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.
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.
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)
Wigner Functions for the Bateman System on Noncommutative Phase Space
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.
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
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)
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.)
Relativistic Hydrogen-Like Atom on a Noncommutative Phase Space
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.
Group theoretical construction of planar noncommutative phase spaces
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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.
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
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.
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)
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
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
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.
Noncommutative products of Euclidean spaces
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.
Mapping spaces and automorphism groups of toric noncommutative spaces
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.
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
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
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.
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
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.)
Noncommutative spaces and Poincaré symmetry
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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.
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)
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
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.
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.
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)
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.
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.)
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.)
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
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.
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.
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
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space
Energy Technology Data Exchange (ETDEWEB)
Zahn, J.W.
2006-12-15
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the {phi}{sup 3} and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
Dispersion relations in quantum electrodynamics on the noncommutative Minkowski space
International Nuclear Information System (INIS)
Zahn, J.W.
2006-12-01
We study field theories on the noncommutative Minkowski space with noncommuting time. The focus lies on dispersion relations in quantized interacting models in the Yang-Feldman formalism. In particular, we compute the two-point correlation function of the field strength in noncommutative quantum electrodynamics to second order. At this, we take into account the covariant coordinates that allow the construction of local gauge invariant quantities (observables). It turns out that this does not remove the well-known severe infrared problem, as one might have hoped. Instead, things become worse, since nonlocal divergences appear. We also show that these cancel in a supersymmetric version of the theory if the covariant coordinates are adjusted accordingly. Furthermore, we study the Φ 3 and the Wess-Zumino model and show that the distortion of the dispersion relations is moderate for parameters typical for the Higgs field. We also discuss the formulation of gauge theories on noncommutative spaces and study classical electrodynamics on the noncommutative Minkowski space using covariant coordinates. In particular, we compute the change of the speed of light due to nonlinear effects in the presence of a background field. Finally, we examine the so-called twist approach to quantum field theory on the noncommutative Minkowski space and point out some conceptual problems of this approach. (orig.)
The Event Horizon of The Schwarzschild Black Hole in Noncommutative Spaces
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.
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...
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)
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.)
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.)
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
Conformal quantum mechanics and holography in noncommutative space-time
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.
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.)
Stringy Fuzziness as the Custodial of Time-Space Noncommutativity
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.
Stringy fuzziness as the custodian of time-space noncommutativity
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).
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.
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.)
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)
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.)
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.
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.
Strong limit theorems in noncommutative L2-spaces
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.
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)
Realization of Cohen-Glashow very special relativity on noncommutative space-time.
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.
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.)
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
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.
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)
Winter School on Operator Spaces, Noncommutative Probability and Quantum Groups
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...
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.)
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.
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
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.
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)
Quantum information aspects of noncommutative quantum mechanics
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.
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.
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.
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
Realization of bicovariant differential calculus on the Lie algebra type noncommutative spaces
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.
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.
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.)
Noncommutative configuration space. Classical and quantum mechanical aspects
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...
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)
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...
Geometry of time-spaces non-commutative algebraic geometry, applied to quantum theory
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
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.
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.
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.
On Yang's Noncommutative Space Time Algebra, Holography, Area Quantization and C-space Relativity
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 ...
Coproduct and star product in field theories on Lie-algebra noncommutative space-times
International Nuclear Information System (INIS)
Amelino-Camelia, Giovanni; Arzano, Michele
2002-01-01
We propose a new approach to field theory on κ-Minkowski noncommutative space-time, a popular example of Lie-algebra space-time. Our proposal is essentially based on the introduction of a star product, a technique which is proving to be very fruitful in analogous studies of canonical noncommutative space-times, such as the ones recently found to play a role in the description of certain string-theory backgrounds. We find to be incorrect the expectation, previously reported in the literature, that the lack of symmetry of the κ-Poincare coproduct should lead to interaction vertices that are not symmetric under exchanges of the momenta of identical particles entering the relevant processes. We show that in κ-Minkowski the coproduct and the star product must indeed treat momenta in a nonsymmetric way, but the overall structure of interaction vertices is symmetric under exchange of identical particles. We also show that in κ-Minkowski field theories it is convenient to introduce the concepts of 'planar' and 'nonplanar' Feynman loop diagrams, again in close analogy with the corresponding concepts previously introduced in the study of field theories in canonical noncommutative space-times
Quantum gravity boundary terms from the spectral action of noncommutative space.
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.
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.
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.
Synthesizing lattice structures in phase space
International Nuclear Information System (INIS)
Guo, Lingzhen; Marthaler, Michael
2016-01-01
In one dimensional systems, it is possible to create periodic structures in phase space through driving, which is called phase space crystals (Guo et al 2013 Phys. Rev. Lett. 111 205303). This is possible even if for particles trapped in a potential without periodicity. In this paper we discuss ultracold atoms in a driven optical lattice, which is a realization of such a phase space crystals. The corresponding lattice structure in phase space is complex and contains rich physics. A phase space lattice differs fundamentally from a lattice in real space, because its coordinate system, i.e., phase space, has a noncommutative geometry, which naturally provides an artificial gauge (magnetic) field. We study the behavior of the quasienergy band structure and investigate the dissipative dynamics. Synthesizing lattice structures in phase space provides a new platform to simulate the condensed matter phenomena and study the intriguing phenomena of driven systems far away from equilibrium. (paper)
Notes on qubit phase space and discrete symplectic structures
International Nuclear Information System (INIS)
Livine, Etera R
2010-01-01
We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.
Noncommutative solitons: moduli spaces, quantization, finite θ effects and stability
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.
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.
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.
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)
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.
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.)
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.)
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.
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.
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)
The moduli space of two U(1) instantons on noncommutative $R^4$ and $R^3\\times S^1$
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...
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
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)
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)
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.
Non-commutative representation for quantum systems on Lie groups
Energy Technology Data Exchange (ETDEWEB)
Raasakka, Matti Tapio
2014-01-27
The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a {sup *}-algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R{sup d}, U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase
Non-commutative representation for quantum systems on Lie groups
International Nuclear Information System (INIS)
Raasakka, Matti Tapio
2014-01-01
The topic of this thesis is a new representation for quantum systems on weakly exponential Lie groups in terms of a non-commutative algebra of functions, the associated non-commutative harmonic analysis, and some of its applications to specific physical systems. In the first part of the thesis, after a review of the necessary mathematical background, we introduce a * -algebra that is interpreted as the quantization of the canonical Poisson structure of the cotangent bundle over a Lie group. From the physics point of view, this represents the algebra of quantum observables of a physical system, whose configuration space is a Lie group. We then show that this quantum algebra can be represented either as operators acting on functions on the group, the usual group representation, or (under suitable conditions) as elements of a completion of the universal enveloping algebra of the Lie group, the algebra representation. We further apply the methods of deformation quantization to obtain a representation of the same algebra in terms of a non-commutative algebra of functions on a Euclidean space, which we call the non-commutative representation of the original quantum algebra. The non-commutative space that arises from the construction may be interpreted as the quantum momentum space of the physical system. We derive the transform between the group representation and the non-commutative representation that generalizes in a natural way the usual Fourier transform, and discuss key properties of this new non-commutative harmonic analysis. Finally, we exhibit the explicit forms of the non-commutative Fourier transform for three elementary Lie groups: R d , U(1) and SU(2). In the second part of the thesis, we consider application of the non-commutative representation and harmonic analysis to physics. First, we apply the formalism to quantum mechanics of a point particle on a Lie group. We define the dual non-commutative momentum representation, and derive the phase space path
Arithmetic noncommutative geometry
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...
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
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)
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)
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
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.
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.
