idea about a possible extension of the standard noncommutative algebra to the formal differential operators framework. In this sense, we develop an analysis and derive an extended noncommutative algebra given by [x a , x b ] * =i(θ+χ) ab where θ ab , is the standard noncommutative parameter and χ ab (x)≡χ ab μ (x)δ μ =1/2(x a θ μ b -x b θ a )δ μ is an antisymmetric non-constant vector-field shown to play the role of the extended deformation parameter. This idea was motivated by the importance of noncommutative geometry framework in the current subject of D-brane and matrix theory physics. (author)

  4. Covariant non-commutative space–time

    Directory of Open Access Journals (Sweden)

    Jonathan J. Heckman

    2015-05-01

    Full Text Available We introduce a covariant non-commutative deformation of 3+1-dimensional conformal field theory. The deformation introduces a short-distance scale ℓp, and thus breaks scale invariance, but preserves all space–time isometries. The non-commutative algebra is defined on space–times with non-zero constant curvature, i.e. dS4 or AdS4. The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor. The polarization tensor takes active part in the non-commutative algebra, which for dS4 takes the form of so(5,1, while for AdS4 it assembles into so(4,2. The structure of the non-commutative correlation functions hints that the deformed theory contains gravitational interactions and a Regge-like trajectory of higher spin excitations.

  5. Entropic force, noncommutative gravity, and ungravity

    International Nuclear Information System (INIS)

    Nicolini, Piero

    2010-01-01

    After recalling the basic concepts of gravity as an emergent phenomenon, we analyze the recent derivation of Newton's law in terms of entropic force proposed by Verlinde. By reviewing some points of the procedure, we extend it to the case of a generic quantum gravity entropic correction to get compelling deviations to the Newton's law. More specifically, we study: (1) noncommutative geometry deviations and (2) ungraviton corrections. As a special result in the noncommutative case, we find that the noncommutative character of the manifold would be equivalent to the temperature of a thermodynamic system. Therefore, in analogy to the zero temperature configuration, the description of spacetime in terms of a differential manifold could be obtained only asymptotically. Finally, we extend the Verlinde's derivation to a general case, which includes all possible effects, noncommutativity, ungravity, asymptotically safe gravity, electrostatic energy, and extra dimensions, showing that the procedure is solid versus such modifications.

  6. Light-like noncommutativity, light-front quantization and new light on UV/IR mixing

    International Nuclear Information System (INIS)

    Sheikh-Jabbari, M.M.; Tureanu, A.

    2011-01-01

    We revisit the problem of quantizing field theories on noncommutative Moyal space-time with light-like noncommutativity. To tackle the issues arising from noncommuting and hence nonlocal time, we argue that for this case light-front quantization procedure should be employed. In this appropriate quantization scheme we perform the non-planar loop analysis for the light-like noncommutative field theories. One of the important and peculiar features of light-front quantization is that the UV cutoff of the light-cone Hamiltonian manifests itself as an IR cutoff for the light-cone momentum, p + . Due to this feature, the naive results of covariant quantization for the light-like case allude to the absence of the UV/IR mixing in the light-front quantization. However, by a careful analysis of non-planar loop integrals we show that this is not the case and the UV/IR mixing persists. In addition, we argue in favour of the perturbative unitarity of light-like noncommutative field theories in the light-front quantization scheme.

  7. PREFACE: Conceptual and Technical Challenges for Quantum Gravity 2014 - Parallel session: Noncommutative Geometry and Quantum Gravity

    Science.gov (United States)

    Martinetti, P.; Wallet, J.-C.; Amelino-Camelia, G.

    2015-08-01

    The conference Conceptual and Technical Challenges for Quantum Gravity at Sapienza University of Rome, from 8 to 12 September 2014, has provided a beautiful opportunity for an encounter between different approaches and different perspectives on the quantum-gravity problem. It contributed to a higher level of shared knowledge among the quantum-gravity communities pursuing each specific research program. There were plenary talks on many different approaches, including in particular string theory, loop quantum gravity, spacetime noncommutativity, causal dynamical triangulations, asymptotic safety and causal sets. Contributions from the perspective of philosophy of science were also welcomed. In addition several parallel sessions were organized. The present volume collects contributions from the Noncommutative Geometry and Quantum Gravity parallel session4, with additional invited contributions from specialists in the field. Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: • from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, • from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, • from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. This volume provides an overview of these various topics, interesting for the specialist as well as accessible to the newcomer. 4partially funded by CNRS PEPS /PTI ''Metric aspect of noncommutative geometry: from Monge to Higgs''

  8. Single-Mode, High Repetition Rate, Compact Ho:YLF Laser for Space-Borne Lidar Applications

    Science.gov (United States)

    Bai, Yingxin; Yu, Jirong; Wong, Teh-Hwa; Chen, Songsheng; Petros, Mulugeta; Singh, Upendra N.

    2014-01-01

    A single transverse/longitudinal mode, compact Q-switched Ho:YLF laser has been designed and demonstrated for space-borne lidar applications. The pulse energy is between 34-40 mJ for 100-200 Hz operation. The corresponding peak power is >1 MW.

  9. A preliminary feasibility study of passive in-core thermionic reactors for highly compact space nuclear power systems

    International Nuclear Information System (INIS)

    Parlos, A.G.; Khan, E.U.; Frymire, R.; Negron, S.; Thomas, J.K.; Peddicord, K.L.

    1991-01-01

    Results of a preliminary feasibility study on a new concept for a highly compact space reactor power systems are presented. Notwithstanding the preliminary nature of the present study, the results which include a new space reactor configuration and its associated technologies indicate promising avenues for the devleopment of highly compact space reactors. The calculations reported in this study include a neutronic design trade-off study using a two-dimensioinal neutron transport model, as well as a simplified one-dimensional thermal analysis of the reactor core. In arriving at the most desirable configuration, various options have been considered and analyzed, and their advantages/disadvantages have been compared. However, because of space limitation, only the most favorable reactor configuration is presented in this summary

  10. Noncommutative gauge theory for Poisson manifolds

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, Branislav E-mail: jurco@mpim-bonn.mpg.de; Schupp, Peter E-mail: schupp@theorie.physik.uni-muenchen.de; Wess, Julius E-mail: wess@theorie.physik.uni-muenchen.de

    2000-09-25

    A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

  11. Noncommutative gauge theory for Poisson manifolds

    International Nuclear Information System (INIS)

    Jurco, Branislav; Schupp, Peter; Wess, Julius

    2000-01-01

    A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem

  12. Non-commutative tomography and signal processing

    International Nuclear Information System (INIS)

    Mendes, R Vilela

    2015-01-01

    Non-commutative tomography is a technique originally developed and extensively used by Professors M A Man’ko and V I Man’ko in quantum mechanics. Because signal processing deals with operators that, in general, do not commute with time, the same technique has a natural extension to this domain. Here, a review is presented of the theory and some applications of non-commutative tomography for time series as well as some new results on signal processing on graphs. (paper)

  13. Non-commutative standard model: model building

    CERN Document Server

    Chaichian, Masud; Presnajder, P

    2003-01-01

    A non-commutative version of the usual electro-weak theory is constructed. We discuss how to overcome the two major problems: (1) although we can have non-commutative U(n) (which we denote by U sub * (n)) gauge theory we cannot have non-commutative SU(n) and (2) the charges in non-commutative QED are quantized to just 0,+-1. We show how the latter problem with charge quantization, as well as with the gauge group, can be resolved by taking the U sub * (3) x U sub * (2) x U sub * (1) gauge group and reducing the extra U(1) factors in an appropriate way. Then we proceed with building the non-commutative version of the standard model by specifying the proper representations for the entire particle content of the theory, the gauge bosons, the fermions and Higgs. We also present the full action for the non-commutative standard model (NCSM). In addition, among several peculiar features of our model, we address the inherentCP violation and new neutrino interactions. (orig.)

  14. Quadratic algebras applied to noncommutative integration of the Klein-Gordon equation: Four-dimensional quadratic algebras containing three-dimensional nilpotent lie algebras

    International Nuclear Information System (INIS)

    Varaksin, O.L.; Firstov, V.V.; Shapovalov, A.V.

    1995-01-01

    The study is continued on noncommutative integration of linear partial differential equations in application to the exact integration of quantum-mechanical equations in a Riemann space. That method gives solutions to the Klein-Gordon equation when the set of noncommutative symmetry operations for that equation forms a quadratic algebra consisting of one second-order operator and of first-order operators forming a Lie algebra. The paper is a continuation of, where a single nontrivial example is used to demonstrate noncommutative integration of the Klein-Gordon equation in a Riemann space not permitting variable separation

  15. Géométrie non-commutative, théorie de jauge et renormalisation

    OpenAIRE

    De Goursac , Axel

    2009-01-01

    Thèse effectuée en cotutelle au Département de Mathématique de l'Université de Münster (Allemagne); Nowadays, noncommutative geometry is a growing domain of mathematics, which can appear as a promising framework for modern physics. Quantum field theories on "noncommutative spaces" are indeed much investigated, and suffer from a new type of divergence called the ultraviolet-infrared mixing. However, this problem has recently been solved by H. Grosse and R. Wulkenhaar by adding to the action of...

  16. Extension of noncommutative soliton hierarchies

    International Nuclear Information System (INIS)

    Dimakis, Aristophanes; Mueller-Hoissen, Folkert

    2004-01-01

    A linear system, which generates a Moyal-deformed two-dimensional soliton equation as an integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The supplementary integrability conditions result in a first-order differential equation with respect to the deformation parameter, the flow of which commutes with the flow of the deformed soliton equation. In this way, a deformed soliton hierarchy can be extended to a bigger hierarchy by including the corresponding deformation equations. We prove the extended hierarchy properties for the deformed AKNS hierarchy, and specialize to the cases of deformed NLS, KdV and mKdV hierarchies. Corresponding results are also obtained for the deformed KP hierarchy. A deformation equation determines a kind of Seiberg-Witten map from classical solutions to solutions of the respective 'noncommutative' deformed equation

  17. Study and Developement of Compact Permanent Magnet Hall Thrusters for Future Brazillian Space Missions

    Science.gov (United States)

    Ferreira, Jose Leonardo; Martins, Alexandre; Cerda, Rodrigo

    2016-07-01

    The Plasma Physics Laboratory of UnB has been developing a Permanent Magnet Hall Thruster (PHALL) for the UNIESPAÇO program, part of the Space Activities Program conducted by AEB- The Brazillian Space Agency since 2004. Electric propulsion is now a very successful method for primary and secondary propulsion systems. It is essential for several existing geostationary satellite station keeping systems and for deep space long duration solar system missions, where the thrusting system can be designed to be used on orbit transfer maneuvering and/or for satellite attitude control in long term space missions. Applications of compact versions of Permanent Magnet Hall Thrusters on future brazillian space missions are needed and foreseen for the coming years beginning with the use of small divergent cusp field (DCFH) Hall Thrusters type on CUBESATS ( 5-10 kg , 1W-5 W power consumption) and on Micro satellites ( 50- 100 kg, 10W-100W). Brazillian (AEB) and German (DLR) space agencies and research institutions are developing a new rocket dedicated to small satellite launching. The VLM- Microsatellite Launch Vehicle. The development of PHALL compact versions can also be important for the recently proposed SBG system, a future brazillian geostationary satellite system that is already been developed by an international consortium of brazillian and foreign space industries. The exploration of small bodies in the Solar System with spacecraft has been done by several countries with increasing frequency in these past twenty five years. Since their historical beginning on the sixties, most of the Solar System missions were based on gravity assisted trajectories very much depended on planet orbit positioning relative to the Sun and the Earth. The consequence was always the narrowing of the mission launch window. Today, the need for Solar System icy bodies in situ exploration requires less dependence on gravity assisted maneuvering and new high precision low thrust navigation methods

  18. A function space from a compact metrizable space to a dendrite with the hypo-graph topology

    Directory of Open Access Journals (Sweden)

    Yang Hanbiao

    2015-03-01

    Full Text Available Let X be an infinite compact metrizable space having only a finite number of isolated points and Y be a non-degenerate dendrite with a distinguished end point v. For each continuous map ƒ : X → Y , we define the hypo-graph ↓vƒ = ∪ x∈X {x} × [v, ƒ (x], where [v, ƒ (x] is the unique arc from v to ƒ (x in Y . Then we can regard ↓v C(X, Y = {↓vƒ | ƒ : X → Y is continuous} as the subspace of the hyperspace Cld(X × Y of nonempty closed sets in X × Y endowed with the Vietoris topology. Let be the closure of ↓v C(X, Y in Cld(X ×Y . In this paper, we shall prove that the pair , ↓v C(X, Y is homeomorphic to (Q, c0, where Q = Iℕ is the Hilbert cube and c0 = {(xi i∈ℕ ∈ Q | limi→∞xi = 0}.

  19. A noncommutative mean ergodic theorem for partial W*-dynamical semigroups

    International Nuclear Information System (INIS)

    Ekhaguere, G.O.S.

    1992-12-01

    A noncommutative mean ergodic theorem for dynamical semigroups of maps on partial W*-algebras of linear operators from a pre-Hilbert space into its completion is proved. This generalizes a similar result of Watanabe for dynamical semigroups of maps on W*-algebras of operators. (author). 14 refs

  20. Exact solutions of the vacuum Einstein's equations allowing for two noncommuting Killing vectors

    International Nuclear Information System (INIS)

    Aliev, V.N.; Leznov, A.N.

    1990-01-01

    Einstein's equations are written in the form of covariant gauge theory in two-dimensional space with binomial solvable gauge group, with respect to two noncommutative of Killing vectors. The theory is exact integrable in one-dimensional case and series of partial exact solutions are constructed in two-dimensional. 5 refs

  1. Non-commutative field theory with twistor-like coordinates

    International Nuclear Information System (INIS)

    Taylor, Tomasz R.

    2007-01-01

    We consider quantum field theory in four-dimensional Minkowski spacetime, with the position coordinates represented by twistors instead of the usual world-vectors. Upon imposing canonical commutation relations between twistors and dual twistors, quantum theory of fields described by non-holomorphic functions of twistor variables becomes manifestly non-commutative, with Lorentz symmetry broken by a time-like vector. We discuss the free field propagation and its impact on the short- and long-distance behavior of physical amplitudes in perturbation theory. In the ultraviolet limit, quantum field theories in twistor space are generically less divergent than their commutative counterparts. Furthermore, there is no infrared-ultraviolet mixing problem

  2. On the Generalized Geometry Origin of Noncommutative Gauge Theory

    CERN Document Server

    Jurco, Branislav; Vysoky, Jan

    2013-01-01

    We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.

  3. Continual Lie algebras and noncommutative counterparts of exactly solvable models

    Science.gov (United States)

    Zuevsky, A.

    2004-01-01

    Noncommutative counterparts of exactly solvable models are introduced on the basis of a generalization of Saveliev-Vershik continual Lie algebras. Examples of noncommutative Liouville and sin/h-Gordon equations are given. The simplest soliton solution to the noncommutative sine-Gordon equation is found.

  4. Some remarks on K_0 of noncommutative tori

    OpenAIRE

    Chakraborty, Sayan

    2017-01-01

    Using Rieffel's construction of projective modules over higher dimensional noncommutative tori, we construct projective modules over some continuous field of C*-algebras whose fibers are noncommutative tori. Using a result of Echterhoff et al., our construction gives generators of K_0 of all noncommutative tori.

  5. q-deformed phase-space and its lattice structure

    International Nuclear Information System (INIS)

    Wess, J.

    1998-01-01

    Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are non-commutative spaces that inherit a well-defined mathematical structure from the quantum group symmetry. In turn, such quantum spaces can be interpreted as non-commutative configuration spaces for physical systems. We study the non-commutative Euclidean space that is based on the quantum group SO q (3)

  6. Essay on physics and non-commutative geometry

    International Nuclear Information System (INIS)

    Connes, A.

    1990-01-01

    Our aim, in this article, is to try to discover what physics would be like if the space in which it took place was not a set of points, but a non-commutative space. We shall not go very far in this direction, and the consequences of this investigation are for the moment either mathematical or only applied to a commutative space-time. It is clear, however, that a tool as remarkable as the Dixmier trace for analyzing logarithmic divergences should be useful to physicists. Moreover we have been able to show that a small modification of our picture of space-time gives a conceptual explanation of the Higgs fields and of the way they appear in the Weinberg-Salam model. This should allow us to make at the classical level explicit predictions of the Higgs mass: a very crude one is discussed. (author)

  7. Quantum thetas on noncommutative T4 from embeddings into lattice

    International Nuclear Information System (INIS)

    Chang-Young, Ee; Kim, Hoil

    2007-01-01

    In this paper, we investigate the theta vector and quantum theta function over noncommutative T 4 from the embedding of RxZ 2 . Manin has constructed the quantum theta functions from the lattice embedding into vector space (x finite group). We extend Manin's construction of the quantum theta function to the embedding of vector space x lattice case. We find that the holomorphic theta vector exists only over the vector space part of the embedding, and over the lattice part we can only impose the condition for the Schwartz function. The quantum theta function built on this partial theta vector satisfies the requirement of the quantum theta function. However, two subsequent quantum translations from the embedding into the lattice part are nonadditive, contrary to the additivity of those from the vector space part

  8. Noncommutativity and unitarity violation in gauge boson scattering

    International Nuclear Information System (INIS)

    Hewett, J. L.; Petriello, F. J.; Rizzo, T. G.

    2002-01-01

    We examine the unitarity properties of spontaneously broken noncommutative gauge theories. We find that the symmetry breaking mechanism in the noncommutative standard model of Chaichian et al. leads to an unavoidable violation of tree-level unitarity in gauge boson scattering at high energies. We then study a variety of simplified spontaneously broken noncommutative theories and isolate the source of this unitarity violation. Given the group theoretic restrictions endemic to noncommutative model building, we conclude that it is difficult to build a noncommutative standard model under the Weyl-Moyal approach that preserves unitarity

  9. Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole

    Directory of Open Access Journals (Sweden)

    G. Abbas

    2014-01-01

    Full Text Available Few years ago, Setare (2006 has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.

  10. Noncommutative unification of general relativity and quantum mechanics

    International Nuclear Information System (INIS)

    Heller, Michael; Pysiak, Leszek; Sasin, Wieslaw

    2005-01-01

    We present a model unifying general relativity and quantum mechanics based on a noncommutative geometry. This geometry is developed in terms of a noncommutative algebra A which is defined on a transformation groupoid Γ given by the action of a noncompact group G on the total space E of a principal fiber bundle over space-time M. The case is important since to obtain physical effects predicted by the model we should assume that G is a Lorentz group or some of its representations. We show that the generalized Einstein equation of the model has the form of the eigenvalue equation for the generalized Ricci operator, and all relevant operators in the quantum sector of the model are random operators; we study their dynamics. We also show that the model correctly reproduces general relativity and the usual quantum mechanics. It is interesting that the latter is recovered by performing the measurement of any observable. In the act of such a measurement the model 'collapses' to the usual quantum mechanics

  11. Renormalization group equations and the Lifshitz point in noncommutative Landau-Ginsburg theory

    International Nuclear Information System (INIS)

    Chen, G.-H.; Wu, Y.-S.

    2002-01-01

    A one-loop renormalization group (RG) analysis is performed for noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a modern version of the Wilsonian RG approach, in which a shell integration in momentum space bypasses the potential IR singularities due to UV-IR mixing. The momentum-dependent trigonometric factors in interaction vertices, characteristic of noncommutative geometry, are marginal under RG transformations, and their marginality is preserved at one loop. A negative Θ-dependent anomalous dimension is discovered as a novel effect of the UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point in less than four dimensions. At large noncommutativity, a momentum space instability is induced by quantum fluctuations, and a consequential first-order phase transition is identified together with a Lifshitz point in the phase diagram. In the vicinity of the Lifshitz point, we introduce two critical exponents ν m and β k , whose values are determined to be 1/4 and 1/2, respectively, at mean-field level

  12. Noncommutative gauge field theories: A no-go theorem

    International Nuclear Information System (INIS)

    Chaichian, M.; Tureanu, A.; Presnajder, P.; Sheikh-Jabbari, M.M.

    2001-06-01

    Studying the mathematical structure of the noncommutative groups in more detail, we prove a no-go theorem for the noncommutative gauge theories. According to this theorem, the closure condition of the gauge algebra implies that: 1) the local noncommutative u(n) algebra only admits the irreducible nxn matrix-representation. Hence the gauge fields, as elements of the algebra, are in nxn matrix form, while the matter fields can only be either in fundamental, adjoint or singlet states; 2) for any gauge group consisting of several simple group factors, the matter fields can transform nontrivially under at most two noncommutative group factors. In other words, the matter fields cannot carry more than two simple noncommutative gauge group charges. This no-go theorem imposes strong restrictions on the construction of the noncommutative version of the Standard Model and in resolving the standing problem of charge quantization in noncommutative QED. (author)

  13. Noncommutative Black Holes at the LHC

    Science.gov (United States)

    Villhauer, Elena Michelle

    2017-12-01

    Based on the latest public results, 13 TeV data from the Large Hadron Collider at CERN has not indicated any evidence of hitherto tested models of quantum black holes, semiclassical black holes, or string balls. Such models have predicted signatures of particles with high transverse momenta. Noncommutative black holes remain an untested model of TeV-scale gravity that offers the starkly different signature of particles with relatively low transverse momenta. Considerations for a search for charged noncommutative black holes using the ATLAS detector will be discussed.

  14. Noncommutative gauge theory without Lorentz violation

    International Nuclear Information System (INIS)

    Carlson, Carl E.; Carone, Christopher D.; Zobin, Nahum

    2002-01-01

    The most popular noncommutative field theories are characterized by a matrix parameter θ μν that violates Lorentz invariance. We consider the simplest algebra in which the θ parameter is promoted to an operator and Lorentz invariance is preserved. This algebra arises through the contraction of a larger one for which explicit representations are already known. We formulate a star product and construct the gauge-invariant Lagrangian for Lorentz-conserving noncommutative QED. Three-photon vertices are absent in the theory, while a four-photon coupling exists and leads to a distinctive phenomenology

  15. Classification of digital affine noncommutative geometries

    Science.gov (United States)

    Majid, Shahn; Pachoł, Anna

    2018-03-01

    It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."

  16. Closed star product on noncommutative ℝ{sup 3} and scalar field dynamics

    Energy Technology Data Exchange (ETDEWEB)

    Jurić, Tajron [Ruđer Bošković Institute, Theoretical Physics Division,Bijenička c. 54, HR-10002 Zagreb (Croatia); Poulain, Timothé; Wallet, Jean-Christophe [Laboratoire de Physique Théorique, CNRS,University of Paris-Sud, University of Paris-Saclay,Bât. 210, 91405 Orsay (France)

    2016-05-25

    We consider the noncommutative space ℝ{sub θ}{sup 3}, a deformation of ℝ{sup 3} for which the star product is closed for the trace functional. We study one-loop IR and UV properties of the 2-point function for real and complex noncommutative scalar field theories with quartic interactions and Laplacian on ℝ{sup 3} as kinetic operator. We find that the 2-point functions for these noncommutative scalar field theories have no IR singularities in the external momenta, indicating the absence of UV/IR mixing. We also find that the 2-point functions are UV finite with the deformation parameter θ playing the role of a natural UV cut-off. The possible origin of the absence of UV/IR mixing in noncommutative scalar field theories on ℝ{sub θ}{sup 3} as well as on ℝ{sub λ}{sup 3}, another deformation of ℝ{sup 3}, is discussed.

  17. Domain wall solitons and Hopf algebraic translational symmetries in noncommutative field theories

    International Nuclear Information System (INIS)

    Sasai, Yuya; Sasakura, Naoki

    2008-01-01

    Domain wall solitons are the simplest topological objects in field theories. The conventional translational symmetry in a field theory is the generator of a one-parameter family of domain wall solutions, and induces a massless moduli field which propagates along a domain wall. We study similar issues in braided noncommutative field theories possessing Hopf algebraic translational symmetries. As a concrete example, we discuss a domain wall soliton in the scalar φ 4 braided noncommutative field theory in Lie-algebraic noncommutative space-time, [x i ,x j ]=2iκε ijk x k (i,j,k=1,2,3), which has a Hopf algebraic translational symmetry. We first discuss the existence of a domain wall soliton in view of Derrick's theorem, and construct explicitly a one-parameter family of solutions in perturbation of the noncommutativity parameter κ. We then find the massless moduli field which propagates on the domain wall soliton. We further extend our analysis to the general Hopf algebraic translational symmetry

  18. Decision Making on Allocating Urban Green Spaces Based upon Spatially-Varying Relationships between Urban Green Spaces and Urban Compaction Degree

    Directory of Open Access Journals (Sweden)

    Hsueh-Sheng Chang

    2015-09-01

    Full Text Available The compact city is becoming a prevailing paradigm in the world to control urban sprawl and achieve a pattern of sustainable urban development. However, discussions of the area's overcrowded neighborhoods, its health problems, and the destruction of its green areas have inspired self-examination with respect to the compact city paradigm. High population density attracts even more residents and frequently renders the existing urban green space (UGS insufficient for use as part of a living environment. Due to the unique benefits that these qualities confer, UGS allocation is now considered a significant contributing factor to urban livability. In addition, the UGS allocation may be different due to the presence of many spatial non-stationarity processes. Therefore, this study employs geographically-weighted regression (GWR to explore the unique and spatially-explicit relationships between the degree of urban compaction and UGS within the Taipei metropolitan area. Maps summarizing the GWR results demonstrate that there is significantly insufficient UGS allocation in the central area, which consists mainly of Taipei City. Townships with higher parameters contain UGS levels that better meet the needs of their residents. Overall, the exploration of conceptualizing spatial heterogeneity of relationships between the degree of urban compaction and UGS can provide insightful analyses for decision-making on allocating UGS.

  19. Moving vortices in noncommutative gauge theory

    International Nuclear Information System (INIS)

    Horvathy, P.A.; Stichel, P.C.

    2004-01-01

    Exact time-dependent solutions of nonrelativistic noncommutative Chern-Simons gauge theory are presented in closed analytic form. They are different from (indeed orthogonal to) those discussed recently by Hadasz, Lindstroem, Rocek and von Unge. Unlike theirs, our solutions can move with an arbitrary constant velocity, and can be obtained from the previously known static solutions by the recently found 'exotic' boost symmetry

  20. Holographic complexity and noncommutative gauge theory

    Science.gov (United States)

    Couch, Josiah; Eccles, Stefan; Fischler, Willy; Xiao, Ming-Lei

    2018-03-01

    We study the holographic complexity of noncommutative field theories. The four-dimensional N=4 noncommutative super Yang-Mills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a type IIB supergravity theory with a stack of D3 branes and non-trivial NS-NS B fields. We start from this example and find that the late time holographic complexity growth rate, based on the "complexity equals action" conjecture, experiences an enhancement when the non-commutativity is turned on. This enhancement saturates a new limit which is exactly 1/4 larger than the commutative value. We then attempt to give a quantum mechanics explanation of the enhancement. Finite time behavior of the complexity growth rate is also studied. Inspired by the non-trivial result, we move on to more general setup in string theory where we have a stack of D p branes and also turn on the B field. Multiple noncommutative directions are considered in higher p cases.

  1. Group field theory with noncommutative metric variables.

    Science.gov (United States)

    Baratin, Aristide; Oriti, Daniele

    2010-11-26

    We introduce a dual formulation of group field theories as a type of noncommutative field theories, making their simplicial geometry manifest. For Ooguri-type models, the Feynman amplitudes are simplicial path integrals for BF theories. We give a new definition of the Barrett-Crane model for gravity by imposing the simplicity constraints directly at the level of the group field theory action.

  2. Non-commutative arithmetic circuits with division

    Czech Academy of Sciences Publication Activity Database

    Hrubeš, Pavel; Wigderson, A.

    2015-01-01

    Roč. 11, Article 14 (2015), s. 357-393 ISSN 1557-2862 EU Projects: European Commission(XE) 339691 - FEALORA Institutional support: RVO:67985840 Keywords : arithmetic circuits * non-commutative rational function * skew field Subject RIV: BA - General Mathematics http://theoryofcomputing.org/articles/v011a014/

  3. Constraining the noncommutative spectral action via astrophysical observations.

    Science.gov (United States)

    Nelson, William; Ochoa, Joseph; Sakellariadou, Mairi

    2010-09-03

    The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of particle physics in this setting, in addition to a modified version of Einstein-Hilbert gravity. In this Letter we use observations of pulsar timings, assuming that no deviation from general relativity has been observed, to constrain the gravitational sector of this theory. While the bounds on the coupling constants remain rather weak, they are comparable to existing bounds on deviations from general relativity in other settings and are likely to be further constrained by future observations.

  4. Noncommutative U(1) gauge theory from a worldline perspective

    Energy Technology Data Exchange (ETDEWEB)

    Ahmadiniaz, Naser [Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas,Ciudad Universitaria, Tuxtla Gutiérrez 29050 (Mexico); Corradini, Olindo [Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas,Ciudad Universitaria, Tuxtla Gutiérrez 29050 (Mexico); Dipartimento di Scienze Fisiche, Informatiche e Matematiche,Università di Modena e Reggio Emilia,Via Campi 213/A, I-41125 Modena (Italy); D’Ascanio, Daniela [Instituto de Física La Plata - CONICET, Universidad Nacional de La Plata,CC 67 (1900), La Plata (Argentina); Estrada-Jiménez, Sendic [Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas,Ciudad Universitaria, Tuxtla Gutiérrez 29050 (Mexico); Pisani, Pablo [Instituto de Física La Plata - CONICET, Universidad Nacional de La Plata,CC 67 (1900), La Plata (Argentina)

    2015-11-10

    We study pure noncommutative U(1) gauge theory representing its one-loop effective action in terms of a phase space worldline path integral. We write the quadratic action using the background field method to keep explicit gauge invariance, and then employ the worldline formalism to write the one-loop effective action, singling out UV-divergent parts and finite (planar and non-planar) parts, and study renormalization properties of the theory. This amounts to employ worldline Feynman rules for the phase space path integral, that nicely incorporate the Fadeev-Popov ghost contribution and efficiently separate planar and non-planar contributions. We also show that the effective action calculation is independent of the choice of the worldline Green’s function, that corresponds to a particular way of factoring out a particle zero-mode. This allows to employ homogeneous string-inspired Feynman rules that greatly simplify the computation.

  5. Relativistic differential-difference momentum operators and noncommutative differential calculus

    International Nuclear Information System (INIS)

    Mir-Kasimov, R.M.

    2011-01-01

    Full text: (author)The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics in the relativistic configuration space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated from the total Hamiltonian. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generation function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the non-commutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS

  6. Recursive relations for processes with n photons of noncommutative QED

    International Nuclear Information System (INIS)

    Jafari, Abolfazl

    2007-01-01

    Recursion relations are derived in the sense of Berends-Giele for the multi-photon processes of noncommutative QED. The relations concern purely photonic processes as well as the processes with two fermions involved, both for arbitrary number of photons at tree level. It is shown that despite of the dependence of noncommutative vertices on momentum, in contrast to momentum-independent color factors of QCD, the recursion relation method can be employed for multi-photon processes of noncommutative QED

  7. Investigations on the renormalizability of a non-commutative u(1) gauge theory

    International Nuclear Information System (INIS)

    Rofner, A.

    2009-01-01

    When considering very small scales near the Planck-length, or equivalently very high energies (far from being reached by today's particle accelerators), space-time is expected to be quantized. Today, all but one forces governing nature (i.e. gravitation) are described via Quantum Field Theories (short QFTs) and more precisely gauge field theories (GFTs). Their heart is the art of renormalization, which allows to handle the divergences for high internal momenta appearing in the course of the perturbative development of the action in a consistent manner. Over the last years numerous attempts have been made to formulate consistent and renormalizable theories also on non-commutative spaces. Yet, it is the latter that represents a major problem for non-commutative QFTs: generally, the non-commutativity is implemented via the so-called star product, which in the simplest case is given by the Moyal-Weyl product, and which leads to a modification of the interaction terms of the theories by introducing additional phase factors depending on the non-commutative parameter theta. Then, this phase leads to a mixing of high and low energies, which is directly linked to the appearance of a new class of divergences for small momenta. While there exist various traditional renormalization schemes in order to handle uV divergences, their counterparts in the IR sector form a major obstacle in formulating consistent non-commutative QFTs. However, a first way out of this misery could be achieved by Grosse and Wulkenhaar for a scalar model. The idea was to add a suitable term to the action, in their case an oscillator term, leading to a decoupling of the high and low energy sectors. Later, the same philosophy has been followed by Gurau et. al. by adding a 1/p 2 like term to the scalar action. Both models have been shown to be renormalizable, and additionally, the latter model leads to a translation invariant propagator, which implies momentum conservation in all space points. Now, the

  8. ComPAQS: a compact concentric UV/visible spectrometer, providing a new tool for air quality monitoring from space

    Science.gov (United States)

    Leigh, Roland J.; Whyte, C.; Cutter, M. A.; Lobb, D. R.; Monks, P. S.

    2017-11-01

    Under the first phase of the Centre for Earth Observation Instrumentation (CEOI), a breadboard demonstrator of a novel UV/VIS spectrometer has been developed. Using designs from Surrey Satellite Technology Ltd (SSTL) the demonstrator has been constructed and tested at the University of Leicester's Space Research Centre. This spectrometer provides an exceptionally compact instrument for differential optical absorption spectroscopy (DOAS) applications from LEO, GEO, HAP or ground-based platforms. Measurement of atmo spheric compounds with climate change or air quality implications is a key driver for the ground and space-based Earth Observation communities. Techniques using UV/VIS spectroscopy such as DOAS provide measurements of ozone profiles, aerosol optical depth, certain Volatile Organic Compounds, halogenated species, and key air quality parameters including tropospheric nitrogen dioxide. Compact instruments providing the necessary optical performance and spectral resolution are therefore a key enabling technology. The Compact Air Quality Spectrometer (CompAQS) features a concentric arrangement of a spherical meniscus lens, a concave spherical mirror and a suitable curved diffraction grating. This compact design provides efficiency and performance benefits over traditional concepts, improving the precision and spatial resolution available from space borne instruments with limited weight and size budgets. The breadboard spectrometer currently operating at the University of Leicester offers high throughput with a spectral range from 310 to 450 nm at 0.5nm(UV) to 1.0nm (visible) resolution, suitable for DOAS applications. The concentric design is capable of handling high relative apertures, owing to spherical aberration and coma being near zero at all surfaces. The design also provides correction for transverse chromatic aberration and distortion, in addition to correcting for the distortion called `smile' - the curvature of the slit image formed at each

  9. 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

  10. Deformation quantization of noncommutative quantum mechanics and dissipation

    Energy Technology Data Exchange (ETDEWEB)

    Bastos, C [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Bertolami, O [Departamento de Fisica, Instituto Superior Tecnico, Avenida Rovisco Pais 1, 1049-001 Lisbon (Portugal); Dias, N C [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal); Prata, J N [Departamento de Matematica, Universidade Lusofona de Humanidades e Tecnologias, Avenida Campo Grande 376, 1749-024 Lisbon (Portugal)

    2007-05-15

    We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a *-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.

  11. Cancellation of soft and collinear divergences in noncommutative QED

    International Nuclear Information System (INIS)

    Mirza, B.; Zarei, M.

    2006-01-01

    In this paper, we investigate the behavior of noncommutative IR divergences and will also discuss their cancellation in the physical cross sections. The commutative IR (soft) divergences existing in the nonplanar diagrams will be examined in order to prove an all-order cancellation of these divergences using the Weinberg's method. In noncommutative QED, collinear divergences due to triple photon splitting vertex, were encountered, which are shown to be canceled out by the noncommutative version of KLN theorem. This guarantees that there is no mixing between the Collinear, soft divergences and noncommutative IR divergences

  12. 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

  13. Marginal and non-commutative deformations via non-abelian T-duality

    Energy Technology Data Exchange (ETDEWEB)

    Hoare, Ben [Institut für Theoretische Physik, ETH Zürich,Wolfgang-Pauli-Strasse 27, 8093 Zürich (Switzerland); Thompson, Daniel C. [Theoretische Natuurkunde, Vrije Universiteit Brussel & The International Solvay Institutes, Pleinlaan 2, B-1050 Brussels (Belgium)

    2017-02-10

    In this short article we develop recent proposals to relate Yang-Baxter sigma-models and non-abelian T-duality. We demonstrate explicitly that the holographic space-times associated to both (multi-parameter)-β-deformations and non-commutative deformations of N=4 super Yang-Mills gauge theory including the RR fluxes can be obtained via the machinery of non-abelian T-duality in Type II supergravity.

  14. Compact state-space models for complex superconducting radio-frequency structures based on model order reduction and concatenation methods

    International Nuclear Information System (INIS)

    Flisgen, Thomas

    2015-01-01

    The modeling of large chains of superconducting cavities with couplers is a challenging task in computational electrical engineering. The direct numerical treatment of these structures can easily lead to problems with more than ten million degrees of freedom. Problems of this complexity are typically solved with the help of parallel programs running on supercomputing infrastructures. However, these infrastructures are expensive to purchase, to operate, and to maintain. The aim of this thesis is to introduce and to validate an approach which allows for modeling large structures on a standard workstation. The novel technique is called State-Space Concatenations and is based on the decomposition of the complete structure into individual segments. The radio-frequency properties of the generated segments are described by a set of state-space equations which either emerge from analytical considerations or from numerical discretization schemes. The model order of these equations is reduced using dedicated model order reduction techniques. In a final step, the reduced-order state-space models of the segments are concatenated in accordance with the topology of the complete structure. The concatenation is based on algebraic continuity constraints of electric and magnetic fields on the decomposition planes and results in a compact state-space system of the complete radio-frequency structure. Compared to the original problem, the number of degrees of freedom is drastically reduced, i.e. a problem with more than ten million degrees of freedom can be reduced on a standard workstation to a problem with less than one thousand degrees of freedom. The final state-space system allows for determining frequency-domain transfer functions, field distributions, resonances, and quality factors of the complete structure in a convenient manner. This thesis presents the theory of the state-space concatenation approach and discusses several validation and application examples. The examples

  15. Prime divisors and noncommutative valuation theory

    CERN Document Server

    Marubayashi, Hidetoshi

    2012-01-01

    Classical valuation theory has applications in number theory and class field theory as well as in algebraic geometry, e.g. in a divisor theory for curves.  But the noncommutative equivalent is mainly applied to finite dimensional skewfields.  Recently however, new types of algebras have become popular in modern algebra; Weyl algebras, deformed and quantized algebras, quantum groups and Hopf algebras, etc. The advantage of valuation theory in the commutative case is that it allows effective calculations, bringing the arithmetical properties of the ground field into the picture.  This arithmetical nature is also present in the theory of maximal orders in central simple algebras.  Firstly, we aim at uniting maximal orders, valuation rings, Dubrovin valuations, etc. in a common theory, the theory of primes of algebras.  Secondly, we establish possible applications of the noncommutative arithmetics to interesting classes of algebras, including the extension of central valuations to nice classes of quantized a...

  16. Exact BPS bound for noncommutative baby Skyrmions

    International Nuclear Information System (INIS)

    Domrin, Andrei; Lechtenfeld, Olaf; Linares, Román; Maceda, Marco

    2013-01-01

    The noncommutative baby Skyrme model is a Moyal deformation of the two-dimensional sigma model plus a Skyrme term, with a group-valued or Grassmannian target. Exact abelian solitonic solutions have been identified analytically in this model, with a singular commutative limit. Inside any given Grassmannian, we establish a BPS bound for the energy functional, which is saturated by these baby Skyrmions. This asserts their stability for unit charge, as we also test in second-order perturbation theory

  17. Ultra-Compact Transmitter for Space-Based Lidar, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — Fibertek, Inc. in partnership with researchers at the Pennsylvania State University Center for Innovative Materials Processing through Direct Digital Deposition...

  18. Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

    Science.gov (United States)

    Hadasz, Leszek; Lindström, Ulf; Roček, Martin; von Unge, Rikard

    2004-05-01

    We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space.