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
Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries
Energy Technology Data Exchange (ETDEWEB)
Meljanac, Daniel [Ruder Boskovic Institute, Division of Materials Physics, Zagreb (Croatia); Meljanac, Stjepan; Pikutic, Danijel [Ruder Boskovic Institute, Division of Theoretical Physics, Zagreb (Croatia)
2017-12-15
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincare-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. (orig.)
Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries
International Nuclear Information System (INIS)
Meljanac, Daniel; Meljanac, Stjepan; Pikutic, Danijel
2017-01-01
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincare-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ-Minkowski spaces and (iii) κ-Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed. (orig.)
Families of vector-like deformations of relativistic quantum phase spaces, twists and symmetries
Meljanac, Daniel; Meljanac, Stjepan; Pikutić, Danijel
2017-12-01
Families of vector-like deformed relativistic quantum phase spaces and corresponding realizations are analyzed. A method for a general construction of the star product is presented. The corresponding twist, expressed in terms of phase space coordinates, in the Hopf algebroid sense is presented. General linear realizations are considered and corresponding twists, in terms of momenta and Poincaré-Weyl generators or gl(n) generators are constructed and R-matrix is discussed. A classification of linear realizations leading to vector-like deformed phase spaces is given. There are three types of spaces: (i) commutative spaces, (ii) κ -Minkowski spaces and (iii) κ -Snyder spaces. The corresponding star products are (i) associative and commutative (but non-local), (ii) associative and non-commutative and (iii) non-associative and non-commutative, respectively. Twisted symmetry algebras are considered. Transposed twists and left-right dual algebras are presented. Finally, some physical applications are discussed.
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.
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
Energy Technology Data Exchange (ETDEWEB)
Chao, Alexander Wu; /SLAC
2012-03-01
As accelerator technology advances, the requirements on accelerator beam quality become increasingly demanding. Facing these new demands, the topic of phase space gymnastics is becoming a new focus of accelerator physics R&D. In a phase space gymnastics, the beam's phase space distribution is manipulated and precision tailored to meet the required beam qualities. On the other hand, all realization of such gymnastics will have to obey accelerator physics principles as well as technological limitations. Recent examples of phase space gymnastics include Emittance exchanges, Phase space exchanges, Emittance partitioning, Seeded FELs and Microbunched beams. The emittance related topics of this list are reviewed in this report. The accelerator physics basis, the optics design principles that provide these phase space manipulations, and the possible applications of these gymnastics, are discussed. This fascinating new field promises to be a powerful tool of the future.
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)].
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)
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)
Bianchi type I cyclic cosmology from Lie-algebraically deformed phase space
International Nuclear Information System (INIS)
Vakili, Babak; Khosravi, Nima
2010-01-01
We study the effects of noncommutativity, in the form of a Lie-algebraically deformed Poisson commutation relations, on the evolution of a Bianchi type I cosmological model with a positive cosmological constant. The phase space variables turn out to correspond to the scale factors of this model in x, y, and z directions. According to the conditions that the structure constants (deformation parameters) should satisfy, we argue that there are two types of noncommutative phase space with Lie-algebraic structure. The exact classical solutions in commutative and type I noncommutative cases are presented. In the framework of this type of deformed phase space, we investigate the possibility of building a Bianchi I model with cyclic scale factors in which the size of the Universe in each direction experiences an endless sequence of contractions and reexpansions. We also obtain some approximate solutions for the type II noncommutative structure by numerical methods and show that the cyclic behavior is repeated as well. These results are compared with the standard commutative case, and similarities and differences of these solutions are discussed.
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.
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.
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.
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
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
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
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.
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
Noncommutative Geometry, Quantum Fields and Motives
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
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
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)
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.
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)
Quantum effects of Aharonov-Bohm type and noncommutative quantum mechanics
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.
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
Quantum magnification of classical sub-Planck phase space features
International Nuclear Information System (INIS)
Hensinger, W.K.; Heckenberg, N.; Rubinsztein-Dunlop, H.; Delande, D.
2002-01-01
Full text: To understand the relationship between quantum mechanics and classical physics a crucial question to be answered is how distinct classical dynamical phase space features translate into the quantum picture. This problem becomes even more interesting if these phase space features occupy a much smaller volume than ℎ in a phase space spanned by two non-commuting variables such as position and momentum. The question whether phase space structures in quantum mechanics associated with sub-Planck scales have physical signatures has recently evoked a lot of discussion. Here we will show that sub-Planck classical dynamical phase space structures, for example regions of regular motion, can give rise to states whose phase space representation is of size ℎ or larger. This is illustrated using period-1 regions of regular motion (modes of oscillatory motion of a particle in a modulated well) whose volume is distinctly smaller than Planck's constant. They are magnified in the quantum picture and appear as states whose phase space representation is of size h or larger. Cold atoms provide an ideal test bed to probe such fundamental aspects of quantum and classical dynamics. In the experiment a Bose-Einstein condensate is loaded into a far detuned optical lattice. The lattice depth is modulated resulting in the emergence of regions of regular motion surrounded by chaotic motion in the phase space spanned by position and momentum of the atoms along the standing wave. Sub-Planck scaled phase space features in the classical phase space are magnified and appear as distinct broad peaks in the atomic momentum distribution. The corresponding quantum analysis shows states of size Ti which can be associated with much smaller classical dynamical phase space features. This effect may considered as the dynamical equivalent of the Goldstone and Jaffe theorem which predicts the existence of at least one bound state at a bend in a two or three dimensional spatial potential
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.
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
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
Foundations of free noncommutative function theory
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.
International Nuclear Information System (INIS)
Malykin, Grigorii B
2010-01-01
In 1909, Arnold Sommerfeld used geometric calculations to show that the relativistic addition of two noncollinear velocities on an imaginary-radius sphere is a noncommutative operation. Sommerfeld was the first to use the geometric phase method to calculate the angle between the resulting velocities depending on the order in which they are added. For this, he related the value of this angle to the excess of the spherical triangle formed by the two original velocities and their sum. In 1931, Sommerfeld applied his method to analyze the Thomas precession. (from the history of physics)
Quantum mechanics on phase space: The hydrogen atom and its Wigner functions
Campos, P.; Martins, M. G. R.; Fernandes, M. C. B.; Vianna, J. D. M.
2018-03-01
Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.
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)
Non-singular Brans–Dicke collapse in deformed phase space
Energy Technology Data Exchange (ETDEWEB)
Rasouli, S.M.M., E-mail: mrasouli@ubi.pt [Departamento de Física, Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200 Covilhã (Portugal); Centro de Matemática e Aplicações (CMA - UBI), Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200 Covilhã (Portugal); Physics Group, Qazvin Branch, Islamic Azad University, Qazvin (Iran, Islamic Republic of); Ziaie, A.H., E-mail: ah_ziaie@sbu.ac.ir [Department of Physics, Shahid Beheshti University, G. C., Evin, 19839 Tehran (Iran, Islamic Republic of); Department of Physics, Shahid Bahonar University, PO Box 76175, Kerman (Iran, Islamic Republic of); Jalalzadeh, S., E-mail: shahram.jalalzadeh@unila.edu.br [Federal University of Latin-American Integration, Technological Park of Itaipu PO box 2123, Foz do Iguaçu-PR, 85867-670 (Brazil); Moniz, P.V., E-mail: pmoniz@ubi.pt [Departamento de Física, Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200 Covilhã (Portugal); Centro de Matemática e Aplicações (CMA - UBI), Universidade da Beira Interior, Rua Marquês d’Avila e Bolama, 6200 Covilhã (Portugal)
2016-12-15
We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.