  19. Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

    International Nuclear Information System (INIS)

    Hadasz, Leszek; Lindstroem, Ulf; Rocek, Martin; Unge, Rikard von

    2004-01-01

    We study one- and two-soliton solutions of noncommutative Chern-Simons theory coupled to a nonrelativistic or a relativistic scalar field. In the nonrelativistic case, we find a tower of new stationary time-dependent solutions, all with the same charge density, but with increasing energies. The dynamics of these solitons cannot be studied using traditional moduli space techniques, but we do find a nontrivial symplectic form on the phase space indicating that the moduli space is not flat. In the relativistic case we find the metric on the two soliton moduli space

  20. Cosmological production of noncommutative black holes

    International Nuclear Information System (INIS)

    Mann, Robert B.; Nicolini, Piero

    2011-01-01

    We investigate the pair creation of noncommutative black holes in a background with a positive cosmological constant. As a first step we derive the noncommutative geometry inspired Schwarzschild-de Sitter solution. By varying the mass and the cosmological constant parameters, we find several spacetimes compatible with the new solution: positive-mass spacetimes admit one cosmological horizon and two, one, or no black hole horizons, while negative-mass spacetimes have just a cosmological horizon. These new black holes share the properties of the corresponding asymptotically flat solutions, including the nonsingular core and thermodynamic stability in the final phase of the evaporation. As a second step we determine the action which generates the matter sector of gravitational field equations and we construct instantons describing the pair production of black holes and the other admissible topologies. As a result we find that for current values of the cosmological constant the de Sitter background is quantum mechanically stable according to experience. However, positive-mass noncommutative black holes and solitons would have plentifully been produced during inflationary times for Planckian values of the cosmological constant. As a special result we find that, in these early epochs of the Universe, Planck size black holes production would have been largely disfavored. We also find a potential instability for production of negative-mass solitons.

  1. Dynamics of Strings in Noncommutative Gauge Theory

    International Nuclear Information System (INIS)

    Gross, David J.; Nekrasov, Nikia A.

    2000-01-01

    We continue our study of solitons in noncommutative gauge theories and present an extremely simple BPS solution of N=4 U(1) noncommutative gauge theory in 4 dimensions, which describes N infinite D1 strings that pierce a D3 brane at various points, in the presence of a background B-field in the Seiberg-Witten limit. We call this solution the N-fluxon. For N=1 we calculate the complete spectrum of small fluctuations about the fluxon and find three kinds of modes: the fluctuations of the superstring in 10 dimensions arising from fundamental strings attached to the D1 strings, the ordinary particles of the gauge theory in 4 dimensions and a set of states with discrete spectrum, localized at the intersection point - corresponding to fundamental strings stretched between the D1 string and the D3 brane. We discuss the fluctuations about the N-fluxon as well and derive explicit expressions for the amplitudes of interactions between these various modes. We show that translations in noncommutative gauge theories are equivalent to gauge transformations (plus a constant shift of the gauge field) and discuss the implications for the translational zeromodes of our solitons. We also find the dyonic versions of N-fluxon, as well as of our previous string-monopole solution. (author)

  2. Probing noncommutative theories with quantum optical experiments

    Directory of Open Access Journals (Sweden)

    Sanjib Dey

    2017-11-01

    Full Text Available One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all such approaches. However, the identification of the appropriate passage to quantum gravity is suffering from the inadequacy of experimental techniques. It is beyond our ability to test the effects of quantum gravity thorough the available scattering experiments, as it is unattainable to probe such high energy scale at which the effects of quantum gravity appear. Here we propose an elegant alternative scheme to test such theories by detecting the deformations emerging from the noncommutative structures. Our protocol relies on the novelty of an opto-mechanical experimental setup where the information of the noncommutative oscillator is exchanged via the interaction with an optical pulse inside an optical cavity. We also demonstrate that our proposal is within the reach of current technology and, thus, it could uncover a feasible route towards the realization of quantum gravitational phenomena thorough a simple table-top experiment.

  3. Geometry of Moishezon and 1-convex spaces II: Projectivity of Moishezon spaces and its non-compact version

    International Nuclear Information System (INIS)

    Sitaramayya, M.

    1993-11-01

    After a brief review of the geometry of Moishezon spaces, their relation with l-convex spaces and a reasonable and up to date understanding of the obstructions for projectivity of Moishezon objects both in singular and non-singular case is given. The geometry of l-convex manifolds and with l-dimensional exceptional set is studied and some problems and conjectures are stated. The tools of cohomology vanishing theorems important for the subject are briefly sketched. Compactifications of C 3 and Stein spaces are finally outlined. given. 111 refs, 2 figs

  4. Sharpness and non-compactness of embeddings of Bessel-potential-type spaces

    Czech Academy of Sciences Publication Activity Database

    Gogatishvili, Amiran; Neves, J. S.; Opic, Bohumír

    2007-01-01

    Roč. 280, č. 10 (2007), s. 1083-1093 ISSN 0025-584X R&D Projects: GA ČR GA201/05/2033 Institutional research plan: CEZ:AV0Z10190503 Keywords : slowly varying functions * Lorentz-Karamata spaces * rearrangement-invariant Banach function spaces Subject RIV: BA - General Mathematics Impact factor: 0.415, year: 2007

  5. Non-Compact and Sharp Embeddings of Logarithmic Bessel Potential Spaces into Hölder-Type Spaces

    Czech Academy of Sciences Publication Activity Database

    Edmunds, D. E.; Gurka, P.; Opic, Bohumír

    2006-01-01

    Roč. 25, č. 1 (2006), s. 73-80 ISSN 0232-2064 R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : generalized Lorentz-Zygmund spaces * logarithmic Bessel potential spaces * Hölder-continuous functions Subject RIV: BA - General Mathematics Impact factor: 0.360, year: 2006

  6. CONFIRMATION OF THE COMPACTNESS OF A z = 1.91 QUIESCENT GALAXY WITH HUBBLE SPACE TELESCOPE'S WIDE FIELD CAMERA 3

    International Nuclear Information System (INIS)

    Szomoru, Daniel; Franx, Marijn; Bouwens, Rychard J.; Van Dokkum, Pieter G.; Trenti, Michele; Illingworth, Garth D.; Labbe, Ivo; Oesch, Pascal A.; Carollo, C. Marcella

    2010-01-01

    We present very deep Wide Field Camera 3 (WFC3) photometry of a massive, compact galaxy located in the Hubble Ultra Deep Field. This quiescent galaxy has a spectroscopic redshift z = 1.91 and has been identified as an extremely compact galaxy by Daddi et al. We use new H F160W imaging data obtained with Hubble Space Telescope/WFC3 to measure the deconvolved surface brightness profile to H ∼ 28 mag arcsec -2 . We find that the surface brightness profile is well approximated by an n = 3.7 Sersic profile. Our deconvolved profile is constructed by a new technique which corrects the best-fit Sersic profile with the residual of the fit to the observed image. This allows for galaxy profiles which deviate from a Sersic profile. We determine the effective radius of this galaxy: r e = 0.42 ± 0.14 kpc in the observed H F160W band. We show that this result is robust to deviations from the Sersic model used in the fit. We test the sensitivity of our analysis to faint 'wings' in the profile using simulated galaxy images consisting of a bright compact component and a faint extended component. We find that due to the combination of the WFC3 imaging depth and our method's sensitivity to extended faint emission we can accurately trace the intrinsic surface brightness profile, and that we can therefore confidently rule out the existence of a faint extended envelope around the observed galaxy down to our surface brightness limit. These results confirm that the galaxy lies a factor ∼10 off from the local mass-size relation.

  7. Positive-definite functions and unitary representations of locally compact groups in a Hilbert space

    International Nuclear Information System (INIS)

    Gali, I.M.; Okb el-Bab, A.S.; Hassan, H.M.

    1977-08-01

    It is proved that the necessary and sufficient condition for the existence of an integral representation of a group of unitary operators in a Hilbert space is that it is positive-definite and continuous in some topology

  8. A cosmological model with compact space sections and low mass density

    International Nuclear Information System (INIS)

    Fagundes, H.V.

    1982-01-01

    A general relativistic cosmological model is presented, which has closed space sections and mass density below a critical density similar to that of Friedmann's models. The model may predict double images of cosmic sources. (Author) [pt

  9. A Compact, Efficient Pyrolysis/Oxidation System for Solid Waste Resource Recovery in Space, Phase II

    Data.gov (United States)

    National Aeronautics and Space Administration — Pyrolysis processing can be used in near term missions for volume reduction, water recovery (drying), stabilization, and enhanced water and oxygen recovery through...

  10. A Compact, Efficient Pyrolysis/Oxidation System for Solid Waste Resource Recovery in Space, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — Both pyrolysis and oxidation steps have been considered as the key solid waste processing step for a Controlled Ecological Life Support System (CELSS). Pyrolysis is...

  11. On tea, donuts and non-commutative geometry

    Directory of Open Access Journals (Sweden)

    Igor V. Nikolaev

    2018-03-01

    Full Text Available As many will agree, it feels good to complement a cup of tea by a donut or two. This sweet relationship is also a guiding principle of non-commutative geometry known as Serre Theorem. We explain the algebra behind this theorem and prove that elliptic curves are complementary to the so-called non-commutative tori.

  12. Linearization of non-commuting operators in the partition function

    International Nuclear Information System (INIS)

    Ahmed, M.

    1983-06-01

    A generalization of the Stratonovich-Hubbard scheme for evaluating the grand canonical partition function is given. The scheme involves linearization of products of non-commuting operators using the functional integral method. The non-commutivity of the operators leads to an additional term which can be absorbed in the single-particle Hamiltonian. (author)

  13. Noncommutative conformally coupled scalar field cosmology and its commutative counterpart

    International Nuclear Information System (INIS)

    Barbosa, G.D.

    2005-01-01

    We study the implications of a noncommutative geometry of the minisuperspace variables for the Friedmann-Robertson-Walker universe with a conformally coupled scalar field. The investigation is carried out by means of a comparative study of the universe evolution in four different scenarios: classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative, the last two employing the Bohmian formalism of quantum trajectories. The role of noncommutativity is discussed by drawing a parallel between its realizations in two possible frameworks for physical interpretation: the NC frame, where it is manifest in the universe degrees of freedom, and in the C frame, where it is manifest through θ-dependent terms in the Hamiltonian. As a result of our comparative analysis, we find that noncommutative geometry can remove singularities in the classical context for sufficiently large values of θ. Moreover, under special conditions, the classical noncommutative model can admit bouncing solutions characteristic of the commutative quantum Friedmann-Robertson-Walker universe. In the quantum context, we find nonsingular universe solutions containing bounces or being periodic in the quantum commutative model. When noncommutativity effects are turned on in the quantum scenario, they can introduce significant modifications that change the singular behavior of the universe solutions or that render them dynamical whenever they are static in the commutative case. The effects of noncommutativity are completely specified only when one of the frames for its realization is adopted as the physical one. Nonsingular solutions in the NC frame can be mapped into singular ones in the C frame

  14. UV / IR mixing in noncommutative field theory via open string loops

    International Nuclear Information System (INIS)

    Kiem, Youngjai; Lee, Sangmin

    2000-01-01

    We explicitly evaluate one-loop (annulus) planar and nonplanar open string amplitudes in the presence of the background NS-NS two-form field. In the decoupling limit of Seiberg and Witten, we find that the nonplanar string amplitudes reproduce the UV/IR mixing of noncommutative field theories. In particular, the investigation of the UV regime of the open string amplitudes shows that certain IR closed string degrees of freedom survive the decoupling limit as previously predicted from the noncommutative field theory analysis. These degrees of freedom are responsible for the quadratic, linear and logarithmic IR singularities when the D-branes embedded in space-time have the codimension zero, one and two, respectively. The analysis is given for both bosonic and supersymmetric open strings

  15. Dolan-Grady relations and noncommutative quasi-exactly solvable systems

    International Nuclear Information System (INIS)

    Klishevich, Sergey M; Plyushchay, Mikhail S

    2003-01-01

    We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives obeying the nonlinear Dolan-Grady relations. This restricts the structure function of the deformed oscillator algebra to a quadratic polynomial. The cases when the coordinates form the su(2) and sl(2,R) algebras are investigated in detail. Reducing the Hamiltonian to 1D finite-difference quasi-exactly solvable operators, we demonstrate partial algebraization of the spectrum of the corresponding systems on the fuzzy sphere and noncommutative hyperbolic plane. A completely covariant method based on the notion of intrinsic algebra is proposed to deal with the spectral problem of such systems

  16. Electric Chern-Simons term, enlarged exotic Galilei symmetry and noncommutative plane

    International Nuclear Information System (INIS)

    Olmo, Mariano A. del; Plyushchay, Mikhail S.

    2006-01-01

    The extended exotic planar model for a charged particle is constructed. It includes a Chern-Simons-like term for a dynamical electric field, but produces usual equations of motion for the particle in background constant uniform electric and magnetic fields. The electric Chern-Simons term is responsible for the noncommutativity of the boost generators in the 10-dimensional enlarged exotic Galilei symmetry algebra of the extended system. The model admits two reduction schemes by the integrals of motion, one of which reproduces the usual formulation for the charged particle in external constant electric and magnetic fields with associated field-deformed Galilei symmetry, whose commuting boost generators are identified with the nonlocal in time Noether charges reduced on-shell. Another reduction scheme, in which electric field transmutes into the commuting space translation generators, extracts from the model a free particle on the noncommutative plane described by the twofold centrally extended Galilei group of the nonrelativistic anyons

  17. Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

    Czech Academy of Sciences Publication Activity Database

    Ali, S.-T.; Engliš, Miroslav

    2011-01-01

    Roč. 44, č. 21 (2011), s. 215206 ISSN 1751-8113 R&D Projects: GA ČR GA201/09/0473 Institutional research plan: CEZ:AV0Z10190503 Keywords : curved spaces Subject RIV: BA - General Mathematics Impact factor: 1.564, year: 2011 http://iopscience.iop.org/1751-8121/44/21/215206

  18. Mu-Spec - A High Performance Ultra-Compact Photon Counting spectrometer for Space Submillimeter Astronomy

    Science.gov (United States)

    Moseley, H.; Hsieh, W.-T.; Stevenson, T.; Wollack, E.; Brown, A.; Benford, D.; Sadleir; U-Yen, I.; Ehsan, N.; Zmuidzinas, J.; hide

    2011-01-01

    We have designed and are testing elements of a fully integrated submillimeter spectrometer based on superconducting microstrip technology. The instrument can offer resolving power R approximately 1500, and its high frequency cutoff is set by the gap of available high performance superconductors. All functions of the spectrometer are integrated - light is coupled to the microstrip circuit with a planar antenna, the spectra discrimination is achieved using a synthetic grating, orders are separated using planar filter, and detected using photon counting MKID detector. This spectrometer promises to revolutionize submillimeter spectroscopy from space. It replaces instruments with the scale of 1m with a spectrometer on a 10 cm Si wafer. The reduction in mass and volume promises a much higher performance system within available resource in a space mission. We will describe the system and the performance of the components that have been fabricated and tested.

  19. Heisenberg groups and noncommutative fluxes

    International Nuclear Information System (INIS)

    Freed, Daniel S.; Moore, Gregory W.; Segal, Graeme

    2007-01-01

    We develop a group-theoretical approach to the formulation of generalized abelian gauge theories, such as those appearing in string theory and M-theory. We explore several applications of this approach. First, we show that there is an uncertainty relation which obstructs simultaneous measurement of electric and magnetic flux when torsion fluxes are included. Next, we show how to define the Hilbert space of a self-dual field. The Hilbert space is Z 2 -graded and we show that, in general, self-dual theories (including the RR fields of string theory) have fermionic sectors. We indicate how rational conformal field theories associated to the two-dimensional Gaussian model generalize to (4k+2)-dimensional conformal field theories. When our ideas are applied to the RR fields of string theory we learn that it is impossible to measure the K-theory class of a RR field. Only the reduction modulo torsion can be measured

  20. A noncommutative convexity in C*-bimodules

    Directory of Open Access Journals (Sweden)

    Mohsen Kian

    2017-02-01

    Full Text Available Let A and B be C*-algebras. We consider a noncommutative convexity in Hilbert A-B-bimodules, called A-B-convexity, as a generalization of C*-convexity in C*-algebras. We show that if X is a Hilbert A-B-bimodule, then Mn(X is a Hilbert Mn(A-Mn(B-bimodule and apply it to show that the closed unit ball of every Hilbert A-B-bimodule is A-B-convex. Some properties of this kind of convexity and various examples have been given.

  1. Remarks on twisted noncommutative quantum field theory

    Energy Technology Data Exchange (ETDEWEB)

    Zahn, J. [Hamburg Univ. (Germany). 2. Inst. fuer Theoretische Physik

    2006-04-15

    We review recent results on twisted noncommutative quantum field theory by embedding it into a general framework for the quantization of systems with a twisted symmetry. We discuss commutation relations in this setting and show that the twisted structure is so rigid that it is hard to derive any predictions, unless one gives up general principles of quantum theory. It is also shown that the twisted structure is not responsible for the presence or absence of UV/IR-mixing, as claimed in the literature. (Orig.)

  2. Non-commutative tools for topological insulators

    International Nuclear Information System (INIS)

    Prodan, Emil

    2010-01-01

    This paper reviews several analytic tools for the field of topological insulators, developed with the aid of non-commutative calculus and geometry. The set of tools includes bulk topological invariants defined directly in the thermodynamic limit and in the presence of disorder, whose robustness is shown to have nontrivial physical consequences for the bulk states. The set of tools also includes a general relation between the current of an observable and its edge index, a relation that can be used to investigate the robustness of the edge states against disorder. The paper focuses on the motivations behind creating such tools and on how to use them.

  3. Instrumented roll technology for the design space development of roller compaction process.

    Science.gov (United States)

    Nesarikar, Vishwas V; Vatsaraj, Nipa; Patel, Chandrakant; Early, William; Pandey, Preetanshu; Sprockel, Omar; Gao, Zhihui; Jerzewski, Robert; Miller, Ronald; Levin, Michael

    2012-04-15

    Instrumented roll technology on Alexanderwerk WP120 roller compactor was developed and utilized successfully for the measurement of normal stress on ribbon during the process. The effects of process parameters such as roll speed (4-12 rpm), feed screw speed (19-53 rpm), and hydraulic roll pressure (40-70 bar) on normal stress and ribbon density were studied using placebo and active pre-blends. The placebo blend consisted of 1:1 ratio of microcrystalline cellulose PH102 and anhydrous lactose with sodium croscarmellose, colloidal silicon dioxide, and magnesium stearate. The active pre-blends were prepared using various combinations of one active ingredient (3-17%, w/w) and lubricant (0.1-0.9%, w/w) levels with remaining excipients same as placebo. Three force transducers (load cells) were installed linearly along the width of the roll, equidistant from each other with one transducer located in the center. Normal stress values recorded by side sensors and were lower than normal stress values recorded by middle sensor and showed greater variability than middle sensor. Normal stress was found to be directly proportional to hydraulic pressure and inversely to screw to roll speed ratio. For active pre-blends, normal stress was also a function of compressibility. For placebo pre-blends, ribbon density increased as normal stress increased. For active pre-blends, in addition to normal stress, ribbon density was also a function of gap. Models developed using placebo were found to predict ribbon densities of active blends with good accuracy and the prediction error decreased as the drug concentration of active blend decreased. Effective angle of internal friction and compressibility properties of active pre blend may be used as key indicators for predicting ribbon densities of active blend using placebo ribbon density model. Feasibility of on-line prediction of ribbon density during roller compaction was demonstrated using porosity-pressure data of pre-blend and normal stress

  4. Design of Compact Particle Detector System Using FPGA for Space Particle Environment Measurement

    Directory of Open Access Journals (Sweden)

    K. Ryu

    2007-06-01

    Full Text Available We have designed a high resolution proton and electron telescope for the detection of high energy particles, which constitute a major part of the space environment. The flux of the particles, in the satellite orbits, can vary abruptly according to the position and solar activities. In this study, a conceptual design of the detector, for adapting these variations with a high energy resolution, was made and the performance was estimated. In addition, a parallel processing algorithm was devised and embodied using FPGA for the high speed data processing, capable of detecting high flux without losing energy resolution, on board a satellite.

  5. Quantum group symmetry of classical and noncommutative geometry

    Indian Academy of Sciences (India)

    Debashish Goswami

    2016-07-01

    Jul 1, 2016 ... universal enveloping algebra U(L) of a Lie algebra L, (iv) ... Kustermans defined locally compact quantum groups too. .... There are other versions of quantum isometries formulated by me ..... classical connected spaces when either the space is ..... Etingof-Walton's paper, we have : (i) M0 is open and dense,.

  6. Optical Nano-antennae as Compact and Efficient Couplers from Free-space to Waveguide Modes

    DEFF Research Database (Denmark)

    Zenin, Vladimir A.; Malureanu, Radu; Volkov, Valentyn

    2015-01-01

    Optical nano-antennae are one of the possible solutions for coupling free-space radiation into subwavelength waveguides. Our efforts were concentrated on coupling between an optical fibre and a plasmonic slot waveguide. Such coupling is still an issue to be solved in order to advance the use...... of plasmonic waveguides for optical interconnects. During the talk, we will present our modelling optimisation, fabrication and measurement of the nano-antennae functionality. For the modelling part, we used CST Microwave studio for optimising the antenna geometry. Various antennae were modelled and fabricated....... The fabrication was based on electron beam lithography and lift-off processes. The measurements were performed with scattering scanning near-field microscope and allowed the retrieval of both amplitude and phase of the propagating plasmon. The obtained values agree very well with the theoretically predicted ones...

  7. Introduction to Dubois-Violette's non-commutative differential geometry

    International Nuclear Information System (INIS)

    Djemai, A.E.F.

    1994-07-01

    In this work, one presents a detailed review of Dubois-Violette et al. approach to non-commutative differential calculus. The non-commutative differential geometry of matrix algebras and the non-commutative Poisson structures are treated in some details. We also present the analog of the Maxwell's theory and the new models of Yang-Mills-Higgs theories that can be constructed in this framework. In particular, some simple models are compared with the standard model. Finally, we discuss some perspectives and open questions. (author). 32 refs

  8. Computational commutative and non-commutative algebraic geometry

    CERN Document Server

    Cojocaru, S; Ufnarovski, V

    2005-01-01

    This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.

  9. Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory

    International Nuclear Information System (INIS)

    Lee, Bum-Hoon; Ro, Daeho; Yang, Hyun Seok

    2017-01-01

    We study localization of five-dimensional supersymmetric U(1) gauge theory on S 3 ×ℝ θ 2 where ℝ θ 2 is a noncommutative (NC) plane. The theory can be isomorphically mapped to three-dimensional supersymmetric U(N→∞) gauge theory on S 3 using the matrix representation on a separable Hilbert space on which NC fields linearly act. Therefore the NC space ℝ θ 2 allows for a flexible path to derive matrix models via localization from a higher-dimensional supersymmetric NC U(1) gauge theory. The result shows a rich duality between NC U(1) gauge theories and large N matrix models in various dimensions.

  10. Weinberg-Salam theory in non-commutative geometry

    International Nuclear Information System (INIS)

    Morita, Katsusada; Okumura, Yoshitaka.

    1994-01-01

    Ordinary differential calculus on smooth manifold is generalized so as to construct gauge theory coupled to fermions on discrete space M 4 xZ 2 which is an underlying space-time in the non-commutative geometry for the standard model. We can reproduce not only the bosonic sector but also the fermionic sector of the Weinberg-Salam theory without recourse to the Dirac operator at the outset. Treatment of the fermionic sector is based on the generalized spinor one-forms from which the Dirac lagrangian is derived through taking the inner product. Two model constructions are presented using our formalism, both giving the classical mass relation m H = √2m w . The first model leaves the Weinberg angle arbitrary as usual, while the second one predicts sin 2 θ w = 1/4 in the tree level. This prediction is the same as that of Connes but we obtain it from correct hypercharge assignment of 2x2 matrix-valued Higgs field and from vanishing photon mass, thereby dispensing with Connes' 0-trace condition or the equivalent. (author)

  11. ((F, D1), D3) bound state, S-duality and noncommutative open string/Yang-Mills theory

    International Nuclear Information System (INIS)

    Lu, J.X.; Roy, S.; Singh, H.

    2000-01-01

    We study decoupling limits and S-dualities for noncommutative open string/Yang-Mills theory in a gravity setup by considering an SL(2,Z) invariant supergravity solution of the form ((F, D1), D3) bound state of type IIB string theory. This configuration can be regarded as D3-branes with both electric and magnetic fields turned on along one of the spatial directions of the brane and preserves half of the space-time supersymmetries of the string theory. Our study indicates that there exists a decoupling limit for which the resulting theory is an open string theory defined in a geometry with noncommutativity in both space-time and space-space directions. We study S-duality of this noncommutative open string (NCOS) and find that the same decoupling limit in the S-dual description gives rise to a space-space noncommutative Yang-Mills theory (NCYM). We also discuss independently the decoupling limit for NCYM in this D3 brane background. Here we find that S-duality of NCYM theory does not always give a NCOS theory. Instead, it can give an ordinary Yang-Mills with a singular metric and an infinitely large coupling. We also find that the open string coupling relation between the two S-duality related theories is modified such that S-duality of a strongly coupled open-string/Yang-Mills theory does not necessarily give a weakly coupled theory. The relevant gravity dual descriptions of NCOS/NCYM are also given. (author)

  12. Noncommutative GUTs, Standard Model and C,P,T

    International Nuclear Information System (INIS)

    Aschieri, P.; Jurco, B.; Schupp, P.; Wess, J.

    2003-01-01

    Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter θ, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in θ. We study in detail the reality, Hermiticity and C,P,T properties of the Seiberg-Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg-Witten map

  13. Noncommutative Yang-Mills from equivalence of star products

    International Nuclear Information System (INIS)

    Jurco, B.; Schupp, P.

    2000-01-01

    It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume. (orig.)

  14. Noncommutative Yang-Mills from equivalence of star products

    Energy Technology Data Exchange (ETDEWEB)

    Jurco, B. [Max-Planck-Institut fuer Mathematik, Bonn (Germany); Schupp, P. [Sektion Physik, Universitaet Muenchen, Theresienstrasse 37, 80333 Muenchen (Germany)

    2000-05-01

    It is shown that the transformation between ordinary and noncommutative Yang-Mills theory as formulated by Seiberg and Witten is due to the equivalence of certain star products on the D-brane world-volume. (orig.)

  15. Noncommutative GUTs, Standard Model and C,P,T

    Energy Technology Data Exchange (ETDEWEB)

    Aschieri, P. E-mail: aschieri@theorie.physik.uni-muenchen.de; Jurco, B. E-mail: jurco@theorie.physik.uni-muenchen.de; Schupp, P. E-mail: p.schupp@iu-bremen.de; Wess, J. E-mail: wess@theorie.physik.uni-muenchen.de

    2003-02-17

    Noncommutative Yang-Mills theories are sensitive to the choice of the representation that enters in the gauge kinetic term. We constrain this ambiguity by considering grand unified theories. We find that at first order in the noncommutativity parameter {theta}, SU(5) is not truly a unified theory, while SO(10) has a unique noncommutative generalization. In view of these results we discuss the noncommutative SM theory that is compatible with SO(10) GUT and find that there are no modifications to the SM gauge kinetic term at lowest order in {theta}. We study in detail the reality, Hermiticity and C,P,T properties of the Seiberg-Witten map and of the resulting effective actions expanded in ordinary fields. We find that in models of GUTs (or compatible with GUTs) right-handed fermions and left-handed ones appear with opposite Seiberg-Witten map.

  16. Noncommutative SO(n) and Sp(n) gauge theories

    International Nuclear Information System (INIS)

    Bonora, L.; INFN, Sezione di Trieste, Trieste; Schnabl, M.; INFN, Sezione di Trieste, Trieste; Sheikh-Jabbari, M.M.; Tomasiello, A.

    2000-08-01

    We study the generalization of noncommutative gauge theories to the case of orthogonal and symplectic groups. We find out that this is possible, since we are allowed to define orthogonal and symplectic subgroups of noncommutative unitary gauge transformations even though the gauge potentials and gauge transformations are not valued in the orthogonal and symplectic subalgebras of the Lie algebra of antihermitean matrices. Our construction relies on an antiautomorphism of the basic noncommutative algebra of functions which generalizes the charge conjugation operator of ordinary field theory. We show that the corresponding noncommutative picture from low energy string theory is obtained via orientifold projection in the presence of a non-trivial NSNS B-field. (author)

  17. Exact master equation for a noncommutative Brownian particle

    International Nuclear Information System (INIS)

    Costa Dias, Nuno; Nuno Prata, Joao

    2009-01-01

    We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale

  18. Accretion onto a noncommutative-inspired Schwarzschild black hole

    Science.gov (United States)

    Gangopadhyay, Sunandan; Paik, Biplab; Mandal, Rituparna

    2018-05-01

    In this paper, we investigate the problem of ordinary baryonic matter accretion onto the noncommutative (NC) geometry-inspired Schwarzschild black hole. The fundamental equations governing the spherically symmetric steady state matter accretion are deduced. These equations are seen to be modified due to the presence of noncommutativity. The matter accretion rate is computed and is found to increase rapidly with the increase in strength of the NC parameter. The sonic radius reduces while the sound speed at the sonic point increases with the increase in the strength of noncommutativity. The profile of the thermal environment is finally investigated below the sonic radius and at the event horizon and is found to be affected by noncommutativity.

  19. Vectors and covectors in non-commutative setting

    OpenAIRE

    Parfionov, G. N.; Romashev, Yu. A.; Zapatrine, R. R.

    1995-01-01

    Following the guidelines of classical differential geometry the `building material' for the tensor calculus in non-commutative geometry is suggested. The algebraic account of moduli of vectors and covectors is carried out.

  20. Baecklund transformation of the noncommutative Gelfand-Dickey hierarchy

    International Nuclear Information System (INIS)

    Zheng Zhong; He Jingsong; Cheng Yi

    2004-01-01

    We study the Baecklund transformation of the noncommutative Gelfand-Dickey(ncGD) hierarchy. By factorizing its Lax operator into the multiplication form of first order differential operator, the noncommutative modified KdV(ncMKdV) hierarchy and the Miura transformations are defined. Our results show that the ncMKdV equations are invariant under the cyclic permutation, and hence induces the Baecklund transformation of the ncGD hierarchy. (author)

  1. Differential Galois obstructions for non-commutative integrability

    Energy Technology Data Exchange (ETDEWEB)

    Maciejewski, Andrzej J. [Institute of Astronomy, University of Zielona Gora, Podgorna 50, PL-65-246 Zielona Gora (Poland)], E-mail: maciejka@astro.ia.uz.zgora.pl; Przybylska, Maria [Torun Centre for Astronomy, N. Copernicus University, Gagarina 11, PL-87-100 Torun (Poland)], E-mail: mprzyb@astri.uni.torun.pl

    2008-08-11

    We show that if a holomorphic Hamiltonian system is holomorphically integrable in the non-commutative sense in a neighbourhood of a non-equilibrium phase curve which is located at a regular level of the first integrals, then the identity component of the differential Galois group of the variational equations along the phase curve is Abelian. Thus necessary conditions for the commutative and non-commutative integrability given by the differential Galois approach are the same.

  2. Towards Noncommutative Linking Numbers via the Seiberg-Witten Map

    Directory of Open Access Journals (Sweden)

    H. García-Compeán

    2015-01-01

    Full Text Available Some geometric and topological implications of noncommutative Wilson loops are explored via the Seiberg-Witten map. In the abelian Chern-Simons theory on a three-dimensional manifold, it is shown that the effect of noncommutativity is the appearance of 6n new knots at the nth order of the Seiberg-Witten expansion. These knots are trivial homology cycles which are Poincaré dual to the higher-order Seiberg-Witten potentials. Moreover the linking number of a standard 1-cycle with the Poincaré dual of the gauge field is shown to be written as an expansion of the linking number of this 1-cycle with the Poincaré dual of the Seiberg-Witten gauge fields. In the process we explicitly compute the noncommutative “Jones-Witten” invariants up to first order in the noncommutative parameter. Finally in order to exhibit a physical example, we apply these ideas explicitly to the Aharonov-Bohm effect. It is explicitly displayed at first order in the noncommutative parameter; we also show the relation to the noncommutative Landau levels.

  3. Abelian Toda field theories on the noncommutative plane

    Science.gov (United States)

    Cabrera-Carnero, Iraida

    2005-10-01

    Generalizations of GL(n) abelian Toda and GL with tilde above(n) abelian affine Toda field theories to the noncommutative plane are constructed. Our proposal relies on the noncommutative extension of a zero-curvature condition satisfied by algebra-valued gauge potentials dependent on the fields. This condition can be expressed as noncommutative Leznov-Saveliev equations which make possible to define the noncommutative generalizations as systems of second order differential equations, with an infinite chain of conserved currents. The actions corresponding to these field theories are also provided. The special cases of GL(2) Liouville and GL with tilde above(2) sinh/sine-Gordon are explicitly studied. It is also shown that from the noncommutative (anti-)self-dual Yang-Mills equations in four dimensions it is possible to obtain by dimensional reduction the equations of motion of the two-dimensional models constructed. This fact supports the validity of the noncommutative version of the Ward conjecture. The relation of our proposal to previous versions of some specific Toda field theories reported in the literature is presented as well.

  4. Noncommutative gauge theories on ℝ{sub λ}{sup 3}: perturbatively finite models

    Energy Technology Data Exchange (ETDEWEB)

    Géré, Antoine [Dipartimento di Matematica, Università di Genova,Via Dodecaneso, 35, I-16146 Genova (Italy); Jurić, Tajron [Ruđer Bošković Institute, Theoretical Physics Division,Bijenička c.54, HR-10002 Zagreb (Croatia); Wallet, Jean-Christophe [Laboratoire de Physique Théorique, CNRS, University Paris-Sud, University Paris-Saclay,Bât. 210, 91405 Orsay (France)

    2015-12-09

    We show that natural noncommutative gauge theory models on ℝ{sub λ}{sup 3} can accommodate gauge invariant harmonic terms, thanks to the existence of a relationship between the center of ℝ{sub λ}{sup 3} and the components of the gauge invariant 1-form canonical connection. This latter object shows up naturally within the present noncommutative differential calculus. Restricting ourselves to positive actions with covariant coordinates as field variables, a suitable gauge-fixing leads to a family of matrix models with quartic interactions and kinetic operators with compact resolvent. Their perturbative behavior is then studied. We first compute the 2-point and 4-point functions at the one-loop order within a subfamily of these matrix models for which the interactions have a symmetric form. We find that the corresponding contributions are finite. We then extend this result to arbitrary order. We find that the amplitudes of the ribbon diagrams for the models of this subfamily are finite to all orders in perturbation. This result extends finally to any of the models of the whole family of matrix models obtained from the above gauge-fixing. The origin of this result is discussed. Finally, the existence of a particular model related to integrable hierarchies is indicated, for which the partition function is expressible as a product of ratios of determinants.

  5. Noncommuting limits of oscillator wave functions

    International Nuclear Information System (INIS)

    Daboul, J.; Pogosyan, G. S.; Wolf, K. B.

    2007-01-01

    Quantum harmonic oscillators with spring constants k > 0 plus constant forces f exhibit rescaled and displaced Hermite-Gaussian wave functions, and discrete, lower bound spectra. We examine their limits when (k, f) → (0, 0) along two different paths. When f → 0 and then k → 0, the contraction is standard: the system becomes free with a double continuous, positive spectrum, and the wave functions limit to plane waves of definite parity. On the other hand, when k → 0 first, the contraction path passes through the free-fall system, with a continuous, nondegenerate, unbounded spectrum and displaced Airy wave functions, while parity is lost. The subsequent f → 0 limit of the nonstandard path shows the dc hysteresis phenomenon of noncommuting contractions: the lost parity reappears as an infinitely oscillating superposition of the two limiting solutions that are related by the symmetry

  6. Noncommutative analysis, operator theory and applications

    CERN Document Server

    Cipriani, Fabio; Colombo, Fabrizio; Guido, Daniele; Sabadini, Irene; Sauvageot, Jean-Luc

    2016-01-01

    This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

  7. A first course in noncommutative rings

    CERN Document Server

    Lam, T Y

    2001-01-01

    A First Course in Noncommutative Rings, an outgrowth of the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-semester course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semisimple rings, Jacobson's theory of the radical, representation theory of groups and algebras, prime and semiprime rings, local and semilocal rings, perfect and semiperfect rings, etc. By aiming the level of writing at the novice rather than the connoisseur and by stressing th the role of examples and motivation, the author has produced a text that is suitable not only for use in a graduate course, but also for self- study in the subject by interested graduate students. More than 400 exercises testing the understanding of the general theory in the text are included in this new edition.

  8. Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole

    Directory of Open Access Journals (Sweden)

    Alexis Larrañaga

    2013-01-01

    Full Text Available The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD. Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.

  9. Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

    International Nuclear Information System (INIS)

    Castro, P.G.; Kullock, R.; Toppan, F.

    2011-01-01

    Nonrelativistic quantum mechanics and conformal quantum mechanics are de- formed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles. (author)

  10. Snyder noncommutativity and pseudo-Hermitian Hamiltonians from a Jordanian twist

    Energy Technology Data Exchange (ETDEWEB)

    Castro, P.G., E-mail: pgcastro@cbpf.b [Universidade Federal de Juiz de Fora (DM/ICE/UFJF), Juiz de Fora, MG (Brazil). Inst. de Ciencias Exatas. Dept. de Matematica; Kullock, R.; Toppan, F., E-mail: ricardokl@cbpf.b, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (TEO/CBPF), Rio de Janeiro, RJ (Brazil). Coordenacao de Fisica Teorica

    2011-07-01

    Nonrelativistic quantum mechanics and conformal quantum mechanics are de- formed through a Jordanian twist. The deformed space coordinates satisfy the Snyder noncommutativity. The resulting deformed Hamiltonians are pseudo-Hermitian Hamiltonians of the type discussed by Mostafazadeh. The quantization scheme makes use of the so-called 'unfolded formalism' discussed in previous works. A Hopf algebra structure, compatible with the physical interpretation of the coproduct, is introduced for the Universal Enveloping Algebra of a suitably chosen dynamical Lie algebra (the Hamiltonian is contained among its generators). The multi-particle sector, uniquely determined by the deformed 2-particle Hamiltonian, is composed of bosonic particles. (author)

  11. Noncommutative gauge theory and symmetry breaking in matrix models

    International Nuclear Information System (INIS)

    Grosse, Harald; Steinacker, Harold; Lizzi, Fedele

    2010-01-01

    We show how the fields and particles of the standard model can be naturally realized in noncommutative gauge theory. Starting with a Yang-Mills matrix model in more than four dimensions, an SU(n) gauge theory on a Moyal-Weyl space arises with all matter and fields in the adjoint of the gauge group. We show how this gauge symmetry can be broken spontaneously down to SU(3) c xSU(2) L xU(1) Q [resp. SU(3) c xU(1) Q ], which couples appropriately to all fields in the standard model. An additional U(1) B gauge group arises which is anomalous at low energies, while the trace-U(1) sector is understood in terms of emergent gravity. A number of additional fields arise, which we assume to be massive, in a pattern that is reminiscent of supersymmetry. The symmetry breaking might arise via spontaneously generated fuzzy spheres, in which case the mechanism is similar to brane constructions in string theory.

  12. Stability analysis of lower dimensional gravastars in noncommutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata (India); Hansraj, Sudan [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

    2016-11-15

    The Banados et al. (Phys. Rev. Lett 69:1849, 1992), black hole solution is revamped from the Einstein field equations in (2 + 1)-dimensional anti-de Sitter spacetime, in a context of noncommutative geometry (Phys. Rev. D 87:084014, 2013). In this article, we explore the exact gravastar solutions in three-dimensional anti-de Sitter space given in the same geometry. As a first step we derive BTZ solution assuming the source of energy density as point-like structures in favor of smeared objects, where the particle mass M, is diffused throughout a region of linear size √(α) and is described by a Gaussian function of finite width rather than a Dirac delta function. We matched our interior solution to an exterior BTZ spacetime at a junction interface situated outside the event horizon. Furthermore, a stability analysis is carried out for the specific case when χ < 0.214 under radial perturbations about the static equilibrium solutions. To give theoretical support we are also trying to explore their physical properties and characteristics. (orig.)

  13. Noncommutative Cantor–Bendixson derivatives and scattered C⁎-algebras

    Czech Academy of Sciences Publication Activity Database

    Ghasemi, Saeed; Koszmider, P.

    2018-01-01

    Roč. 240, 15 May (2018), s. 183-209 ISSN 0166-8641 Institutional support: RVO:67985840 Keywords : C*-algebras * Cantor-Bendixson derivative * scattered locally compact spaces Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.377, year: 2016 https://www.sciencedirect.com/science/ article /pii/S0166864118301688?via%3Dihub

  14. Noncommutative Cantor–Bendixson derivatives and scattered C⁎-algebras

    Czech Academy of Sciences Publication Activity Database

    Ghasemi, Saeed; Koszmider, P.