Non-singular Brans–Dicke collapse in deformed phase space
International Nuclear Information System (INIS)
Rasouli, S.M.M.; Ziaie, A.H.; Jalalzadeh, S.; Moniz, P.V.
2016-01-01
We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.
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.
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
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)
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.)
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.
Noncommutative Valuation of Options
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.
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)
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.)
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
Quantum computers in phase space
International Nuclear Information System (INIS)
Miquel, Cesar; Paz, Juan Pablo; Saraceno, Marcos
2002-01-01
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to measure directly the Wigner function in a given phase-space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm
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
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.
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.)
Quantum mechanics in phase space
DEFF Research Database (Denmark)
Hansen, Frank
1984-01-01
A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...
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.
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.
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
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.)
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)
Beam phase space and emittance
International Nuclear Information System (INIS)
Buon, J.
1990-12-01
The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation and to treat two particular examples
Index theory for locally compact noncommutative geometries
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.
Schleich, Wolfgang P.
2001-04-01
Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.
On total noncommutativity in quantum mechanics
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.
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
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.)
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 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.
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
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.
Longitudinal Phase Space Tomography with Space Charge
Hancock, S; Lindroos, M
2000-01-01
Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the non-linearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of...
Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields
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.
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
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
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.
Inflationary universe in deformed phase space scenario
Rasouli, S. M. M.; Saba, Nasim; Farhoudi, Mehrdad; Marto, João; Moniz, P. V.
2018-06-01
We consider a noncommutative (NC) inflationary model with a homogeneous scalar field minimally coupled to gravity. The particular NC inflationary setting herein proposed, produces entirely new consequences as summarized in what follows. We first analyze the free field case and subsequently examine the situation where the scalar field is subjected to a polynomial and exponential potentials. We propose to use a canonical deformation between momenta, in a spatially flat Friedmann-Lemaî tre-Robertson-Walker (FLRW) universe, and while the Friedmann equation (Hamiltonian constraint) remains unaffected the Friedmann acceleration equation (and thus the Klein-Gordon equation) is modified by an extra term linear in the NC parameter. This concrete noncommutativity on the momenta allows interesting dynamics that other NC models seem not to allow. Let us be more precise. This extra term behaves as the sole explicit pressure that under the right circumstances implies a period of accelerated expansion of the universe. We find that in the absence of the scalar field potential, and in contrast with the commutative case, in which the scale factor always decelerates, we obtain an inflationary phase for small negative values of the NC parameter. Subsequently, the period of accelerated expansion is smoothly replaced by an appropriate deceleration phase providing an interesting model regarding the graceful exit problem in inflationary models. This last property is present either in the free field case or under the influence of the scalar field potentials considered here. Moreover, in the case of the free scalar field, we show that not only the horizon problem is solved but also there is some resemblance between the evolution equation of the scale factor associated to our model and that for the R2 (Starobinsky) inflationary model. Therefore, our herein NC model not only can be taken as an appropriate scenario to get a successful kinetic inflation, but also is a convenient setting to
Phase space quark counting rule
International Nuclear Information System (INIS)
Wei-gin, C.; Lo, S.
1980-01-01
A simple quark counting rule based on phase space consideration suggested before is used to fit all 39 recent experimental data points on inclusive reactions. Parameter free relations are found to agree with experiments. Excellent detail fits are obtained for 11 inclusive reactions
Quantum Shuttle in Phase Space
DEFF Research Database (Denmark)
Novotny, Tomas; Donarini, Andrea; Jauho, Antti-Pekka
2003-01-01
Abstract: We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a crossover from the tunneling to the shuttling regime, thus...
Relativistic phase space: dimensional recurrences
International Nuclear Information System (INIS)
Delbourgo, R; Roberts, M L
2003-01-01
We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius R and taking the limit as R→∞. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension
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.
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.
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
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
A non-perturbative study of 4d U(1) non-commutative gauge theory — the fate of one-loop instability
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.
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.)
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.)
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
On Dual Phase-Space Relativity, the Machian Principle and Modified Newtonian Dynamics
Castro, C
2004-01-01
We investigate the consequences of the Mach's principle of inertia within the context of the Dual Phase Space Relativity which is compatible with the Eddington-Dirac large numbers coincidences and may provide with a physical reason behind the observed anomalous Pioneer acceleration and a solution to the riddle of the cosmological constant problem ( Nottale ). The cosmological implications of Non-Archimedean Geometry by assigning an upper impassible scale in Nature and the cosmological variations of the fundamental constants are also discussed. We study the corrections to Newtonian dynamics resulting from the Dual Phase Space Relativity by analyzing the behavior of a test particle in a modified Schwarzschild geometry (due to the the effects of the maximal acceleration) that leads in the weak-field approximation to essential modifications of the Newtonian dynamics and to violations of the equivalence principle. Finally we follow another avenue and find modified Newtonian dynamics induced by the Yang's Noncommut...
Beam phase space and emittance
International Nuclear Information System (INIS)
Buon, J.
1992-02-01
The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation, with three particular examples, and to introduce a beam envelope-ellipse and the β-function, emphasing the statistical features of its properties. (author) 14 refs.; 11 figs
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...
One-loop beta functions for the orientable non-commutative Gross Neveu model TH1"-->
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.
International Nuclear Information System (INIS)
Fechner, Susanne
2008-01-01
The von Neumann-representation introduced in this thesis describes each laser pulse in a one-to-one manner as a sum of bandwidth-limited, Gaussian laser pulses centered around different points in phase space. These pulses can be regarded as elementary building blocks from which every single laser pulse can be constructed. The von Neumann-representation combines different useful properties for applications in quantum control. First, it is a one-to-one map between the degrees of freedom of the pulse shaper and the phase-space representation of the corresponding shaped laser pulse. In other words: Every possible choice of pulse shaper parameters corresponds to exactly one von Neumann-representation and vice versa. Moreover, since temporal and spectral structures become immediately sizable, the von Neumann-representation, as well as the Husimi- or the Wigner-representations, allows for an intuitive interpretation of the represented laser pulse. (orig.)
International Nuclear Information System (INIS)
Chetouani, L.; Hammann, T.F.
1987-01-01
The Hamiltonian of the three-dimensional hydrogen atom is reduced, in parabolic coordinates, to the Hamiltonians of two bidimensional harmonic oscillators, by doing several space-time transformations,separating the movement along the three parabolic directions (ξ,eta,phi), and introducing two auxiliary angular variables psi and psi', 0≤psi, psi'≤2π. The Green's function is developed into partial Green's functions, and expressed in terms of two Green's functions that describe the movements along both the ξ and eta axes. Introducing auxiliary Hamiltonians allows one to calculate the Green's function in the configurational space, via the phase-space evolution function of the two-dimensional harmonic oscillator. The auxiliary variables psi and psi' are eliminated by projection. The thus-obtained Green's function, save for a multiplicating factor, coincides with that calculated following the path-integral formalism
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)
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
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.
Self-dual phase space for (3 +1 )-dimensional lattice Yang-Mills theory
Riello, Aldo
2018-01-01
I propose a self-dual deformation of the classical phase space of lattice Yang-Mills theory, in which both the electric and magnetic fluxes take value in the compact gauge Lie group. A local construction of the deformed phase space requires the machinery of "quasi-Hamiltonian spaces" by Alekseev et al., which is reviewed here. The results is a full-fledged finite-dimensional and gauge-invariant phase space, the self-duality properties of which are largely enhanced in (3 +1 ) spacetime dimensions. This enhancement is due to a correspondence with the moduli space of an auxiliary noncommutative flat connection living on a Riemann surface defined from the lattice itself, which in turn equips the duality between electric and magnetic fluxes with a neat geometrical interpretation in terms of a Heegaard splitting of the space manifold. Finally, I discuss the consequences of the proposed deformation on the quantization of the phase space, its quantum gravitational interpretation, as well as its relevance for the construction of (3 +1 )-dimensional topological field theories with defects.
Vacuum energy from noncommutative models
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.
An invitation to noncommutative geometry
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
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
Multiparametric quantum symplectic phase space
International Nuclear Information System (INIS)
Parashar, P.; Soni, S.K.
1992-07-01
We formulate a consistent multiparametric differential calculus on the quadratic coordinate algebra of the quantum vector space and use this as a tool to obtain a deformation of the associated symplectic phase space involving n(n-1)/2+1 deformation parameters. A consistent calculus on the relation subspace is also constructed. This is achieved with the help of a restricted ansatz and solving the consistency conditions to directly arrive at the main commutation structures without any reference to the R-matrix. However, the non-standard R-matrices for GL r,qij (n) and Sp r,qij (2n) can be easily read off from the commutation relations involving coordinates and derivatives. (author). 9 refs
Passive longitudinal phase space linearizer
Directory of Open Access Journals (Sweden)
P. Craievich
2010-03-01
Full Text Available We report on the possibility to passively linearize the bunch compression process in electron linacs for the next generation x-ray free electron lasers. This can be done by using the monopole wakefields in a dielectric-lined waveguide. The optimum longitudinal voltage loss over the length of the bunch is calculated in order to compensate both the second-order rf time curvature and the second-order momentum compaction terms. Thus, the longitudinal phase space after the compression process is linearized up to a fourth-order term introduced by the convolution between the bunch and the monopole wake function.
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
Phase Space Exchange in Thick Wedge Absorbers
Energy Technology Data Exchange (ETDEWEB)
Neuffer, David [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
2017-01-01
The problem of phase space exchange in wedge absorbers with ionization cooling is discussed. The wedge absorber exchanges transverse and longitudinal phase space by introducing a position-dependent energy loss. In this paper we note that the wedges used with ionization cooling are relatively thick, so that single wedges cause relatively large changes in beam phase space. Calculation methods adapted to such “thick wedge” cases are presented, and beam phase-space transformations through such wedges are discussed.
Miniature Active Space Radiation Dosimeter, Phase II
National Aeronautics and Space Administration — Space Micro will extend our Phase I R&D to develop a family of miniature, active space radiation dosimeters/particle counters, with a focus on biological/manned...
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
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)
The eigenvalue problem in phase space.
Cohen, Leon
2018-06-30
We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.
Nuclear dynamics in phase space
International Nuclear Information System (INIS)
Di Toro, M.
1984-07-01
We present a unified semiclassical picture of nuclear dynamics, from collective states to heavy ion physics, based on a study of the time evolution of the Wigner distribution function. We discuss in particular the mean field dynamics, in this ''quantal'' phase space, which is ruled by the nuclear Vlasov equation. Simple approximate solutions are worked out for rotational and vibrational collective motions. Giant resonances are shown to be quite well described as scaling modes, which are equivalent to a lowest multipole (up to 1sub(max)=2) distortions of the momentum distribution. Applications are shown to heavy ion physics to study giant resonances on high spin states and dynamical collective effects in subthreshold π-production. Several possible extensions and in particular the inclusion of two-body collision terms are finally discussed
Noncommutative quantum mechanics
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.
Can noncommutativity resolve the Big-Bang singularity?
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.
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
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.
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
Non-commutative flux representation for loop quantum gravity
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.
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)
Phase-space quantization of field theory
International Nuclear Information System (INIS)
Curtright, T.; Zachos, C.
1999-01-01
In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999
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.
Testing Non-commutative QED, Constructing Non-commutative MHD
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 ...
Instantons, quivers and noncommutative Donaldson-Thomas theory
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.
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.
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.
Nonlinear transport of dynamic system phase space
International Nuclear Information System (INIS)
Xie Xi; Xia Jiawen
1993-01-01
The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example
Impenetrable Barriers in Phase-Space
International Nuclear Information System (INIS)
Wiggins, S.; Wiesenfeld, L.; Jaffe, C.; Uzer, T.
2001-01-01
Dynamical systems theory is used to construct a general phase-space version of transition state theory. Special multidimensional separatrices are found which act as impenetrable barriers in phase-space between reacting and nonreacting trajectories. The elusive momentum-dependent transition state between reactants and products is thereby characterized. A practical algorithm is presented and applied to a strongly coupled Hamiltonian
Diagrammatic methods in phase-space regularization
International Nuclear Information System (INIS)
Bern, Z.; Halpern, M.B.; California Univ., Berkeley
1987-11-01
Using the scalar prototype and gauge theory as the simplest possible examples, diagrammatic methods are developed for the recently proposed phase-space form of continuum regularization. A number of one-loop and all-order applications are given, including general diagrammatic discussions of the nogrowth theorem and the uniqueness of the phase-space stochastic calculus. The approach also generates an alternate derivation of the equivalence of the large-β phase-space regularization to the more conventional coordinate-space regularization. (orig.)
Modeling beams with elements in phase space
International Nuclear Information System (INIS)
Nelson, E.M.
1998-01-01
Conventional particle codes represent beams as a collection of macroparticles. An alternative is to represent the beam as a collection of current carrying elements in phase space. While such a representation has limitations, it may be less noisy than a macroparticle model, and it may provide insights about the transport of space charge dominated beams which would otherwise be difficult to gain from macroparticle simulations. The phase space element model of a beam is described, and progress toward an implementation and difficulties with this implementation are discussed. A simulation of an axisymmetric beam using 1d elements in phase space is demonstrated
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.)
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])...
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.
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)
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 ...
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)
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
Noncommutative Blackwell-Ross martingale inequality
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.
Quantum Riemannian geometry of phase space and nonassociativity
Directory of Open Access Journals (Sweden)
Beggs Edwin J.
2017-04-01
Full Text Available Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of ℂℙn where the commutation relations have the canonical form [wi, w̄j] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.
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
Phase space diffusion in turbulent plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1990-01-01
. The second type are particles introduced at a prescribed phase space position at a certain time and which then self-consistently participate in the phase space dynamics of the turbulence. The latter "active" type of particles can be subject to an effective frictional force due to radiation of plasma waves....... In terms of these test particle types, two basically different problems can be formulated. One deals with the diffusion of a particle with respect to its point of release in phase space. Alternatively the relative diffusion between many, or just two, particles can be analyzed. Analytical expressions...
On the phase space representations. 1
International Nuclear Information System (INIS)
Polubarinov, I.V.
1978-01-01
The Dirac representation theory deals usually with the amplitude formalism of the quantum theory. An introduction is given into a theory of some other representations, which are applicable in the density matrix formalism and can naturally be called phase space representations (PSR). They use terms of phase space variables (x and p simultaneously) and give a description, close to the classical phase space description. Definitions and algebraic properties are given in quantum mechanics for such PSRs as the Wigner representation, coherent state representation and others. Completeness relations of a matrix type are used as a starting point. The case of quantum field theory is also outlined
Linear entropy in quantum phase space
International Nuclear Information System (INIS)
Rosales-Zarate, Laura E. C.; Drummond, P. D.
2011-01-01
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
Linear entropy in quantum phase space
Energy Technology Data Exchange (ETDEWEB)
Rosales-Zarate, Laura E. C.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)
2011-10-15
We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.
RADON reconstruction in longitudinal phase space
International Nuclear Information System (INIS)
Mane, V.; Peggs, S.; Wei, J.