    2018-01-01

    Roč. 240, 15 May (2018), s. 183-209 ISSN 0166-8641 Institutional support: RVO:67985840 Keywords : C*-algebras * Cantor-Bendixson derivative * scattered locally compact spaces Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.377, year: 2016 https://www.sciencedirect.com/science/article/pii/S0166864118301688?via%3Dihub

  15. On a direct approach to quasideterminant solutions of a noncommutative modified KP equation

    International Nuclear Information System (INIS)

    Gilson, C R; Nimmo, J J C; Sooman, C M

    2008-01-01

    A noncommutative version of the modified KP equation and a family of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of Darboux transformations and the solutions are verified directly. We also verify directly an explicit connection between quasideterminant solutions of the noncommutative mKP equation and the noncommutative KP equation arising from the Miura transformation

  16. CMB statistical anisotropy from noncommutative gravitational waves

    Energy Technology Data Exchange (ETDEWEB)

    Shiraishi, Maresuke; Ricciardone, Angelo [Dipartimento di Fisica e Astronomia ' ' G. Galilei' ' , Università degli Studi di Padova, via Marzolo 8, I-35131, Padova (Italy); Mota, David F. [Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029 Blindern, N-0315 Oslo (Norway); Arroja, Frederico, E-mail: maresuke.shiraishi@pd.infn.it, E-mail: d.f.mota@astro.uio.no, E-mail: angelo.ricciardone@pd.infn.it, E-mail: arroja@pd.infn.it [INFN, Sezione di Padova, via Marzolo 8, I-35131, Padova (Italy)

    2014-07-01

    Primordial statistical anisotropy is a key indicator to investigate early Universe models and has been probed by the cosmic microwave background (CMB) anisotropies. In this paper, we examine tensor-mode CMB fluctuations generated from anisotropic gravitational waves, parametrised by P{sub h}(k) = P{sub h}{sup (0)}(k) [ 1 + ∑{sub LM} f{sub L}(k) g{sub LM} Y{sub LM} ( k-circumflex )], where P{sub h}{sup (0)}(k) is the usual scale-invariant power spectrum. Such anisotropic tensor fluctuations may arise from an inflationary model with noncommutativity of fields. It is verified that in this model, an isotropic component and a quadrupole asymmetry with f{sub 0}(k) = f{sub 2}(k) ∝ k{sup -2} are created and hence highly red-tilted off-diagonal components arise in the CMB power spectra, namely ℓ{sub 2} = ℓ{sub 1} ± 2 in TT, TE, EE and BB, and ℓ{sub 2} = ℓ{sub 1} ± 1 in TB and EB. We find that B-mode polarisation is more sensitive to such signals than temperature and E-mode polarisation due to the smallness of large-scale cosmic variance and we can potentially measure g{sub 00} = 30 and g{sub 2M} = 58 at 68% CL in a cosmic-variance-limited experiment. Such a level of signal may be measured in a PRISM like experiment, while the instrumental noise contaminates it in the Planck experiment. These results imply that it is impossible to measure the noncommutative parameter if it is small enough for the perturbative treatment to be valid. Our formalism and methodology for dealing with the CMB tensor statistical anisotropy are general and straightforwardly applicable to other early Universe models.

  17. Soldering formalism in noncommutative field theory: a brief note

    International Nuclear Information System (INIS)

    Ghosh, Subir

    2004-01-01

    In this Letter, I develop the soldering formalism in a new domain--the noncommutative planar field theories. The soldering mechanism fuses two distinct theories showing opposite or complimentary properties of some symmetry, taking into account the interference effects. The above mentioned symmetry is hidden in the composite (or soldered) theory. In the present work it is shown that a pair of noncommutative Maxwell-Chern-Simons theories, having opposite signs in their respective topological terms, can be consistently soldered to yield the Proca model (Maxwell theory with a mass term) with corrections that are at least quadratic in the noncommutativity parameter. We further argue that this model can be thought of as the noncommutative generalization of the Proca theory of ordinary spacetime. It is well known that abelian noncommutative gauge theory bears a close structural similarity with non-abelian gauge theory. This fact is manifested in a non-trivial way if the present Letter is compared with existing literature, where soldering of non-abelian models are discussed. Thus the present work further establishes the robustness of the soldering programme. The subtle role played by gauge invariance (or the lack of it), in the above soldering process, is revealed in an interesting way

  18. Overview of the Performance of the Compact Total Electron Content Sensor (CTECS) on the Space Environmental NanoSatellite Experiment (SENSE)

    Science.gov (United States)

    Bishop, R. L.; Hansel, S.; Stoffel, D.; Ping, D.; Bardeen, J.; Chin, A.; Bielat, S.; Mulligan, T. L.

    2014-12-01

    The Air Force's Space & Missile Systems Center (SMC) SENSE mission consists of two identical cubesat buses with space weather payloads. One of the goals of the SENSE mission is to demonstrate the operational potential and usefulness of space weather measurements from a cubesat platform. The payloads on the two cubesats include the Cubesat Tiny Ionospheric Photometer (SRI), Wind Ion Neutral Composite Suite (NRL), and Compact Total Electron Content GPS radio occultation sensor (CTECS). After initial contact with both space vehicles (SV), we were able to confirm successful operation of both CTECS. Because of power issues on SV2, only SV1 has provided consistent data. In this presentation, we present an overview of the CTECS sensor. Then we present initial CTECS data, discuss the data quality, and lessons learned.

  19. Aspects of solitons in noncommutative field theories. The modified Ward model

    International Nuclear Information System (INIS)

    Petersen, S.

    2006-01-01

    In this thesis several aspects of solutions to the equations of motions to noncommutative field theories are investigated in detail. The main focus of the analysis is on the integrable chiral or modified unitary sigma model with U(n)-valued fields as introduced by Ward and its noncommutative extension where the above mentioned new solutions arise. Of particular interest in this context are to us the question of stability of static solitons and the applicability of the so-called adiabatic approach to as a means to approximate time-dependent solutions by geodesic motion in the moduli space of static solutions. After some introductory remarks we proceed to present the Ward model together with its noncommutative extension and give a unified exposition of its known static solutions. This model, as the prime example of an almost Lorentz-invariant field theory in 1+2 dimensions, has several virtues which make its analysis worthwhile. First of all it is integrable thus allowing for powerful, well developed, techniques to generate soliton solutions. At the same time these feature interaction among them. Furthermore, the commutative counterpart of the Ward model has been investigated in great detail such that many results are available for comparison. Next, the question of stability for the present static solutions is considered. This stability is governed by the quadratic form of the fluctuations, which, upon concentrating on the case of diagonal U(1) solutions, is explicitly computed. We show that the considered solutions are stable within a certain subsector of possible configurations, namely the grassmannian ones, and become unstable upon embedding them into the full unitary sigma model. Finally, we remark on some possible generalization of these results. This subject is followed, after a brief review of time-dependent Ward model solutions, by the application of the adiabatic approach, as proposed by Manton, to the static solutions. (orig.)

  20. A very strong difference property for semisimple compact connected lie groups

    Science.gov (United States)

    Shtern, A. I.

    2011-06-01

    Let G be a topological group. For a function f: G → ℝ and h ∈ G, the difference function Δ h f is defined by the rule Δ h f( x) = f( xh) - f( x) ( x ∈ G). A function H: G → ℝ is said to be additive if it satisfies the Cauchy functional equation H( x + y) = H( x) + H( y) for every x, y ∈ G. A class F of real-valued functions defined on G is said to have the difference property if, for every function f: G → ℝ satisfying Δ h f ∈ F for each h ∈ G, there is an additive function H such that f - H ∈ F. Erdős' conjecture claiming that the class of continuous functions on ℝ has the difference property was proved by N. G. de Bruijn; later on, F. W. Carroll and F. S. Koehl obtained a similar result for compact Abelian groups and, under the additional assumption that the other one-sided difference function ∇ h f defined by ∇ h f( x) = f( xh) - f( x) ( x ∈ G, h ∈ G) is measurable for any h ∈ G, also for noncommutative compact metric groups. In the present paper, we consider a narrower class of groups, namely, the family of semisimple compact connected Lie groups. It turns out that these groups admit a significantly stronger difference property. Namely, if a function f: G → ℝ on a semisimple compact connected Lie group has continuous difference functions Δ h f for any h ∈ G (without the additional assumption concerning the measurability of the functions of the form ∇ h f), then f is automatically continuous, and no nontrivial additive function of the form H is needed. Some applications are indicated, including difference theorems for homogeneous spaces of compact connected Lie groups.

  1. Feynman's Operational Calculi: Spectral Theory for Noncommuting Self-adjoint Operators

    International Nuclear Information System (INIS)

    Jefferies, Brian; Johnson, Gerald W.; Nielsen, Lance

    2007-01-01

    The spectral theorem for commuting self-adjoint operators along with the associated functional (or operational) calculus is among the most useful and beautiful results of analysis. It is well known that forming a functional calculus for noncommuting self-adjoint operators is far more problematic. The central result of this paper establishes a rich functional calculus for any finite number of noncommuting (i.e. not necessarily commuting) bounded, self-adjoint operators A 1 ,..., A n and associated continuous Borel probability measures μ 1 , ?, μ n on [0,1]. Fix A 1 ,..., A n . Then each choice of an n-tuple (μ 1 ,...,μ n ) of measures determines one of Feynman's operational calculi acting on a certain Banach algebra of analytic functions even when A 1 , ..., A n are just bounded linear operators on a Banach space. The Hilbert space setting along with self-adjointness allows us to extend the operational calculi well beyond the analytic functions. Using results and ideas drawn largely from the proof of our main theorem, we also establish a family of Trotter product type formulas suitable for Feynman's operational calculi

  2. Towards Noncommutative Topological Quantum Field Theory: Tangential Hodge-Witten cohomology

    International Nuclear Information System (INIS)

    Zois, I P

    2014-01-01

    Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called ''tangential cohomology'' of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for tangential cohomology of foliations by mimicing Witten's approach to ordinary Morse theory by perturbations of the Laplacian

  3. Towards Noncommutative Topological Quantum Field Theory – Hodge theory for cyclic cohomology

    International Nuclear Information System (INIS)

    Zois, I P

    2014-01-01

    Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called ''tangential cohomology'' of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for cyclic and Hochschild cohomology for the corresponding C*-algebra of a foliation

  4. Inhomogeneous compact extra dimensions

    Energy Technology Data Exchange (ETDEWEB)

    Bronnikov, K.A. [Center of Gravity and Fundamental Metrology, VNIIMS, 46 Ozyornaya st., Moscow 119361 (Russian Federation); Budaev, R.I.; Grobov, A.V.; Dmitriev, A.E.; Rubin, Sergey G., E-mail: kb20@yandex.ru, E-mail: buday48@mail.ru, E-mail: alexey.grobov@gmail.com, E-mail: alexdintras@mail.ru, E-mail: sergeirubin@list.ru [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow (Russian Federation)

    2017-10-01

    We show that an inhomogeneous compact extra space possesses two necessary features— their existence does not contradict the observable value of the cosmological constant Λ{sub 4} in pure f ( R ) theory, and the extra dimensions are stable relative to the 'radion mode' of perturbations, the only mode considered. For a two-dimensional extra space, both analytical and numerical solutions for the metric are found, able to provide a zero or arbitrarily small Λ{sub 4}. A no-go theorem has also been proved, that maximally symmetric compact extra spaces are inconsistent with 4D Minkowski space in the framework of pure f ( R ) gravity.

  5. Interacting open Wilson lines from noncommutative field theories

    International Nuclear Information System (INIS)

    Kiem, Youngjai; Lee, Sangmin; Rey, Soo-Jong; Sato, Haru-Tada

    2002-01-01

    In noncommutative field theories, it is known that the one-loop effective action describes the propagation of noninteracting open Wilson lines, obeying the flying dipole's relation. We show that the two-loop effective action describes the cubic interaction among 'closed string' states created by open Wilson line operators. Taking d-dimensional λ[Φ 3 ] * theory as the simplest setup, we compute the nonplanar contribution at a low-energy and large noncommutativity limit. We find that the contribution is expressible in a remarkably simple cubic interaction involving scalar open Wilson lines only and nothing else. We show that the interaction is purely geometrical and noncommutative in nature, depending only on the size of each open Wilson line

  6. Optimization of polynomials in non-commuting variables

    CERN Document Server

    Burgdorf, Sabine; Povh, Janez

    2016-01-01

    This book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.

  7. Quantization, geometry and noncommutative structures in mathematics and physics

    CERN Document Server

    Morales, Pedro; Ocampo, Hernán; Paycha, Sylvie; Lega, Andrés

    2017-01-01

    This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf a...

  8. A non-perturbative study of 4d U(1) non-commutative gauge theory - the fate of one-loop instability

    International Nuclear Information System (INIS)

    Bietenholz, Wolfgang; Nishimura, Jun; Susaki, Yoshiaki; Volkholz, Jan

    2006-01-01

    Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d = 2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter θ, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on θ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking

  9. A non-perturbative study of 4d U(1) non-commutative gauge theory — the fate of one-loop instability

    Science.gov (United States)

    Bietenholz, Wolfgang; Nishimura, Jun; Susaki, Yoshiaki; Volkholz, Jan

    2006-10-01

    Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d = 2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter θ, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on θ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.

  10. MCNP Simulations of Measurement of Insulation Compaction in the Cryogenic Rocket Fuel Tanks at Kennedy Space Center by Fast/Thermal Neutron Techniques

    Science.gov (United States)

    Livingston, R. A.; Schweitzer, J. S.; Parsons, A. M.; Arens, E. E.

    2010-01-01

    MCNP simulations have been run to evaluate the feasibility of using a combination of fast and thermal neutrons as a nondestructive method to measure of the compaction of the perlite insulation in the liquid hydrogen and oxygen cryogenic storage tanks at John F. Kennedy Space Center (KSC). Perlite is a feldspathic volcanic rock made up of the major elements Si, AI, Na, K and 0 along with some water. When heated it expands from four to twenty times its original volume which makes it very useful for thermal insulation. The cryogenic tanks at Kennedy Space Center are spherical with outer diameters of 69-70 feet and lined with a layer of expanded perlite with thicknesses on the order of 120 cm. There is evidence that some of the perlite has compacted over time since the tanks were built 1965, affecting the thermal properties and possibly also the structural integrity of the tanks. With commercially available portable neutron generators it is possible to produce simultaneously fluxes of neutrons in two energy ranges: fast (14 Me V) and thermal (25 me V). The two energy ranges produce complementary information. Fast neutrons produce gamma rays by inelastic scattering, which is sensitive to Fe and O. Thermal neutrons produce gamma rays by prompt gamma neutron activation (PGNA) and this is sensitive to Si, Al, Na, K and H. The compaction of the perlite can be measured by the change in gamma ray signal strength which is proportional to the atomic number densities of the constituent elements. The MCNP simulations were made to determine the magnitude of this change. The tank wall was approximated by a I-dimensional slab geometry with an 11/16" outer carbon steel wall, an inner stainless wall and 120 cm thick perlite zone. Runs were made for cases with expanded perlite, compacted perlite or with various void fractions. Runs were also made to simulate the effect of adding a moderator. Tallies were made for decay-time analysis from t=0 to 10 ms; total detected gamma

  11. Modular Theory, Non-Commutative Geometry and Quantum Gravity

    Directory of Open Access Journals (Sweden)

    Wicharn Lewkeeratiyutkul

    2010-08-01

    Full Text Available This paper contains the first written exposition of some ideas (announced in a previous survey on an approach to quantum gravity based on Tomita-Takesaki modular theory and A. Connes non-commutative geometry aiming at the reconstruction of spectral geometries from an operational formalism of states and categories of observables in a covariant theory. Care has been taken to provide a coverage of the relevant background on modular theory, its applications in non-commutative geometry and physics and to the detailed discussion of the main foundational issues raised by the proposal.

  12. Intersecting Quantum Gravity with Noncommutative Geometry - a Review

    Directory of Open Access Journals (Sweden)

    Johannes Aastrup

    2012-03-01

    Full Text Available We review applications of noncommutative geometry in canonical quantum gravity. First, we show that the framework of loop quantum gravity includes natural noncommutative structures which have, hitherto, not been explored. Next, we present the construction of a spectral triple over an algebra of holonomy loops. The spectral triple, which encodes the kinematics of quantum gravity, gives rise to a natural class of semiclassical states which entail emerging fermionic degrees of freedom. In the particular semiclassical approximation where all gravitational degrees of freedom are turned off, a free fermionic quantum field theory emerges. We end the paper with an extended outlook section.

  13. Infinite volume of noncommutative black hole wrapped by finite surface

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Baocheng, E-mail: zhangbc.zhang@yahoo.com [School of Mathematics and Physics, China University of Geosciences, Wuhan 430074 (China); You, Li, E-mail: lyou@mail.tsinghua.edu.cn [State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, Beijing 100084 (China)

    2017-02-10

    The volume of a black hole under noncommutative spacetime background is found to be infinite, in contradiction with the surface area of a black hole, or its Bekenstein–Hawking (BH) entropy, which is well-known to be finite. Our result rules out the possibility of interpreting the entropy of a black hole by counting the number of modes wrapped inside its surface if the final evaporation stage can be properly treated. It implies the statistical interpretation for the BH entropy can be independent of the volume, provided spacetime is noncommutative. The effect of radiation back reaction is found to be small and doesn't influence the above conclusion.

  14. Charged thin-shell gravastars in noncommutative geometry

    Energy Technology Data Exchange (ETDEWEB)

    Oevguen, Ali [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Eastern Mediterranean University, Physics Department, Famagusta, Northern Cyprus (Turkey); Banerjee, Ayan [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Jusufi, Kimet [State University of Tetovo, Physics Department, Tetovo (Macedonia, The Former Yugoslav Republic of); Institute of Physics, Ss. Cyril and Methodius University, Faculty of Natural Sciences and Mathematics, Skopje (Macedonia, The Former Yugoslav Republic of)

    2017-08-15

    In this paper we construct a charged thin-shell gravastar model within the context of noncommutative geometry. To do so, we choose the interior of the nonsingular de Sitter spacetime with an exterior charged noncommutative solution by cut-and-paste technique and apply the generalized junction conditions. We then investigate the stability of a charged thin-shell gravastar under linear perturbations around the static equilibrium solutions as well as the thermodynamical stability of the charged gravastar. We find the stability regions, by choosing appropriate parameter values, located sufficiently close to the event horizon. (orig.)

  15. Conceptual Explanation for the Algebra in the Noncommutative Approach to the Standard Model

    International Nuclear Information System (INIS)

    Chamseddine, Ali H.; Connes, Alain

    2007-01-01

    The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input

  16. Quantum groups, non-commutative differential geometry and applications

    International Nuclear Information System (INIS)

    Schupp, P.; California Univ., Berkeley, CA

    1993-01-01

    The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related sciences. A generalization of unitary time evolution is proposed and studied for a simple 2-level system, leading to non-conservation of microscopic entropy, a phenomenon new to quantum mechanics. A Cartan calculus that combines functions, forms, Lie derivatives and inner derivations along general vector fields into one big algebra is constructed for quantum groups and then extended to quantum planes. The construction of a tangent bundle on a quantum group manifold and an BRST type approach to quantum group gauge theory are given as further examples of applications. The material is organized in two parts: Part I studies vector fields on quantum groups, emphasizing Hopf algebraic structures, but also introducing a ''quantum geometric'' construction. Using a generalized semi-direct product construction we combine the dual Hopf algebras A of functions and U of left-invariant vector fields into one fully bicovariant algebra of differential operators. The pure braid group is introduced as the commutant of Δ(U). It provides invariant maps A → U and thereby bicovariant vector fields, casimirs and metrics. This construction allows the translation of undeformed matrix expressions into their less obvious quantum algebraic counter parts. We study this in detail for quasitriangular Hopf algebras, giving the determinant and orthogonality relation for the ''reflection'' matrix. Part II considers the additional structures of differential forms and finitely generated quantum Lie algebras -- it is devoted to the construction of the Cartan calculus, based on an undeformed Cartan identity

  17. Noncommutative Schur polynomials and the crystal limit of the U_{q} \\widehat{\\mathfrak {sl}}(2)-vertex model

    Science.gov (United States)

    Korff, Christian

    2010-10-01

    Starting from the Verma module of U_{q}\\mathfrak {sl}(2) we consider the evaluation module for affine U_{q}\\widehat{\\mathfrak {sl}}(2) and discuss its crystal limit (q → 0). There exists an associated integrable statistical mechanics model on a square lattice defined in terms of vertex configurations. Its transfer matrix is the generating function for noncommutative complete symmetric polynomials in the generators of the affine plactic algebra, an extension of the finite plactic algebra first discussed by Lascoux and Schützenberger. The corresponding noncommutative elementary symmetric polynomials were recently shown to be generated by the transfer matrix of the so-called phase model discussed by Bogoliubov, Izergin and Kitanine. Here we establish that both generating functions satisfy Baxter's TQ-equation in the crystal limit by tying them to special U_{q}\\widehat{ \\mathfrak {sl}}(2) solutions of the Yang-Baxter equation. The TQ-equation amounts to the well-known Jacobi-Trudi formula leading naturally to the definition of noncommutative Schur polynomials. The latter can be employed to define a ring which has applications in conformal field theory and enumerative geometry: it is isomorphic to the fusion ring of the \\widehat{\\mathfrak {sl}}(n)_{k} Wess-Zumino-Novikov-Witten model whose structure constants are the dimensions of spaces of generalized θ-functions over the Riemann sphere with three punctures.