1997-01-01
Longitudinal particle motion in circular accelerators is typically monitoring by one dimensional (1-D) profiles. Adiabatic particle motion in two dimensional (2-D) phase space can be reconstructed with tomographic techniques, using 1-D profiles. A computer program RADON has been developed in C++ to process digitized mountain range data and perform the phase space reconstruction for the AGS, and later for Relativistic Heavy Ion Collider (RHIC)
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.)
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.)
Foundations of phase-space quantum mechanics
International Nuclear Information System (INIS)
Guz, W.
1984-01-01
In the present paper a general concept of a phase-space representation of the ordinary Hilbert-space quantum theory is formulated, and then, by using some elementary facts of functional analysis, several equivalent forms of that concept are analyzed. Several important physical examples are presented in Section 3 of the paper. (author)
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 .
Noncommutative mathematics for quantum systems
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...
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)
Resonance controlled transport in phase space
Leoncini, Xavier; Vasiliev, Alexei; Artemyev, Anton
2018-02-01
We consider the mechanism of controlling particle transport in phase space by means of resonances in an adiabatic setting. Using a model problem describing nonlinear wave-particle interaction, we show that captures into resonances can be used to control transport in momentum space as well as in physical space. We design the model system to provide creation of a narrow peak in the distribution function, thus producing effective cooling of a sub-ensemble of the particles.
Connecting dissipation and noncommutativity: A Bateman system case study
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.
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.
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
Incomplete information and fractal phase space
International Nuclear Information System (INIS)
Wang, Qiuping A.
2004-01-01
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter ω which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of ω on the basis of fractal phase space. ω is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process
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)
On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere
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.
Discrete phase space based on finite fields
International Nuclear Information System (INIS)
Gibbons, Kathleen S.; Hoffman, Matthew J.; Wootters, William K.
2004-01-01
The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a 2Nx2N discrete phase space for a system with N orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having N elements. There exists such a field if and only if N is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our NxN phase space also leads naturally to a method of constructing a complete set of N+1 mutually unbiased bases for the state space
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)
Phase space density representations in fluid dynamics
International Nuclear Information System (INIS)
Ramshaw, J.D.
1989-01-01
Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable
Phase space approach to quantum dynamics
International Nuclear Information System (INIS)
Leboeuf, P.
1991-03-01
The Schroedinger equation for the time propagation of states of a quantised two-dimensional spherical phase space is replaced by the dynamics of a system of N particles lying in phase space. This is done through factorization formulae of analytic function theory arising in coherent-state representation, the 'particles' being the zeros of the quantum state. For linear Hamiltonians, like a spin in a uniform magnetic field, the motion of the particles is classical. However, non-linear terms induce interactions between the particles. Their time propagation is studied and it is shown that, contrary to integrable systems, for chaotic maps they tend to fill, as their classical counterpart, the whole phase space. (author) 13 refs., 3 figs
Phase space diffusion in turbulent plasmas
International Nuclear Information System (INIS)
Pecseli, H.L.
1990-01-01
Turbulent diffusion of charged test particles in electrostatic plasma turbulence is reviewed. Two different types of test particles can be distinguished. First passice particles which are subject to the fluctuating electric fields without themselves contributing to the local space charge. The second type are particles introduced at a prescribed phase space position at a certain time and which then self-consistently participate in the phase space dynamics of the turbulent. The latter ''active'' type of particles can be subjected to an effective frictional force due to radiation of plasma waves. In terms of these test particle types, two basically different problems can be formulated. One deals with the diffusion of a particle with respect to its point of release in phase space. Alternatively the relative diffusion between many, or just two, particles can be analyzed. Analytical expressions for the mean square particle displacements in phase space are discussed. More generally equations for the full probability densities are derived and these are solved analytically in special limits. (orig.)
Identifying Phase Space Boundaries with Voronoi Tessellations
Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao
2016-11-24
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.
Grassmann phase space theory for fermions
Energy Technology Data Exchange (ETDEWEB)
Dalton, Bryan J. [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria, 3122 (Australia); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow, G4 ONG (United Kingdom); Barnett, Stephen M. [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom)
2017-06-15
A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Freeform aberrations in phase space: an example.
Babington, James
2017-06-01
We consider how optical propagation and aberrations of freeform systems can be formulated in phase space. As an example system, a freeform prism is analyzed and discussed. Symmetry considerations and their group theory descriptions are given some importance. Numerical aberrations are also highlighted and put into the context of the underlying aberration theory.
Phase-space quark counting rule
Energy Technology Data Exchange (ETDEWEB)
Wei-Gin, Chao; Lo, Shui-Yin [Academia Sinica, Beijing (China). Inst. of High Energy Physics
1981-05-21
A simple quark counting rule based on the phase-space consideration suggested before is used to fit all 39 recent experimental data points on inclusive reactions. Parameter-free relations are found to agree with experiments. Excellent detail fits are obtained for 11 inclusive reactions.
Phase space representations for spin23
International Nuclear Information System (INIS)
Polubarinov, I.V.
1991-01-01
General properties of spin matrices and density ones are considered for any spin s. For spin 2 3 phase space representations are constructed. Representations, similar to the Bell one, for the correlator of projections of two spins 2 3 in the singlet state are found. Quantum analogs of the Bell inequality are obtained. 14 refs
Meson phase space density from interferometry
International Nuclear Information System (INIS)
Bertsch, G.F.
1993-01-01
The interferometric analysis of meson correlations a measure of the average phase space density of the mesons in the final state. The quantity is a useful indicator of the statistical properties of the systems, and it can be extracted with a minimum of model assumptions. Values obtained from recent measurements are consistent with the thermal value, but do not rule out superradiance effects
Nonlinear transport of accelerator beam phase space
International Nuclear Information System (INIS)
Xie Xi; Xia Jiawen
1995-01-01
Based on the any order analytical solution of accelerator beam dynamics, the general theory for nonlinear transport of accelerator beam phase space is developed by inverse transformation method. The method is general by itself, and hence can also be applied to the nonlinear transport of various dynamic systems in physics, chemistry and biology
Formation of Ion Phase-Space Vortexes
DEFF Research Database (Denmark)
Pécseli, Hans; Trulsen, J.; Armstrong, R. J.
1984-01-01
The formation of ion phase space vortexes in the ion two stream region behind electrostatic ion acoustic shocks are observed in a laboratory experiment. A detailed analysis demonstrates that the evolution of such vortexes is associated with ion-ion beam instabilities and a nonlinear equation for ...
Quantum mechanics and dynamics in phase space
International Nuclear Information System (INIS)
Zlatev, I.S.
1979-01-01
Attention is paid to formal similarity of quantum mechanics and classical statistical physics. It is supposed that quantum mechanics can be reformulated by means of the quasiprobabilistic distributions (QPD). The procedure of finding a possible dynamics of representative points in a phase space is described. This procedure would lead to an equation of the Liouville type for the given QPD. It is shown that there is always a dynamics for which the phase volume is preserved and there is another dynamics for which the equations of motion are ''canonical''. It follows from the paper that in terms of the QPD the quantum mechanics is analogous to the classical statistical mechanics and it can be interpreted as statistics of phase points, their motion obeying the canonical equations. The difference consists in the fact that in the classical statistical physics constructed is statistics of points in a phase space which depict real, existing, observable states of the system under consideration. In the quantum mechanics constructed is statistics of points in a phase space which correspond to the ''substrate'' of quantum-mechanical objects which have no any physical sense and cannot be observed separately
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.
The Quantum Space Phase Transitions for Particles and Force Fields
Chung D.-Y.; Krasnoholovets V.
2006-01-01
We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment spac...
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.
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
Phase transitions in de Sitter space
Directory of Open Access Journals (Sweden)
Alexander Vilenkin
1983-10-01
Full Text Available An effective potential in de Sitter space is calculated for a model of two interacting scalar fields in one-loop approximation and in a self-consistent approximation which takes into account an infinite set of diagrams. Various approaches to renormalization in de Sitter space are discussed. The results are applied to analyze the phase transition in the Hawking-Moss version of the inflationary universe scenario. Requiring that inflation is sufficiently large, we derive constraints on the parameters of the model.
Wavelet analysis of the nuclear phase space
Energy Technology Data Exchange (ETDEWEB)
Jouault, B.; Sebille, F.; Mota, V. de la
1997-12-31
The description of transport phenomena in nuclear matter is addressed in a new approach based on the mathematical theory of wavelets and the projection methods of statistical physics. The advantage of this framework is to offer the opportunity to use information concepts common to both the formulation of physical properties and the mathematical description. This paper focuses on two features, the extraction of relevant informations using the geometrical properties of the underlying phase space and the optimization of the theoretical and numerical treatments based on convenient choices of the representation spaces. (author). 34 refs.
Wavelet analysis of the nuclear phase space
International Nuclear Information System (INIS)
Jouault, B.; Sebille, F.; Mota, V. de la.
1997-01-01
The description of transport phenomena in nuclear matter is addressed in a new approach based on the mathematical theory of wavelets and the projection methods of statistical physics. The advantage of this framework is to offer the opportunity to use information concepts common to both the formulation of physical properties and the mathematical description. This paper focuses on two features, the extraction of relevant informations using the geometrical properties of the underlying phase space and the optimization of the theoretical and numerical treatments based on convenient choices of the representation spaces. (author)
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
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.
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.
The Morse oscillator in position space, momentum space, and phase space
DEFF Research Database (Denmark)
Dahl, Jens Peder; Springborg, Michael
1988-01-01
We present a unified description of the position-space wave functions, the momentum-space wave functions, and the phase-space Wigner functions for the bound states of a Morse oscillator. By comparing with the functions for the harmonic oscillator the effects of anharmonicity are visualized....... Analytical expressions for the wave functions and the phase space functions are given, and it is demonstrated how a numerical problem arising from the summation of an alternating series in evaluating Laguerre functions can be circumvented. The method is applicable also for other problems where Laguerre...... functions are to be calculated. The wave and phase space functions are displayed in a series of curves and contour diagrams. An Appendix discusses the calculation of the modified Bessel functions of real, positive argument and complex order, which is required for calculating the phase space functions...
Quantum algorithms for phase-space tomography
International Nuclear Information System (INIS)
Paz, Juan Pablo; Roncaglia, Augusto Jose; Saraceno, Marcos
2004-01-01
We present efficient circuits that can be used for the phase-space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood, and Husimi distributions. These quantum gate arrays can be programmed by initializing appropriate computational states. The Husimi circuit relies on a subroutine that is also interesting in its own right: the efficient preparation of a coherent state, which is the ground state of the Harper Hamiltonian
Liouville's theorem and phase-space cooling
International Nuclear Information System (INIS)
Mills, R.L.; Sessler, A.M.
1993-01-01
A discussion is presented of Liouville's theorem and its consequences for conservative dynamical systems. A formal proof of Liouville's theorem is given. The Boltzmann equation is derived, and the collisionless Boltzmann equation is shown to be rigorously true for a continuous medium. The Fokker-Planck equation is derived. Discussion is given as to when the various equations are applicable and, in particular, under what circumstances phase space cooling may occur
Periodic orbits and TDHF phase space structure
Energy Technology Data Exchange (ETDEWEB)
Hashimoto, Yukio; Iwasawa, Kazuo [Tsukuba Univ., Ibaraki (Japan). Inst. of Physics; Tsukuma, Hidehiko; Sakata, Fumihiko
1998-03-01
The collective motion of atomic nuclei is closely coupled with the motion of nucleons, therefore, it is nonlinear, and the contents of the motion change largely with the increase of its amplitude. As the framework which describes the collective motion accompanied by the change of internal structure, time-dependent Hurtley Fock (TDHF) method is suitable. At present, the authors try to make the method for studying the large region structure in quantum system by utilizing the features of the TDHF phase space. The studies made so far are briefed. In this report, the correspondence of the large region patterns appearing in the band structure chart of three-level model with the periodic orbit group in the TDHF phase space is described. The Husimi function is made, and it possesses the information on the form of respective corresponding intrinsic state. The method of making the band structure chart is explained. There are three kinds of the tendency in the intrinsic state group. The E-T charts are made for the band structure charts to quantitatively express the large region tendency. The E-T chart and the T{sub r}-T chart are drawn for a selected characteristic orbit group. It became to be known that the large region properties of the quantum intrinsic state group of three-level model can be forecast by examining the properties of the periodic orbit group in the TDHF phase space. (K.I.)
Stochastic inflation: Quantum phase-space approach
International Nuclear Information System (INIS)
Habib, S.
1992-01-01
In this paper a quantum-mechanical phase-space picture is constructed for coarse-grained free quantum fields in an inflationary universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase-space quantum distribution function are found for the cases of power-law and exponential expansions. The expectation values of dynamical variables with respect to these solutions are compared to the corresponding cutoff regularized field-theoretic results (we do not restrict ourselves only to left-angle Φ 2 right-angle). Fair agreement is found provided the coarse-graining scale is kept within certain limits. By focusing on the full phase-space distribution function rather than a reduced distribution it is shown that the thermodynamic interpretation of the stochastic formalism faces several difficulties (e.g., there is no fluctuation-dissipation theorem). The coarse graining does not guarantee an automatic classical limit as quantum correlations turn out to be crucial in order to get results consistent with standard quantum field theory. Therefore, the method does not by itself constitute an explanation of the quantum to classical transition in the early Universe. In particular, we argue that the stochastic equations do not lead to decoherence
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.
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
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
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.
Dolan Grady relations and noncommutative quasi-exactly solvable systems
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.
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
Equations of motion in phase space
International Nuclear Information System (INIS)
Broucke, R.
1979-01-01
The article gives a general review of methods of constructing equations of motion of a classical dynamical system. The emphasis is however on the linear Lagrangian in phase space and the corresponding form of Pfaff's equations of motion. A detailed examination of the problem of changes of variables in phase space is first given. It is shown that the Linear Lagrangian theory falls very naturally out of the classical quadratic Lagrangian theory; we do this with the use of the well-known Lagrange multiplier method. Another important result is obtained very naturally as a by-product of this analysis. If the most general set of 2n variables (coordinates in phase space) is used, the coefficients of the equations of motion are the Poisson Brackets of these variables. This is therefore the natural way of introducing not only Poisson Brackets in Dynamics formulations but also the associated Lie Algebras and their important properties and consequences. We give then several examples to illustrate the first-order equations of motion and their simplicity in relation to general changes of variables. The first few examples are elementary (the harmonic Oscillator) while the last one concerns the motion of a rigid body about a fixed point. In the next three sections we treat the first-order equations of motion as derived from a Linear differential form, sometimes called Birkhoff's equations. We insist on the generality of the equations and especially on the unity of the space-time concept: the time t and the coordinates are here completely identical variables, without any privilege to t. We give a brief review of Cartan's 2-form and the corresponding equations of motion. As an illustration the standard equations of aircraft flight in a vertical plane are derived from Cartan's exterior differential 2-form. Finally we mention in the last section the differential forms that were proposed by Gallissot for the derivation of equations of motion
Noncommutative geometry inspired Einstein–Gauss–Bonnet black holes
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.
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.)
Quantum Thetas on Noncommutative T^d with General Embeddings
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...