  18. Duality and free measures in vector spaces, the spectral theory of actions of non-locally compact groups

    OpenAIRE

    Vershik, A.

    2017-01-01

    The paper presents a general duality theory for vector measure spaces taking its origin in the author's papers written in the 1960s. The main result establishes a direct correspondence between the geometry of a measure in a vector space and the properties of the space of measurable linear functionals on this space regarded as closed subspaces of an abstract space of measurable functions. An example of useful new features of this theory is the notion of a free measure and its applications.

  19. Flare-generated clouds as compact force-free toroidal configurations: magnetic measurements by the Vega-1 and Vega-2 space probes

    International Nuclear Information System (INIS)

    Ivanov, K.G.; Kharshiladze, A.F.; Eroshenko, E.G.; Styazhkin, V.A.

    1988-01-01

    Magnetic field experimental profiles, obtained during Vega-I and Vega-2 space vehicles passing through interplanetary cloud on the 16.02.1986, are compared with approximate theoretical profiles, taken from different hypotheses about such clouds structure. Maximum correlation of the theory and experiment is obtained with cloud presentation as flattened compact force-free toroid, which equatorial plane is approximately parallel to great circle plane, passing through flare on the 14.02.86 parallel to magnetic axis nearest to bipolar group flare

  20. Major integration issues in evolving the configuration design space for the Aries-Cs compact stellarator power plant

    International Nuclear Information System (INIS)

    Raffray, A.R.; Malang, S.; El-Guebaly, L.; Ihli, T.; Najmabadi, F.; Wang, X.

    2006-01-01

    The Aries-Cs study has been launched with the goal of developing through physics and engineering optimization an attractive power plant concept based on a compact stellarator configuration. The first phase of the study involved scoping out different physics configurations including two and three field period options. The engineering effort during that phase aimed at scoping out maintenance schemes and power core designs best suited to a compact stellarator configuration. This led to a down selection of the most attractive blanket configurations and maintenance schemes for more detailed studies during the second phase of the study. This paper summarizes early results from the second phase of the Aries-Cs study with a particular emphasis on the engineering effort

  1. A 4D spacetime embedded in a 5D pseudo-Euclidean space describing interior of compact stars

    Energy Technology Data Exchange (ETDEWEB)

    Singh, K.N. [National Defence Academy, Department of Physics, Khadakwasla (India); Murad, Mohammad Hassan [BRAC University, Department of Mathematics and Natural Sciences, Dhaka (Bangladesh); Pant, Neeraj [National Defence Academy, Department of Mathematics, Khadakwasla (India)

    2017-02-15

    The present paper provides a new model of compact stars satisfying the Karmarkar condition. The model is obtained by assuming a new type of metric potential for g{sub rr} from the condition of embedding class I. The model parameters are obtained accordingly by employing the metric potentials to Einstein's field equations. Our model is free from geometric singularity and satisfies all the physical conditions. The obtained mass and radius of the compact stars Cen X-3, EXO 1785-248 and SAX 1808.4-3658 obtained from the model are consistent with the observational data of T. Gangopadhyay et al. Detailed analyses of these neutron stars (Cen X-3, EXO 1785-248 and SAX 1808.4-3658) are also given with the help of graphical representations. (orig.)

  2. On the stringy nature of winding modes in noncommutative thermal field theories

    CERN Document Server

    Arcioni, G; Gomis, J P; Vázquez-Mozo, Miguel Angel; Gomis, Joaquim

    2000-01-01

    We show that thermal noncommutative field theories admit a version of `channel duality' reminiscent of open/closed string duality, where non-planar thermal loops can be replaced by an infinite tower of tree-level exchanges of effective fields. These effective fields resemble closed strings in three aspects: their mass spectrum is that of closed-string winding modes, their interaction vertices contain extra moduli, and they can be regarded as propagating in a higher-dimensional `bulk' space-time. In noncommutative models that can be embedded in a D-brane, we show the precise relation between the effective `winding fields' and closed strings propagating off the D-brane. The winding fields represent the coherent coupling of the infinite tower of closed-string oscillator states. We derive a sum rule that expresses this effective coupling in terms of the elementary couplings of closed strings to the D-brane. We furthermore clarify the relation between the effective propagating dimension of the winding fields and t...

  3. Metric interpretation of gauge fields in noncommutative geometry

    International Nuclear Information System (INIS)

    Martinetti, P.

    2007-01-01

    We shall give an overview of the metric interpretation of gauge fields in noncommutative geometry, via Connes distance formula. Especially we shall focus on the Higgs fields in the standard model, and gauge fields in various models of fiber bundle. (author)

  4. Two lectures on D-geometry and noncommutative geometry

    International Nuclear Information System (INIS)

    Douglas, M.R.

    1999-01-01

    This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

  5. 3D quantum gravity and effective noncommutative quantum field theory.

    Science.gov (United States)

    Freidel, Laurent; Livine, Etera R

    2006-06-09

    We show that the effective dynamics of matter fields coupled to 3D quantum gravity is described after integration over the gravitational degrees of freedom by a braided noncommutative quantum field theory symmetric under a kappa deformation of the Poincaré group.

  6. The M5-brane and non-commutative open strings

    NARCIS (Netherlands)

    Bergshoeff, E.; Berman, D.S.; Schaar, J.P. van der; Sundell, P.

    2001-01-01

    The M-theory origin of non-commutative open-string theory is examined by investigating the M-theory 5-brane at near critical field strength. In particular, it is argued that the open-membrane metric provides the appropriate moduli when calculating the duality relations between M and II

  7. General classical solutions in the noncommutative CPN-1 model

    International Nuclear Information System (INIS)

    Foda, O.; Jack, I.; Jones, D.R.T.

    2002-01-01

    We give an explicit construction of general classical solutions for the noncommutative CP N-1 model in two dimensions, showing that they correspond to integer values for the action and topological charge. We also give explicit solutions for the Dirac equation in the background of these general solutions and show that the index theorem is satisfied

  8. Notes on algebraic invariants for non-commutative dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Longo, R [Rome Univ. (Italy). Istituto di Matematica

    1979-11-01

    We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariant T of Connes. Further comments are included, in particular on the type of certain algebras of local observables

  9. Quadratic algebras in the noncommutative integration method of wave equation

    International Nuclear Information System (INIS)

    Varaksin, O.L.

    1995-01-01

    The paper deals with the investigation of applications of the method of noncommutative integration of linear differential equations by partial derivatives. Nontrivial example was taken for integration of three-dimensions wave equation with the use of non-Abelian quadratic algebras

  10. quasi hyperrigidity and weak peak points for non-commutative ...

    Indian Academy of Sciences (India)

    7

    Abstract. In this article, we introduce the notions of weak boundary repre- sentation, quasi hyperrigidity and weak peak points in the non-commutative setting for operator systems in C∗-algebras. An analogue of Saskin's theorem relating quasi hyperrigidity and weak Choquet boundary for particular classes of C∗-algebras is ...

  11. The foundation of quantum theory and noncommutative spectral theory: Part 2

    International Nuclear Information System (INIS)

    Kummer, H.

    1991-01-01

    The present paper comprises Sects. 5-8 of a work which proposes an axiomatic approach to quantum mechanics in which the concept of a filter is the central primitive concept. Having laid down the foundations in the first part of this work, the author arrived at a dual pair left-angle Y,M right-angle consisting of a base norm space Y and an order unit space M, being in order and norm duality with respect to each other. This is precisely the setting of noncommutative spectral theory, a theory which has been developed during the late nineteen seventies by Alfsen and Shultz. In this part he added to the four axioms (Axioms S, DP, R, SP) of Sect. 3 three further axioms (Axioms E, O, L). These axioms are suggested by the work of Alfsen and Shultz and and enable him to derive the JB-algebra structure of quantum mechanics (cf. Theorem 8.9)

  12. HUBBLE SPACE TELESCOPE WFC3 GRISM SPECTROSCOPY AND IMAGING OF A GROWING COMPACT GALAXY AT z = 1.9

    International Nuclear Information System (INIS)

    Van Dokkum, Pieter G.; Brammer, Gabriel

    2010-01-01

    We present HST/WFC3 grism near-IR spectroscopy of the brightest galaxy at z > 1.5 in the GOODS-South WFC3 ERS grism pointing. The spectrum is of remarkable quality and shows the redshifted Balmer lines Hβ, Hγ, and Hδ in absorption at z = 1.902 ± 0.002. The absorption lines can be produced by a post-starburst stellar population with a luminosity-weighted age of ∼0.5 Gyr. The mass-to-light ratio inferred from the spectrum implies a stellar mass of (4 ± 1) x 10 11 M sun . We determine the morphology of the galaxy from a deep WFC3 H 160 image. Similar to other massive galaxies at z ∼ 2 the galaxy is compact, with an effective radius of 2.1 ± 0.3 kpc. Although most of the light is in a compact core, the galaxy has two red, smooth spiral arms that appear to be tidally induced. The spatially resolved spectroscopy demonstrates that the center of the galaxy is quiescent whereas the surrounding disk is forming stars, as it shows Hβ in emission. The galaxy interacts with a companion at a projected distance of 18 kpc, which also shows prominent tidal features. The companion is a factor of ∼10 fainter than the primary galaxy and may have a lower metallicity. It is tempting to interpret these observations as evidence for the growth of compact, quiescent high-redshift galaxies through minor mergers, which has been proposed by several recent observational and theoretical studies. Interestingly both objects host luminous active galactic nuclei, which implies that these mergers can be accompanied by significant black hole growth.

  13. Quantum field theory in generalised Snyder spaces

    International Nuclear Information System (INIS)

    Meljanac, S.; Meljanac, D.; Mignemi, S.; Štrajn, R.

    2017-01-01

    We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.

  14. Quantum field theory in generalised Snyder spaces

    Energy Technology Data Exchange (ETDEWEB)

    Meljanac, S.; Meljanac, D. [Rudjer Bošković Institute, Bijenička cesta 54, 10002 Zagreb (Croatia); Mignemi, S., E-mail: smignemi@unica.it [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy); Štrajn, R. [Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123 Cagliari (Italy); INFN, Sezione di Cagliari, Cittadella Universitaria, 09042 Monserrato (Italy)

    2017-05-10

    We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate perturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.

  15. Manin's quantum spaces and standard quantum mechanics

    International Nuclear Information System (INIS)

    Floratos, E.G.

    1990-01-01

    Manin's non-commutative coordinate algebra of quantum groups is shown to be identical, for unitary coordinates, with the conventional operator algebras of quantum mechanics. The deformation parameter q is a pure phase for unitary coordinates. When q is a root of unity. Manin's algebra becomes the matrix algebra of quantum mechanics for a discretized and finite phase space. Implications for quantum groups and the associated non-commutative differential calculus of Wess and Zumino are discussed. (orig.)

  16. Holomorphic representation of constant mean curvature surfaces in Minkowski space: Consequences of non-compactness in loop group methods

    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...

  17. Dispersion relations for the self-energy in noncommutative field theories

    International Nuclear Information System (INIS)

    Brandt, F.T.; Das, Ashok; Frenkel, J.

    2002-01-01

    We study the IR-UV connection in noncommutative φ 3 theory as well as in noncommutative QED from the point of view of the dispersion relation for self-energy. We show that, although the imaginary part of the self-energy is well behaved as the parameter of noncommutativity vanishes, the real part becomes divergent as a consequence of the high energy behavior of the dispersion integral. Some other interesting features that arise from this analysis are also briefly discussed

  18. Open membranes in a constant C-field background and noncommutative boundary strings

    International Nuclear Information System (INIS)

    Kawamoto, Shoichi; Sasakura, Naoki

    2000-01-01

    We investigate the dynamics of open membrane boundaries in a constant C-field background. We follow the analysis for open strings in a B-field background, and take some approximations. We find that open membrane boundaries do show noncommutativity in this case by explicit calculations. Membrane boundaries are one dimensional strings, so we face a new type of noncommutativity, that is, noncommutative strings. (author)

  19. Invariant subsets under compact quantum group actions

    OpenAIRE

    Huang, Huichi

    2012-01-01

    We investigate compact quantum group actions on unital $C^*$-algebras by analyzing invariant subsets and invariant states. In particular, we come up with the concept of compact quantum group orbits and use it to show that countable compact metrizable spaces with infinitely many points are not quantum homogeneous spaces.

  20. Compactly packaged monolithic four-wavelength VCSEL array with 100-GHz wavelength spacing for future-proof mobile fronthaul transport.

    Science.gov (United States)

    Lee, Eun-Gu; Mun, Sil-Gu; Lee, Sang Soo; Lee, Jyung Chan; Lee, Jong Hyun

    2015-01-12

    We report a cost-effective transmitter optical sub-assembly using a monolithic four-wavelength vertical-cavity surface-emitting laser (VCSEL) array with 100-GHz wavelength spacing for future-proof mobile fronthaul transport using the data rate of common public radio interface option 6. The wavelength spacing is achieved using selectively etched cavity control layers and fine current adjustment. The differences in operating current and output power for maintaining the wavelength spacing of four VCSELs are fiber without any dispersion-compensation techniques.

  1. Design and Development of a compact and ruggest phase and flouresence microscope for space utilization, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — In this SBIR Phase 1 we propose to develop a novel microscope by integrating Fourier phase contrast microscopy (FPCM) and epi-fluorescence microscopy. In FPCM, the...

  2. High-Temperature, Wirebondless, Ultra-Compact Wide Bandgap Power Semiconductor Modules for Space Power Systems, Phase I

    Data.gov (United States)

    National Aeronautics and Space Administration — Silicon carbide (SiC) and other wide band-gap semiconductors offer great promise of high power rating, high operating temperature, simple thermal management, and...

  3. Feasibility study for measurement of insulation compaction in the cryogenic rocket fuel storage tanks at Kennedy Space Center by fast/thermal neutron techniques

    Energy Technology Data Exchange (ETDEWEB)

    Livingston, R. A. [Materials Science and Engineering Dept., U. of Maryland, College Park, MD (United States); Schweitzer, J. S. [Physics Dept., U. of Connecticut, Storrs (United States); Parsons, A. M. [Goddard Space Flight Center, Greenbelt (United States); Arens, E. E. [John F. Kennedy Space Center, FL (United States)

    2014-02-18

    The liquid hydrogen and oxygen cryogenic storage tanks at John F. Kennedy Space Center (KSC) use expanded perlite as thermal insulation. Some of the perlite may have compacted over time, compromising the thermal performance and also the structural integrity of the tanks. Neutrons can readily penetrate through the 1.75 cm outer steel shell and through the entire 120 cm thick perlite zone. Neutrons interactions with materials produce characteristic gamma rays which are then detected. In compacted perlite the count rates in the individual peaks in the gamma ray spectrum will increase. Portable neutron generators can produce neutron simultaneous fluxes in two energy ranges: fast (14 MeV) and thermal (25 meV). Fast neutrons produce gamma rays by inelastic scattering which is sensitive to Si, Al, Fe and O. Thermal neutrons produce gamma rays by radiative capture in prompt gamma neutron activation (PGNA), which is sensitive to Si, Al, Na, K and H among others. The results of computer simulations using the software MCNP and measurements on a test article suggest that the most promising approach would be to operate the system in time-of-flight mode by pulsing the neutron generator and observing the subsequent die away curve in the PGNA signal.

  4. Gauging the twisted Poincare symmetry as a noncommutative theory of gravitation

    International Nuclear Information System (INIS)

    Chaichian, M.; Tureanu, A.; Oksanen, M.; Zet, G.

    2009-01-01

    Einstein's theory of general relativity was formulated as a gauge theory of Lorentz symmetry by Utiyama in 1956, while the Einstein-Cartan gravitational theory was formulated by Kibble in 1961 as the gauge theory of Poincare transformations. In this framework, we propose a formulation of the gravitational theory on canonical noncommutative space-time by covariantly gauging the twisted Poincare symmetry, in order to fulfil the requirement of covariance under the general coordinate transformations, an essential ingredient of the theory of general relativity. It appears that the twisted Poincare symmetry cannot be gauged by generalizing the Abelian twist to a covariant non-Abelian twist, nor by introducing a more general covariant twist element. The advantages of such a formulation as well as the related problems are discussed and possible ways out are outlined.

  5. Noncommutative geometry inspired black holes in Rastall gravity

    Energy Technology Data Exchange (ETDEWEB)

    Ma, Meng-Sen [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China); Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China)

    2017-09-15

    Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR. (orig.)

  6. Chirality Quantum Phase Transition in Noncommutative Dirac Oscillator

    International Nuclear Information System (INIS)

    Wang Shao-Hua; Hou Yu-Long; Jing Jian; Wang Qing; Long Zheng-Wen

    2014-01-01

    The charged Dirac oscillator on a noncommutative plane coupling to a uniform perpendicular magnetic held is studied in this paper. We map the noncommutative plane to a commutative one by means of Bopp shift and study this problem on the commutative plane. We find that this model can be mapped onto a quantum optics model which contains Anti—Jaynes—Cummings (AJC) or Jaynes—Cummings (JC) interactions when a dimensionless parameter ζ (which is the function of the intensity of the magnetic held) takes values in different regimes. Furthermore, this model behaves as experiencing a chirality quantum phase transition when the dimensionless parameter ζ approaches the critical point. Several evidences of the chirality quantum phase transition are presented. We also study the non-relativistic limit of this model and find that a similar chirality quantum phase transition takes place in its non-relativistic limit. (physics of elementary particles and fields)

  7. Quantum aspects of the noncommutative Sine-Gordon model

    International Nuclear Information System (INIS)

    Kuerkcueoglu

    2007-01-01

    In this talk, I will first present some of the quantum field theoretical aspects of the integrable noncommutative sine-Gordon model proposed in [hep-th/0406065] using standard semi-classical methods. In particular, I will discuss the fluctuations at quadratic order around the static kink solution using the background field method. I will argue that at 0(θ 2 ) the spectrum of fluctuations remains essentially the same as that of the corresponding commutative theory. A brief analysis of one-loop two-point functions will also be presented and it will be followed by some remarks on the obstacles in determining the noncommutativity corrections to the quantum mass of the kink. (author)

  8. Non-commuting variations in mathematics and physics a survey

    CERN Document Server

    Preston, Serge

    2016-01-01

    This text presents and studies the method of so –called noncommuting variations in Variational Calculus. This method was pioneered by Vito Volterra who noticed that the conventional Euler-Lagrange (EL-) equations are not applicable in Non-Holonomic Mechanics and suggested to modify the basic rule used in Variational Calculus. This book presents a survey of Variational Calculus with non-commutative variations and shows that most basic properties of conventional Euler-Lagrange Equations are, with some modifications, preserved for EL-equations with K-twisted (defined by K)-variations. Most of the book can be understood by readers without strong mathematical preparation (some knowledge of Differential Geometry is necessary). In order to make the text more accessible the definitions and several necessary results in Geometry are presented separately in Appendices I and II Furthermore in Appendix III a short presentation of the Noether Theorem describing the relation between the symmetries of the differential equa...

  9. Stability of a non-commutative Jackiw-Teitelboim gravity

    Energy Technology Data Exchange (ETDEWEB)

    Vassilevich, D.V. [Universitaet Leipzig, Institut fuer Theoretische Physik, Postfach 100 920, Leipzig (Germany); St. Petersburg University, V.A. Fock Institute of Physics, St. Petersburg (Russian Federation); Fresneda, R.; Gitman, D.M. [Sao Paulo Univ. (Brazil). Inst. de Fisica

    2006-07-15

    We start with a non-commutative version of the Jackiw-Teitelboim gravity in two dimensions which has a linear potential for the dilaton fields. We study whether it is possible to deform this model by adding quadratic terms to the potential but preserving the number of gauge symmetries. We find that no such deformation exists (provided one does not twist the gauge symmetries). (orig.)

  10. Semiclassical and quantum motions on the non-commutative plane

    International Nuclear Information System (INIS)

    Baldiotti, M.C.; Gazeau, J.P.; Gitman, D.M.

    2009-01-01

    We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a θ-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the 'classical' trajectories is investigated, and we present numerical explorations of some semiclassical quantities.

  11. Semiclassical and quantum motions on the non-commutative plane

    Energy Technology Data Exchange (ETDEWEB)

    Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.f [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil)

    2009-10-19

    We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a theta-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the 'classical' trajectories is investigated, and we present numerical explorations of some semiclassical quantities.

  12. Clifford algebras, noncommutative tori and universal quantum computers

    OpenAIRE

    Vlasov, Alexander Yu.

    2001-01-01

    Recently author suggested [quant-ph/0010071] an application of Clifford algebras for construction of a "compiler" for universal binary quantum computer together with later development [quant-ph/0012009] of the similar idea for a non-binary base. The non-binary case is related with application of some extension of idea of Clifford algebras. It is noncommutative torus defined by polynomial algebraic relations of order l. For l=2 it coincides with definition of Clifford algebra. Here is presente...

  13. Commutative and Non-commutative Parallelogram Geometry: an Experimental Approach

    OpenAIRE

    Bertram, Wolfgang

    2013-01-01

    By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via exercises using dynamical software (such as geogebra), hopefully accessible to a wide mathematical audience, from undergraduate students and high school teachers to researchers, proceeding in three steps: (1) experimental geometry, (2) algebra (linear algebr...

  14. Euler Polynomials and Identities for Non-Commutative Operators

    OpenAIRE

    De Angelis, V.; Vignat, C.

    2015-01-01

    Three kinds of identities involving non-commutating operators and Euler and Bernoulli polynomials are studied. The first identity, as given by Bender and Bettencourt, expresses the nested commutator of the Hamiltonian and momentum operators as the commutator of the momentum and the shifted Euler polynomial of the Hamiltonian. The second one, due to J.-C. Pain, links the commutators and anti-commutators of the monomials of the position and momentum operators. The third appears in a work by Fig...

  15. Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes

    Science.gov (United States)

    Ghosh, Sushant G.

    2018-04-01

    Low energy limits of a string theory suggests that the gravity action should include quadratic and higher-order curvature terms, in the form of dimensionally continued Gauss–Bonnet densities. Einstein–Gauss–Bonnet is a natural extension of the general relativity to higher dimensions in which the first and second-order terms correspond, respectively, to general relativity and Einstein–Gauss–Bonnet gravity. We obtain five-dimensional (5D) black hole solutions, inspired by a noncommutative geometry, with a static spherically symmetric, Gaussian mass distribution as a source both in the general relativity and Einstein–Gauss–Bonnet gravity cases, and we also analyzes their thermodynamical properties. Owing the noncommutative corrected black hole, the thermodynamic quantities have also been modified, and phase transition is shown to be achievable. The phase transitions for the thermodynamic stability, in both the theories, are characterized by a discontinuity in the specific heat at r_+=rC , with the stable (unstable) branch for r ) rC . The metric of the noncommutative inspired black holes smoothly goes over to the Boulware–Deser solution at large distance. The paper has been appended with a calculation of black hole mass using holographic renormalization.

  16. On Born's deformed reciprocal complex gravitational theory and noncommutative gravity

    International Nuclear Information System (INIS)

    Castro, Carlos

    2008-01-01

    Born's reciprocal relativity in flat spacetimes is based on the principle of a maximal speed limit (speed of light) and a maximal proper force (which is also compatible with a maximal and minimal length duality) and where coordinates and momenta are unified on a single footing. We extend Born's theory to the case of curved spacetimes and construct a deformed Born reciprocal general relativity theory in curved spacetimes (without the need to introduce star products) as a local gauge theory of the deformed Quaplectic group that is given by the semi-direct product of U(1,3) with the deformed (noncommutative) Weyl-Heisenberg group corresponding to noncommutative generators [Z a ,Z b ]≠0. The Hermitian metric is complex-valued with symmetric and nonsymmetric components and there are two different complex-valued Hermitian Ricci tensors R μν ,S μν . The deformed Born's reciprocal gravitational action linear in the Ricci scalars R,S with Torsion-squared terms and BF terms is presented. The plausible interpretation of Z μ =E μ a Z a as noncommuting p-brane background complex spacetime coordinates is discussed in the conclusion, where E μ a is the complex vielbein associated with the Hermitian metric G μν =g (μν) +ig [μν] =E μ a E-bar ν b η ab . This could be one of the underlying reasons why string-theory involves gravity

  17. Topological entropy of continuous actions of compactly generated groups

    OpenAIRE

    Schneider, Friedrich Martin

    2015-01-01

    We introduce a notion of topological entropy for continuous actions of compactly generated topological groups on compact Hausdorff spaces. It is shown that any continuous action of a compactly generated topological group on a compact Hausdorff space with vanishing topological entropy is amenable. Given an arbitrary compactly generated locally compact Hausdorff topological group $G$, we consider the canonical action of $G$ on the closed unit ball of $L^{1}(G)' \\cong L^{\\infty}(G)$ endowed with...

  18. Joint probabilities of noncommuting observables and the Einstein-Podolsky-Rosen question in Wiener-Siegel quantum theory

    International Nuclear Information System (INIS)

    Warnock, R.L.

    1996-02-01

    Ordinary quantum theory is a statistical theory without an underlying probability space. The Wiener-Siegel theory provides a probability space, defined in terms of the usual wave function and its ''stochastic coordinates''; i.e., projections of its components onto differentials of complex Wiener processes. The usual probabilities of quantum theory emerge as measures of subspaces defined by inequalities on stochastic coordinates. Since each point α of the probability space is assigned values (or arbitrarily small intervals) of all observables, the theory gives a pseudo-classical or ''hidden-variable'' view in which normally forbidden concepts are allowed. Joint probabilities for values of noncommuting variables are well-defined. This paper gives a brief description of the theory, including a new generalization to incorporate spin, and reports the first concrete calculation of a joint probability for noncommuting components of spin of a single particle. Bohm's form of the Einstein-Podolsky-Rosen Gedankenexperiment is discussed along the lines of Carlen's paper at this Congress. It would seem that the ''EPR Paradox'' is avoided, since to each α the theory assigns opposite values for spin components of two particles in a singlet state, along any axis. In accordance with Bell's ideas, the price to pay for this attempt at greater theoretical detail is a disagreement with usual quantum predictions. The disagreement is computed and found to be large

  19. Compact, High Energy 2-micron Coherent Doppler Wind Lidar Development for NASA's Future 3-D Winds Measurement from Space

    Science.gov (United States)

    Singh, Upendra N.; Koch, Grady; Yu, Jirong; Petros, Mulugeta; Beyon, Jeffrey; Kavaya, Michael J.; Trieu, Bo; Chen, Songsheng; Bai, Yingxin; Petzar, paul; hide

    2010-01-01

    This paper presents an overview of 2-micron laser transmitter development at NASA Langley Research Center for coherent-detection lidar profiling of winds. The novel high-energy, 2-micron, Ho:Tm:LuLiF laser technology developed at NASA Langley was employed to study laser technology currently envisioned by NASA for future global coherent Doppler lidar winds measurement. The 250 mJ, 10 Hz laser was designed as an integral part of a compact lidar transceiver developed for future aircraft flight. Ground-based wind profiles made with this transceiver will be presented. NASA Langley is currently funded to build complete Doppler lidar systems using this transceiver for the DC-8 aircraft in autonomous operation. Recently, LaRC 2-micron coherent Doppler wind lidar system was selected to contribute to the NASA Science Mission Directorate (SMD) Earth Science Division (ESD) hurricane field experiment in 2010 titled Genesis and Rapid Intensification Processes (GRIP). The Doppler lidar system will measure vertical profiles of horizontal vector winds from the DC-8 aircraft using NASA Langley s existing 2-micron, pulsed, coherent detection, Doppler wind lidar system that is ready for DC-8 integration. The measurements will typically extend from the DC-8 to the earth s surface. They will be highly accurate in both wind magnitude and direction. Displays of the data will be provided in real time on the DC-8. The pulsed Doppler wind lidar of NASA Langley Research Center is much more powerful than past Doppler lidars. The operating range, accuracy, range resolution, and time resolution will be unprecedented. We expect the data to play a key role, combined with the other sensors, in improving understanding and predictive algorithms for hurricane strength and track. 1

  20. Relativistic Equations for Spin Particles: What can We Learn from Noncommutativity?

    International Nuclear Information System (INIS)

    Dvoeglazov, V. V.

    2009-01-01

    We derive relativistic equations for charged and neutral spin particles. The approach for higher-spin particles is based on generalizations of the Bargmann-Wigner formalism. Next, we study, what new physical information can give the introduction of non-commutativity. Additional non-commutative parameters can provide a suitable basis for explanation of the origin of mass.

  1. Dirac-Kahler fermion with noncommutative differential forms on a lattice

    International Nuclear Information System (INIS)

    Kanamori, I.; Kawamoto, N.

    2004-01-01

    Noncommutativity between a differential form and a function allows us to define differential operator satisfying Leibniz's rule on a lattice. We propose a new associative Clifford product defined on the lattice by introducing the noncommutative differential forms. We show that this Clifford product naturally leads to the Dirac-Kaehler fermion on the lattice

  2. On the development of non-commutative translation-invariant quantum gauge field models

    International Nuclear Information System (INIS)

    Sedmik, R.I.P.

    2009-01-01

    Aiming to understand the most fundamental principles of nature one has to approach the highest possible energy scales corresponding to the smallest possible distances - the Planck scale. Historically, three different theoretical fields have been developed to treat the problems appearing in this endeavor: string theory, quantum gravity, and non-commutative (NC) quantum field theory (QFT). The latter was originally motivated by the conjecture that the introduction of uncertainty relations between space-time coordinates introduces a natural energy cutoff, which should render the resulting computations well defined and finite. Despite failing to fulfill this expectation, NC physics is a challenging field of research, which has proved to be a fruitful source for new ideas and methods. Mathematically, non-commutativity is implemented by the so called Weyl quantization, giving rise to a modified product - the Groenewold-Moyal product. It realizes an operator ordering, and allows to work within the well established framework of QFT on non-commutative spaces. The main obstacle of NCQFT is the appearance of singularities being shifted from high to low energies. This effect, being referred to as 'uV/IR mixing', is a direct consequence of the deformation of the product, and inhibits or complicates the direct application of well approved renormalization schemes. In order to remedy this problem, several approaches have been worked out during the past decade which, unfortunately, all have shortcomings such as the breaking of translation invariance or an inappropriate alternation of degrees of freedom. Thence, the resulting theories are either being rendered 'unphysical', or considered a priori to be toy models. Nonetheless, these efforts have helped to analyze the mechanisms leading to uV/IR mixing and finally led to the insight that renormalizability can only be achieved by respecting the inherent connection of long and short distances (scales) of NCQFT in the construction of

  3. Isometric coactions of compact quantum groups on compact ...

    Indian Academy of Sciences (India)

    a compact quantum metric space in the framework of Rieffel, where the ... This problem can be formulated and studied in various settings. ... The spaces we are interested in this paper are metric spaces, both classical and quantum. ... He has given a definition for a quantum symmetry of a classical ...... by the construction of I.

  4. Target-space duality between simple compact Lie groups and Lie algebras under the Hamiltonian formalism. Pt. 1. Remnants of duality at the classic level

    International Nuclear Information System (INIS)

    Alvarez, O.; Liu Chienhao

    1996-01-01

    It has been suggested that a possible classical remnant of the phenomenon of target-space duality (T-duality) would be the equivalence of the classical string Hamiltonian systems. Given a simple compact Lie group G with a bi-invariant metric and a generating function Γ suggested in the physics literature, we follow the above line of thought and work out the canonical transformation Φ generated by Γ together with an Ad-invariant metric and a B-field on the associated Lie algebra g of G so that G and g form a string target-space dual pair at the classical level under the Hamiltonian formalism. In this article, some general features of this Hamiltonian setting are discussed. We study properties of the canonical transformation Φ including a careful analysis of its domain and image. The geometry of the T-dual structure on g is lightly touched. We leave the task of tracing back the Hamiltonian formalism at the quantum level to the sequel of this paper. (orig.). With 4 figs

  5. Open Wilson lines and generalized star product in noncommutative scalar field theories

    International Nuclear Information System (INIS)

    Kiem, Youngjai; Sato, Haru-Tada; Rey, Soo-Jong; Yee, Jung-Tay

    2002-01-01

    Open Wilson line operators and a generalized star product have been studied extensively in noncommutative gauge theories. We show that they also show up in noncommutative scalar field theories as universal structures. We first point out that the dipole picture of noncommutative geometry provides an intuitive argument for the robustness of the open Wilson lines and generalized star products therein. We calculate the one-loop effective action of noncommutative scalar field theory with a cubic self-interaction and show explicitly that the generalized star products arise in the nonplanar part. It is shown that, at the low-energy, large noncommutativity limit, the nonplanar part is expressible solely in terms of the scalar open Wilson line operator and descendants

  6. 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

  7. 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

  8. On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

    Energy Technology Data Exchange (ETDEWEB)

    Amini, Nina H. [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States); CNRS, Laboratoire des Signaux et Systemes (L2S) CentraleSupelec, Gif-sur-Yvette (France); Miao, Zibo; Pan, Yu; James, Matthew R. [Australian National University, ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Canberra, ACT (Australia); Mabuchi, Hideo [Stanford University, Edward L. Ginzton Laboratory, Stanford, CA (United States)

    2015-12-15

    The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice. (orig.)

  9. Reconstruction of the spontaneously broken gauge theory in non-commutative geometry

    International Nuclear Information System (INIS)

    Okumura, Y.; Morita, K.

    1996-01-01

    The scheme previously proposed by the present authors is modified to incorporate the strong interaction by affording the direct product internal symmetry. The authors do not need to prepare the extra discrete space for the colour gauge group responsible for the strong interaction to reconstruct the standard model and the left-right symmetric gauge model (LRSM). The approach based on non-commutative geometry leads us to present many attractive points such as the unified picture of the gauge and Higgs field as the generalized connection on the discrete space M 4 x Z N . This approach leads to unified picture of gauge and Higgs fields as the generalized connection. The standard model needs N=2 discrete space for reconstruction in this formalism. LRSM is still alive as a model with the intermediate symmetry of the spontaneously broken SO(10) grand unified theory (GUT). N=3 discrete space is needed for the reconstruction of LRSM to include two Higgs φ and ξ bosons usual transformed as (2, 2 * , 0) and (1, 3, -2) under SU(2) L x SU(2) R x U(1) Y , respectively. ξ is responsible to make v R Majorana fermion and so well explains the seesaw mechanism. Up and down quarks have different masses through the vacuum expectation value of φ

  10. Some open problems in noncommutative probability

    International Nuclear Information System (INIS)

    Kruszynski, P.

    1981-01-01

    A generalization of probability measures to non-Boolean structures is discussed. The starting point of the theory is the Gleason theorem about the form of measures on closed subspaces of a Hilbert space. The problems are formulated in terms of probability on lattices of projections in arbitrary von Neumann algebras. (Auth.)

  11. Physically detached 'compact groups'

    Science.gov (United States)

    Hernquist, Lars; Katz, Neal; Weinberg, David H.

    1995-01-01

    A small fraction of galaxies appear to reside in dense compact groups, whose inferred crossing times are much shorter than a Hubble time. These short crossing times have led to considerable disagreement among researchers attempting to deduce the dynamical state of these systems. In this paper, we suggest that many of the observed groups are not physically bound but are chance projections of galaxies well separated along the line of sight. Unlike earlier similar proposals, ours does not require that the galaxies in the compact group be members of a more diffuse, but physically bound entity. The probability of physically separated galaxies projecting into an apparent compact group is nonnegligible if most galaxies are distributed in thin filaments. We illustrate this general point with a specific example: a simulation of a cold dark matter universe, in which hydrodynamic effects are included to identify galaxies. The simulated galaxy distribution is filamentary and end-on views of these filaments produce apparent galaxy associations that have sizes and velocity dispersions similar to those of observed compact groups. The frequency of such projections is sufficient, in principle, to explain the observed space density of groups in the Hickson catalog. We discuss the implications of our proposal for the formation and evolution of groups and elliptical galaxies. The proposal can be tested by using redshift-independent distance estimators to measure the line-of-sight spatial extent of nearby compact groups.

  12. On the UV renormalizability of noncommutative field theories

    International Nuclear Information System (INIS)

    Sarkar, Swarnendu

    2002-01-01

    UV/IR mixing is one of the most important features of noncommutative field theories. As a consequence of this coupling of the UV and IR sectors, the configuration of fields at the zero momentum limit in these theories is a very singular configuration. We show that the renormalization conditions set at a particular momentum configuration with a fixed number of zero momenta, renormalizes the Green's functions for any general momenta only when this configuration has same set of zero momenta. Therefore only when renormalization conditions are set at a point where all the external momenta are nonzero, the quantum theory is renormalizable for all values of nonzero momentum. This arises as a result of different scaling behaviors of Green's functions with respect to the UV cutoff (Λ) for configurations containing different set of zero momenta. We study this in the noncommutative φ 4 theory and analyse similar results for the Gross-Neveu model at one loop level. We next show this general feature using Wilsonian RG of Polchinski in the globally O(N) symmetric scalar theory and prove the renormalizability of the theory to all orders with an infrared cutoff. In the context of spontaneous symmetry breaking (SSB) in noncommutative scalar theory, it is essential to note the different scaling behaviors of Green's functions with respect to Λ for different set of zero momenta configurations. We show that in the broken phase of the theory the Ward identities are satisfied to all orders only when one keeps an infrared regulator by shifting to a nonconstant vacuum. (author)

  13. Noncommutativity and Duality through the Symplectic Embedding Formalism

    Directory of Open Access Journals (Sweden)

    Everton M.C. Abreu

    2010-07-01

    Full Text Available This work is devoted to review the gauge embedding of either commutative and noncommutative (NC theories using the symplectic formalism framework. To sum up the main features of the method, during the process of embedding, the infinitesimal gauge generators of the gauge embedded theory are easily and directly chosen. Among other advantages, this enables a greater control over the final Lagrangian and brings some light on the so-called ''arbitrariness problem''. This alternative embedding formalism also presents a way to obtain a set of dynamically dual equivalent embedded Lagrangian densities which is obtained after a finite number of steps in the iterative symplectic process, oppositely to the result proposed using the BFFT formalism. On the other hand, we will see precisely that the symplectic embedding formalism can be seen as an alternative and an efficient procedure to the standard introduction of the Moyal product in order to produce in a natural way a NC theory. In order to construct a pedagogical explanation of the method to the nonspecialist we exemplify the formalism showing that the massive NC U(1 theory is embedded in a gauge theory using this alternative systematic path based on the symplectic framework. Further, as other applications of the method, we describe exactly how to obtain a Lagrangian description for the NC version of some systems reproducing well known theories. Naming some of them, we use the procedure in the Proca model, the irrotational fluid model and the noncommutative self-dual model in order to obtain dual equivalent actions for these theories. To illustrate the process of noncommutativity introduction we use the chiral oscillator and the nondegenerate mechanics.

  14. Non-Commutative Orders. A Preliminary Study

    International Nuclear Information System (INIS)

    Brzezinski, T.

    2011-01-01

    The first steps towards linearization of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that makes the linearization (almost) automatic. The linearization is then achieved by replacing sets by coalgebras and the Cartesian product by the tensor product of vector spaces. As a result, definitions of orders and equivalence relations on coalgebras are proposed. These are illustrated by explicit examples that include relations on coalgebras spanned by grouplike elements (or linearized sets), the diagonal relation, and an order on a three-dimensional non-cocommutative coalgebra. Although relations on coalgebras are defined for vector spaces, all the definitions are formulated in a way that is immediately applicable to other braided monoidal categories. (author)

  15. Symmetries of noncommutative scalar field theory

    International Nuclear Information System (INIS)

    De Goursac, Axel; Wallet, Jean-Christophe

    2011-01-01

    We investigate symmetries of the scalar field theory with a harmonic term on the Moyal space with the Euclidean scalar product and general symplectic form. The classical action is invariant under the orthogonal group if this group acts also on the symplectic structure. We find that the invariance under the orthogonal group can also be restored at the quantum level by restricting the symplectic structures to a particular orbit.