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.
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.
Alternating phase focussing including space charge
International Nuclear Information System (INIS)
Cheng, W.H.; Gluckstern, R.L.
1992-01-01
Longitudinal stability can be obtained in a non-relativistic drift tube accelerator by traversing each gap as the rf accelerating field rises. However, the rising accelerating field leads to a transverse defocusing force which is usually overcome by magnetic focussing inside the drift tubes. The radio frequency quadrupole is one way of providing simultaneous longitudinal and transverse focusing without the use of magnets. One can also avoid the use of magnets by traversing alternate gaps between drift tubes as the field is rising and falling, thus providing an alternation of focussing and defocusing forces in both the longitudinal and transverse directions. The stable longitudinal phase space area is quite small, but recent efforts suggest that alternating phase focussing (APF) may permit low velocity acceleration of currents in the 100-300 ma range. This paper presents a study of the parameter space and a test of crude analytic predictions by adapting the code PARMILA, which includes space charge, to APF. 6 refs., 3 figs
Phase space methods for Majorana fermions
Rushin Joseph, Ria; Rosales-Zárate, Laura E. C.; Drummond, Peter D.
2018-06-01
Fermionic phase space representations are a promising method for studying correlated fermion systems. The fermionic Q-function and P-function have been defined using Gaussian operators of fermion annihilation and creation operators. The resulting phase-space of covariance matrices belongs to the symmetry class D, one of the non-standard symmetry classes. This was originally proposed to study mesoscopic normal-metal-superconducting hybrid structures, which is the type of structure that has led to recent experimental observations of Majorana fermions. Under a unitary transformation, it is possible to express these Gaussian operators using real anti-symmetric matrices and Majorana operators, which are much simpler mathematical objects. We derive differential identities involving Majorana fermion operators and an antisymmetric matrix which are relevant to the derivation of the corresponding Fokker–Planck equations on symmetric space. These enable stochastic simulations either in real or imaginary time. This formalism has direct relevance to the study of fermionic systems in which there are Majorana type excitations, and is an alternative to using expansions involving conventional Fermi operators. The approach is illustrated by showing how a linear coupled Hamiltonian as used to study topological excitations can be transformed to Fokker–Planck and stochastic equation form, including dissipation through particle losses.
Coherent and squeezed states in phase space
International Nuclear Information System (INIS)
Jannussis, A.; Bartzis, V.; Vlahos, E.
1990-01-01
In the present paper, the coherent and the squeezed states in phase space have been studied. From the wave functions of the coherent and the squeezed state, their corresponding Wigner distribution functions are calculated. Especially the calculation of the corresponding Wigner functions for the above states permits the determination of the mean values of position and momentum and thus the Heisenberg uncertainty relation. In fact, from the related results, it is concluded that the uncertainty relation of the coherent and associated squeezed states is the same
Born's reciprocity principle in stochastic phase space
International Nuclear Information System (INIS)
Prugovecki, E.
1981-01-01
It is shown that the application of Born's reciprocity principle to relativistic quantum mechanics in stochastic phase space (by the requirement that the proper wave functions of extended particles satisfy the Born-Lande as well as the Klein-Gordon equation) leads to the unique determination of these functions for any given value of their rms radius. The resulting particle propagators display not only Lorentz but also reciprocal invariance. This feature remains true even in the case of mass-zero particles, such as photons, when their localization is achieved by means of extended test particles whose proper wave functions obey the reciprocity principle. (author)
Experimental Observations of Ion Phase-Space Vortices
DEFF Research Database (Denmark)
Pécseli, Hans; Armstrong, R. J.; Trulsen, J.
1981-01-01
Experimental observations of ion phase-space vortices are reported. The ion phase-space vortices form in the region of heated ions behind electrostatic ion acoustic shocks. The results are in qualitative agreement with numerical and analytic studies....
Space Transportation Engine Program (STEP), phase B
1990-01-01
The Space Transportation Engine Program (STEP) Phase 2 effort includes preliminary design and activities plan preparation that will allow smooth and time transition into a Prototype Phase and then into Phases 3, 4, and 5. A Concurrent Engineering approach using Total Quality Management (TQM) techniques, is being applied to define an oxygen-hydrogen engine. The baseline from Phase 1/1' studies was used as a point of departure for trade studies and analyses. Existing STME system models are being enhanced as more detailed module/component characteristics are determined. Preliminary designs for the open expander, closed expander, and gas generator cycles were prepared, and recommendations for cycle selection made at the Design Concept Review (DCR). As a result of July '90 DCR, and information subsequently supplied to the Technical Review Team, a gas generator cycle was selected. Results of the various Advanced Development Programs (ADP's) for the Advanced Launch Systems (ALS) were contributive to this effort. An active vehicle integration effort is supplying the NASA, Air Force, and vehicle contractors with engine parameters and data, and flowing down appropriate vehicle requirements. Engine design and analysis trade studies are being documented in a data base that was developed and is being used to organize information. To date, seventy four trade studies were input to the data base.
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
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.)
Tomographic Measurements of Longitudinal Phase Space Density
Hancock, S; McIntosh, E; Metcalf, M
1999-01-01
Tomography : the reconstruction of a two-dimensional image from a series of its one-dimensional projections is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. One of the simplest algorithms has been modified to take into account the non-linearity of large-amplitude synchrotron motion in a particle accelerator. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The algorithm was developed in Mathematica TM in order to exploit the extensive built-in functions and graphics. Subsequently, it has been recoded in Fortran 90 with the aim of reducing the execution time by at least a factor of one hundred. The choice of Fortran 90 was governed by the desire ultimately to exploit parallel architectures, but sequential compilation and execution have already largely yielded the required gain in speed. The use of the method to produce longitudinal phase space plots, animated sequences o...
The theory of pseudo-differential operators on the noncommutative n-torus
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.
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)
The Quantum Space Phase Transitions for Particles and Force Fields
Directory of Open Access Journals (Sweden)
Chung D.-Y.
2006-07-01
Full Text Available We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment space is miscible to detachment space, and there is no separation between attachment space and detachment spaces. In binary partition space, detachment space and attachment space are in two separat continuous regions. The transition from wavefunction to the collapse of wavefuction under interference becomes the quantum space phase transition from binary lattice space to miscible space. At extremely conditions, the gauge boson force field undergoes a quantum space phase transition to a "hedge boson force field", consisting of a "vacuum" core surrounded by a hedge boson shell, like a bubble with boundary.
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
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
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
Phase-space networks of geometrically frustrated systems.
Han, Yilong
2009-11-01
We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.
Optimal observables and phase-space ambiguities
International Nuclear Information System (INIS)
Nachtmann, O.; Nagel, F.
2005-01-01
Optimal observables are known to lead to minimal statistical errors on parameters for a given normalised event distribution of a physics reaction. Thereby all statistical correlations are taken into account. Therefore, on the one hand they are a useful tool to extract values on a set of parameters from measured data. On the other hand one can calculate the minimal constraints on these parameters achievable by any data-analysis method for the specific reaction. In case the final states can be reconstructed without ambiguities optimal observables have a particularly simple form. We give explicit formulae for the optimal observables for generic reactions in case of ambiguities in the reconstruction of the final state and for general parameterisation of the final-state phase space. (orig.)
Semiclassical scar functions in phase space
International Nuclear Information System (INIS)
Rivas, Alejandro M F
2007-01-01
We develop a semiclassical approximation for the scar function in the Weyl-Wigner representation in the neighborhood of a classically unstable periodic orbit of chaotic two-dimensional systems. The prediction of hyperbolic fringes, asymptotic to the stable and unstable manifolds, is verified computationally for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus. Characteristic fringe patterns can be distinguished even for quasi-energies where the fixed point is not Bohr-quantized. Also the patterns are highly localized in the neighborhood of the periodic orbit and along its stable and unstable manifolds without any long distance patterns that appear for the case of the spectral Wigner function
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
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
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)
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.