  16. Noncommutative spectral geometry, Bogoliubov transformations and neutrino oscillations

    International Nuclear Information System (INIS)

    Gargiulo, Maria Vittoria; Vitiello, Giuseppe; Sakellariadou, Mairi

    2015-01-01

    In this report we show that neutrino mixing is intrinsically contained in Connes’ noncommutatives pectral geometry construction, thanks to the introduction of the doubling of algebra, which is connected to the Bogoliubov transformation. It is known indeed that these transformations are responsible for the mixing, turning the mass vacuum state into the flavor vacuum state, in such a way that mass and flavor vacuum states are not unitary equivalent. There is thus a red thread that binds the doubling of algebra of Connes’ model to the neutrino mixing. (paper)

  17. Non-commutative geometry inspired charged black holes

    International Nuclear Information System (INIS)

    Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro

    2007-01-01

    We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario

  18. Samples of noncommutative products in certain differential equations

    International Nuclear Information System (INIS)

    Legare, M

    2010-01-01

    A set of associative noncommutative products is considered in different differential equations of the ordinary and partial types. A method of separation of variables is considered for a large set of those systems. The products involved include for example some * products and some products based on Nijenhuis tensors, which are embedded in the differential equations of the Laplace/Poisson, Lax and Schroedinger styles. A comment on the *-products of Reshetikhin-Jambor-Sykora type is also given in relation to *-products of Vey type.

  19. An associative and noncommutative product for the low energy effective theory of a D-brane in curved backgrounds and bi-local fields

    International Nuclear Information System (INIS)

    Hayasaka, Kiyoshi; Nakayama, Ryuichi

    2002-01-01

    We point out that when a D-brane is placed in an NS-NS B field background with nonvanishing field strength (H=dB) along the D-brane worldvolume, the coordinate of one end of the open string does not commute with that of the other in the low energy limit. The degrees of the freedom associated with both ends are not decoupled and accordingly, the effective action must be quite different from that of the ordinary noncommutative gauge theory for a constant B background. We construct an associative and noncommutative product * which operates on the coordinates of both ends of the string and propose a new type of noncommutative gauge action for the low energy effective theory of a Dp-brane. This effective theory is bi-local and lives in twice as large dimensions (2D=2(p+1)) as in the H=0 case. When viewed as a theory in the D-dimensional space, this theory is nonlocal and we must force the two ends of the string to coincide. We will then propose a prescription for reducing this bi-local effective action to that in D dimensions and obtaining a local effective action

  20. Noncommutative geometry and the standard model vacuum

    International Nuclear Information System (INIS)

    Barrett, John W.; Dawe Martins, Rachel A.

    2006-01-01

    The space of Dirac operators for the Connes-Chamseddine spectral action for the standard model of particle physics coupled to gravity is studied. The model is extended by including right-handed neutrino states, and the S 0 -reality axiom is not assumed. The possibility of allowing more general fluctuations than the inner fluctuations of the vacuum is proposed. The maximal case of all possible fluctuations is studied by considering the equations of motion for the vacuum. While there are interesting nontrivial vacua with Majorana-type mass terms for the leptons, the conclusion is that the equations are too restrictive to allow solutions with the standard model mass matrix

  1. A non-commutative formula for the isotropic magneto-electric response

    International Nuclear Information System (INIS)

    Leung, Bryan; Prodan, Emil

    2013-01-01

    A non-commutative formula for the isotropic magneto-electric response of disordered insulators under magnetic fields is derived using the methods of non-commutative geometry. Our result follows from an explicit evaluation of the Ito derivative with respect to the magnetic field of the non-commutative formula for the electric polarization reported in Schulz-Baldes and Teufel (2012 arXiv:1201.4812v1). The quantization, topological invariance and connection to a second Chern number of the magneto-electric response are discussed in the context of three-dimensional, disordered, time-reversal or inversion symmetric topological insulators. (paper)

  2. Non-commutative gauge Gravity: Second- order Correction and Scalar Particles Creation

    International Nuclear Information System (INIS)

    Zaim, S.

    2009-01-01

    A noncommutative gauge theory for a charged scalar field is constructed. The invariance of this model under local Poincare and general coordinate transformations is verified. Using the general modified field equation, a general Klein-Gordon equation up to the second order of the noncommu- tativity parameter is derived. As an application, we choose the Bianchi I universe. Using the Seiberg-Witten maps, the deformed noncommutative metric is obtained and a particle production process is studied. It is shown that the noncommutativity plays the same role as an electric field, gravity and chemical potential.

  3. Noncommutative Gröbner bases and filtered-graded transfer

    CERN Document Server

    Li, Huishi

    2002-01-01

    This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.

  4. Non-commutative multiple-valued logic algebras

    CERN Document Server

    Ciungu, Lavinia Corina

    2014-01-01

    This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects.   A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing.   Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

  5. Moyal noncommutative integrability and the Burgers-KdV mapping

    International Nuclear Information System (INIS)

    Sedra, M.B.

    2005-12-01

    The Moyal momentum algebra, is once again used to discuss some important aspects of NC integrable models and 2d conformal field theories. Among the results presented, we set up algebraic structures and makes useful convention notations leading to extract non trivial properties of the Moyal momentum algebra. We study also the Lax pair building mechanism for particular examples namely, the noncommutative KdV and Burgers systems. We show in a crucial step that these two systems are mapped to each other through the following crucial mapping ∂ t 2 → ∂ t 3 ≡ ∂ t 2 ∂ x + α∂ x 3 . This makes a strong constraint on the NC Burgers system which corresponds to linearizing its associated differential equation. From the CFT's point of view, this constraint equation is nothing but the analogue of the conservation law of the conformal current. We believe that the considered mapping might help to bring new insights towards understanding the integrability of noncommutative 2d-systems. (author)

  6. Bootstrapping non-commutative gauge theories from L∞ algebras

    Science.gov (United States)

    Blumenhagen, Ralph; Brunner, Ilka; Kupriyanov, Vladislav; Lüst, Dieter

    2018-05-01

    Non-commutative gauge theories with a non-constant NC-parameter are investigated. As a novel approach, we propose that such theories should admit an underlying L∞ algebra, that governs not only the action of the symmetries but also the dynamics of the theory. Our approach is well motivated from string theory. We recall that such field theories arise in the context of branes in WZW models and briefly comment on its appearance for integrable deformations of AdS5 sigma models. For the SU(2) WZW model, we show that the earlier proposed matrix valued gauge theory on the fuzzy 2-sphere can be bootstrapped via an L∞ algebra. We then apply this approach to the construction of non-commutative Chern-Simons and Yang-Mills theories on flat and curved backgrounds with non-constant NC-structure. More concretely, up to the second order, we demonstrate how derivative and curvature corrections to the equations of motion can be bootstrapped in an algebraic way from the L∞ algebra. The appearance of a non-trivial A∞ algebra is discussed, as well.

  7. Anosov actions on non-commutative algebras

    International Nuclear Information System (INIS)

    Emch, G.G.; Narnhofer, H.; Thirring, W.; Sewell, G.L.

    1994-01-01

    We construct an axiomatic framework for a quantum mechanical extension to the theory of Anosov systems, and show that this retains some of the characteristic features of its classical counterpart, e.g. positive Lyapunov exponents, a vectorial K-property, and exponential clustering. We then investigate the effects of quantisation on two prototype examples of Anosov systems, namely the iterations of an automorphism of the torus (the 'Arnold Cat' model) and the free dynamics of a particle on a surface of negative curvature. It emerges that the Anosov property survives quantisation in the case of the former model, but not of the latter one. Finally, we show that the modular dynamics of a relativistic quantum field on the Rindler wedge of Minkowski space is that of an Anosov system. (authors)

  8. Compact NMR

    Energy Technology Data Exchange (ETDEWEB)

    Bluemich, Bernhard; Haber-Pohlmeier, Sabina; Zia, Wasif [RWTH Aachen Univ. (Germany). Inst. fuer Technische und Makromolekulare Chemie (ITMC)

    2014-06-01

    Nuclear Magnetic Resonance (NMR) spectroscopy is the most popular method for chemists to analyze molecular structures, while Magnetic Resonance Imaging (MRI) is a non-invasive diagnostic tool for medical doctors that provides high-contrast images of biological tissue. In both applications, the sample (or patient) is positioned inside a large, superconducting magnet to magnetize the atomic nuclei. Interrogating radio-frequency pulses result in frequency spectra that provide the chemist with molecular information, the medical doctor with anatomic images, and materials scientist with NMR relaxation parameters. Recent advances in magnet technology have led to a variety of small permanent magnets to allow compact and low-cost instruments. The goal of this book is to provide an introduction to the practical use of compact NMR at a level nearly as basic as the operation of a smart phone.

  9. Compact vortices

    Energy Technology Data Exchange (ETDEWEB)

    Bazeia, D.; Losano, L.; Marques, M.A.; Zafalan, I. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)

    2017-02-15

    We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane. (orig.)

  10. Compact stars

    Science.gov (United States)

    Estevez-Delgado, Gabino; Estevez-Delgado, Joaquin

    2018-05-01

    An analysis and construction is presented for a stellar model characterized by two parameters (w, n) associated with the compactness ratio and anisotropy, respectively. The reliability range for the parameter w ≤ 1.97981225149 corresponds with a compactness ratio u ≤ 0.2644959374, the density and pressures are positive, regular and monotonic decrescent functions, the radial and tangential speed of sound are lower than the light speed, moreover, than the plausible stability. The behavior of the speeds of sound are determinate for the anisotropy parameter n, admitting a subinterval where the speeds are monotonic crescent functions and other where we have monotonic decrescent functions for the same speeds, both cases describing a compact object that is also potentially stable. In the bigger value for the observational mass M = 2.05 M⊙ and radii R = 12.957 Km for the star PSR J0348+0432, the model indicates that the maximum central density ρc = 1.283820319 × 1018 Kg/m3 corresponds to the maximum value of the anisotropy parameter and the radial and tangential speed of the sound are monotonic decrescent functions.

  11. Possibility of higher-dimensional anisotropic compact star

    International Nuclear Information System (INIS)

    Bhar, Piyali; Rahaman, Farook; Ray, Saibal; Chatterjee, Vikram

    2015-01-01

    We provide a new class of interior solutions for anisotropic stars admitting conformal motion in higher-dimensional noncommutative spacetime. The Einstein field equations are solved by choosing a particular density distribution function of Lorentzian type as provided by Nazari and Mehdipour [1, 2] under a noncommutative geometry. Several cases with 4 and higher dimensions, e.g. 5, 6, and 11 dimensions, are discussed separately. An overall observation is that the model parameters, such as density, radial pressure, transverse pressure, and anisotropy, all are well behaved and represent a compact star with mass 2.27 M s un and radius 4.17 km. However, emphasis is put on the acceptability of the model from a physical point of view. As a consequence it is observed that higher dimensions, i.e. beyond 4D spacetime, exhibit several interesting yet bizarre features, which are not at all untenable for a compact stellar model of strange quark type; thus this dictates the possibility of its extra-dimensional existence. (orig.)

  12. Possibility of higher-dimensional anisotropic compact star

    Energy Technology Data Exchange (ETDEWEB)

    Bhar, Piyali; Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India); Chatterjee, Vikram [Central Footwear Training Centre, Department of Physics, Parganas, West Bengal (India)

    2015-05-15

    We provide a new class of interior solutions for anisotropic stars admitting conformal motion in higher-dimensional noncommutative spacetime. The Einstein field equations are solved by choosing a particular density distribution function of Lorentzian type as provided by Nazari and Mehdipour [1, 2] under a noncommutative geometry. Several cases with 4 and higher dimensions, e.g. 5, 6, and 11 dimensions, are discussed separately. An overall observation is that the model parameters, such as density, radial pressure, transverse pressure, and anisotropy, all are well behaved and represent a compact star with mass 2.27 M{sub s}un and radius 4.17 km. However, emphasis is put on the acceptability of the model from a physical point of view. As a consequence it is observed that higher dimensions, i.e. beyond 4D spacetime, exhibit several interesting yet bizarre features, which are not at all untenable for a compact stellar model of strange quark type; thus this dictates the possibility of its extra-dimensional existence. (orig.)

  13. On compact multipliers of topological algebras

    International Nuclear Information System (INIS)

    Mohammad, N.

    1994-08-01

    It is shown that if the maximal ideal space Δ(A) of a semisimple commutative complete metrizable locally convex algebra contains no isolated points, then every compact multiplier is trivial. Particularly, compact multipliers on semisimple commutative Frechet algebras whose maximal ideal space has no isolated points are identically zero. (author). 5 refs

  14. Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity

    International Nuclear Information System (INIS)

    Martinetti, Pierre

    2015-01-01

    Noncommutative geometry in its many incarnations appears at the crossroad of many researches in theoretical and mathematical physics: from models of quantum spacetime(with or without breaking of Lorentz symmetry) to loop gravity and string theory, from early considerations on UV-divergenciesin quantum field theory to recent models of gauge theories on noncommutatives pacetime, from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. We list several of these applications, emphasizing also the original point of view brought by noncommutative geometry on the nature of time. This text serves as an introduction to the volume of proceedings of the parallel session “Noncommutative geometry and quantum gravity”, as a part of the conference “Conceptual and technical challenges in quantum gravity” organized at the University of Rome La Sapienza sin September 2014. (paper)

  15. Noncommutative o*(N) and usp*(2N) algebras and the corresponding gauge field theories

    International Nuclear Information System (INIS)

    Bars, I.; Sheikh-Jabbari, M.M.; Vasiliev, M.A.

    2001-03-01

    The extension of the noncommutative u * (N) Lie algebra to noncommutative orthogonal and symplectic Lie algebras is studied. Using an anti-automorphism of the star-matrix algebra, we show that the u * (N) can consistently be restricted to o * (N) and usp * (N) algebras that have new mathematical structures. We give explicit fundamental matrix representations of these algebras, through which the formulation for the corresponding noncommutative gauge field theories are obtained. In addition, we present a D-brane configuration with an orientifold which realizes geometrically our algebraic construction, thus embedding the new noncommutative gauge theories in superstring theory in the presence of a constant background magnetic field. Some algebraic generalizations that may have applications in other areas of physics are also discussed. (author)

  16. Metamaterials mimicking dynamic spacetime, D-brane and noncommutativity in string theory

    International Nuclear Information System (INIS)

    Miao Rongxin; Zheng Rui; Li Miao

    2011-01-01

    We propose a scheme to mimic the expanding cosmos in 1+2 dimensions in laboratory. Furthermore, we develop a general procedure to use nonlinear metamaterials to mimic D-brane and noncommutativity in string theory.

  17. Hubble Space Telescope Imaging of the Ultra-compact High Velocity Cloud AGC 226067: A Stripped Remnant in the Virgo Cluster

    Energy Technology Data Exchange (ETDEWEB)

    Sand, D. J.; Crnojević, D. [Texas Tech University, Physics and Astronomy Department, Box 41051, Lubbock, TX 79409-1051 (United States); Seth, A. C. [Department of Physics and Astronomy, University of Utah, Salt Lake City, UT 84112 (United States); Spekkens, K. [Royal Military College of Canada, Department of Physics, P.O. Box 17000, Station Forces, Kingston, Ontario, K7K 7B4 (Canada); Strader, J. [Center for Data Intensive and Time Domain Astronomy, Department of Physics and Astronomy, Michigan State University, 567 Wilson Road, East Lansing, MI 48824 (United States); Adams, E. A. K. [ASTRON, Netherlands Institute for Radio Astronomy, Postbus 2, 7900 AA Dwingeloo (Netherlands); Caldwell, N.; Randall, S. [Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138 (United States); Guhathakurta, P. [UCO/Lick Observatory, University of California, Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 (United States); Kenney, J. [Yale University Astronomy Department, P.O. Box 208101, New Haven, CT 06520-8101 (United States); Simon, J. D. [Observatories of the Carnegie Institution for Science, 813 Santa Barbara Street, Pasadena, CA 91101 (United States); Toloba, E. [Department of Physics, University of the Pacific, 3601 Pacific Avenue, Stockton, CA 95211 (United States); Willman, B., E-mail: david.sand@ttu.edu [Steward Observatory, University of Arizona, 933 North Cherry Avenue, Tucson, AZ 85721 (United States)

    2017-07-10

    We analyze the optical counterpart to the ultra-compact high velocity cloud AGC 226067, utilizing imaging taken with the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope . The color–magnitude diagram of the main body of AGC 226067 reveals an exclusively young stellar population, with an age of ∼7–50 Myr, and is consistent with a metallicity of [Fe/H] ∼ −0.3 as previous work has measured via H ii region spectroscopy. Additionally, the color–magnitude diagram is consistent with a distance of D ≈ 17 Mpc, suggesting an association with the Virgo cluster. A secondary stellar system located ∼1.′6 (∼8 kpc) away in projection has a similar stellar population. The lack of an old red giant branch (≳5 Gyr) is contrasted with a serendipitously discovered Virgo dwarf in the ACS field of view (Dw J122147+132853), and the total diffuse light from AGC 226067 is consistent with the luminosity function of the resolved ∼7–50 Myr stellar population. The main body of AGC 226067 has a M {sub V} = −11.3 ± 0.3, or M {sub stars} = 5.4 ± 1.3 × 10{sup 4} M {sub ⊙} given the stellar population. We searched 20 deg{sup 2} of imaging data adjacent to AGC 226067 in the Virgo Cluster, and found two similar stellar systems dominated by a blue stellar population, far from any massive galaxy counterpart—if this population has star-formation properties that are similar to those of AGC 226067, it implies ∼0.1 M {sub ⊙} yr{sup −1} in Virgo intracluster star formation. Given its unusual stellar population, AGC 226067 is likely a stripped remnant and is plausibly the result of compressed gas from the ram pressure stripped M86 subgroup (∼350 kpc away in projection) as it falls into the Virgo Cluster.

  18. κ-Rindler space

    International Nuclear Information System (INIS)

    Kowalski-Glikman, J.

    2009-01-01

    In this paper we construct, and investigate some thermal properties of, the noncommutative counterpart of Rindler space, which we call κ-Rindler space. This space is obtained by changing variables in the defining commutators of κ-Minkowski space. We then rederive the commutator structure of κ-Rindler space with the help of an appropriate star product, obtained from the κ-Minkowski one. Using this star product, following the idea of Padmanabhan, we find the leading order, 1/κ correction to the Hawking thermal spectrum.

  19. UV/IR mixing and the Goldstone theorem in noncommutative field theory

    International Nuclear Information System (INIS)

    Ruiz Ruiz, F.

    2002-01-01

    Noncommutative IR singularities and UV/IR mixing in relation with the Goldstone theorem for complex scalar field theory are investigated. The classical model has two coupling constants, λ 1 and λ 2 , associated to the two noncommutative extensions phi*starphistarphi* starphi and phistarphi*starphistarphi of the interaction term vertical bar phi vertical bar 4 on commutative spacetime. It is shown that the symmetric phase is one-loop renormalizable for all λ 1 and λ 2 compatible with perturbation theory, whereas the broken phase is proved to exist at one loop only if λ 2 =0, a condition required by the Ward identities for global U(1) invariance. Explicit expressions for the noncommutative IR singularities in the 1PI Green functions of both phases are given. They show that UV/IR duality does not hold for any of the phases and that the broken phase is free of quadratic noncommutative IR singularities. More remarkably, the pion selfenergy does not have noncommutative IR singularities at all, which proves essential to formulate the Goldstone theorem at one loop for all values of the spacetime noncommutativity parameter θ

  20. Unusual high-energy phenomenology of Lorentz-invariant noncommutative field theories

    International Nuclear Information System (INIS)

    Carone, Christopher D.; Kwee, Herry J.

    2006-01-01

    It has been suggested that one may construct a Lorentz-invariant noncommutative field theory by extending the coordinate algebra to additional, fictitious coordinates that transform nontrivially under the Lorentz group. Integration over these coordinates in the action produces a four-dimensional effective theory with Lorentz invariance intact. Previous applications of this approach, in particular, to a specific construction of noncommutative QED, have been studied only in a low-momentum approximation. Here we discuss Lorentz-invariant field theories in which the relevant physics can be studied without requiring an expansion in the inverse scale of noncommutativity. Qualitatively, we find that tree-level scattering cross sections are dramatically suppressed as the center-of-mass energy exceeds the scale of noncommutativity, that cross sections that are isotropic in the commutative limit can develop a pronounced angular dependence, and that nonrelativistic potentials (for example, the Coloumb potential) become nonsingular at the origin. We consider a number of processes in noncommutative QED that may be studied at a future linear collider. We also give an example of scattering via a four-fermion operator in which the noncommutative modifications of the interaction can unitarize the tree-level amplitude, without requiring any other new physics in the ultraviolet