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.
The Extended Relativity Theory in Clifford Spaces
Castro, C
2004-01-01
A brief review of some of the most important features of the Extended Relativity theory in Clifford-spaces ( $C$-spaces) is presented whose " point" coordinates are noncommuting Clifford-valued quantities and which incoporate the lines, areas, volumes, .... degrees of freedom associated with the collective particle, string, membrane, ... dynamics of the $p$-loop histories (closed p-branes) living in target $D$-dimensional spacetime backgrounds. $C$-space Relativity naturally incoporates the ideas of an invariant length (Planck scale), maximal acceleration, noncommuting coordinates, supersymmetry, holography, superluminal propagation, higher derivative gravity with torsion and variable dimensions/signatures that allows to study the dynamics of all (closed ) p-branes, for all values of $ p $, in a unified footing. It resolves the ordering ambiguities in QFT and the problem of time in Cosmology. A discussion of the maximal-acceleration Relativity principle in phase-spaces follows along with the study of the inva...
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.
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''
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.
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
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)
Non-commutative standard model: model building
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.)
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
Géométrie non-commutative, théorie de jauge et renormalisation
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...
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
Securing Data for Space Communications, Phase I
National Aeronautics and Space Administration — NASA's vision of data exchange between space and ground nodes would involve the space network accessing public infrastructure such as the internet. Hence, advanced...
Space Plastic Recycling System, Phase I
National Aeronautics and Space Administration — Techshot's proposed Space Plastic Recycler (SPR) is an automated closed loop plastic recycling system that allows the automated conversion of disposable ISS...
Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
International Nuclear Information System (INIS)
Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.
2008-01-01
We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties
A computational non-commutative geometry program for disordered topological insulators
Prodan, Emil
2017-01-01
This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder. In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the co...
Phase-space formalism: Operational calculus and solution of evolution equations in phase-space
International Nuclear Information System (INIS)
Dattoli, G.; Torre, A.
1995-05-01
Phase-space formulation of physical problems offers conceptual and practical advantages. A class of evolution type equations, describing the time behaviour of a physical system, using an operational formalism useful to handle time ordering problems has been described. The methods proposed generalize the algebraic ordering techniques developed to deal with the ordinary Schroedinger equation, and how they are taylored suited to treat evolution problems both in classical and quantum dynamics has been studied
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
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
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
On the Generalized Geometry Origin of Noncommutative Gauge Theory
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.
Titanium Loop Heat Pipes for Space Nuclear Radiators, Phase I
National Aeronautics and Space Administration — This Small Business Innovation Research Phase I project will develop titanium Loop Heat Pipes (LHPs) that can be used in low-mass space nuclear radiators, such as...
On phase-space representations of quantum mechanics using
Indian Academy of Sciences (India)
space representations of quantum mechanics using Glauber coherent states. DIÓGENES CAMPOS. Research Article Volume 87 Issue 2 August ... Keywords. Phase-space quantum mechanics, coherent states, Husimi function, Wigner function ...
Overview of Phase Space Manipulations of Relativistic Electron Beams
Energy Technology Data Exchange (ETDEWEB)
Xiang, Dao; /SLAC
2012-08-31
Phase space manipulation is a process to rearrange beam's distribution in 6-D phase space. In this paper, we give an overview of the techniques for tailoring beam distribution in 2D, 4D, and 6D phase space to meet the requirements of various applications. These techniques become a new focus of accelerator physics R&D and very likely these advanced concepts will open up new opportunities in advanced accelerators and the science enabled by them.
Overview of Phase Space Manipulations of Relativistic Electron Beams
International Nuclear Information System (INIS)
Xiang, Dao
2012-01-01
Phase space manipulation is a process to rearrange beam's distribution in 6-D phase space. In this paper, we give an overview of the techniques for tailoring beam distribution in 2D, 4D, and 6D phase space to meet the requirements of various applications. These techniques become a new focus of accelerator physics R and D and very likely these advanced concepts will open up new opportunities in advanced accelerators and the science enabled by them.
Phase-space topography characterization of nonlinear ultrasound waveforms.
Dehghan-Niri, Ehsan; Al-Beer, Helem
2018-03-01
Fundamental understanding of ultrasound interaction with material discontinuities having closed interfaces has many engineering applications such as nondestructive evaluation of defects like kissing bonds and cracks in critical structural and mechanical components. In this paper, to analyze the acoustic field nonlinearities due to defects with closed interfaces, the use of a common technique in nonlinear physics, based on a phase-space topography construction of ultrasound waveform, is proposed. The central idea is to complement the "time" and "frequency" domain analyses with the "phase-space" domain analysis of nonlinear ultrasound waveforms. A nonlinear time series method known as pseudo phase-space topography construction is used to construct equivalent phase-space portrait of measured ultrasound waveforms. Several nonlinear models are considered to numerically simulate nonlinear ultrasound waveforms. The phase-space response of the simulated waveforms is shown to provide different topographic information, while the frequency domain shows similar spectral behavior. Thus, model classification can be substantially enhanced in the phase-space domain. Experimental results on high strength aluminum samples show that the phase-space transformation provides a unique detection and classification capabilities. The Poincaré map of the phase-space domain is also used to better understand the nonlinear behavior of ultrasound waveforms. It is shown that the analysis of ultrasound nonlinearities is more convenient and informative in the phase-space domain than in the frequency domain. Copyright © 2017 Elsevier B.V. All rights reserved.
Continual Lie algebras and noncommutative counterparts of exactly solvable models
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.
Some remarks on K_0 of noncommutative tori
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.
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.
Space Radiation Intelligence System (SPRINTS), Phase I
National Aeronautics and Space Administration — NextGen Federal Systems proposes an innovative SPace Radiation INTelligence System (SPRINTS) which provides an interactive and web-delivered capability that...
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)
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
Phase-space dynamics of Bianchi IX cosmological models
International Nuclear Information System (INIS)
Soares, I.D.
1985-01-01
The complex phase-space dynamical behaviour of a class of Biachi IX cosmological models is discussed, as the chaotic gravitational collapse due Poincare's homoclinic phenomena, and the n-furcation of periodic orbits and tori in the phase space of the models. Poincare maps which show this behaviour are constructed merically and applications are discussed. (Author) [pt
Kinetic theory in maximal-acceleration invariant phase space
International Nuclear Information System (INIS)
Brandt, H.E.
1989-01-01
A vanishing directional derivative of a scalar field along particle trajectories in maximal acceleration invariant phase space is identical in form to the ordinary covariant Vlasov equation in curved spacetime in the presence of both gravitational and nongravitational forces. A natural foundation is thereby provided for a covariant kinetic theory of particles in maximal-acceleration invariant phase space. (orig.)
The Bohr-Heisenberg correspondence principle viewed from phase space
DEFF Research Database (Denmark)
Dahl, Jens Peder
2002-01-01
Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can...
Microcanonical rates, gap times, and phase space dividing surfaces
Ezra, Gregory S.; Waalkens, Holger; Wiggins, Stephen
2009-01-01
The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. Key concepts, such as the phase space dividing surface separating reactants from products, the
Beam envelope profile of non-centrosymmetric polygonal phase space
International Nuclear Information System (INIS)
Chen Yinbao; Xie Xi
1984-01-01
The general theory of beam envelope profile of non-centrosymmetric polygonal phase space is developed. By means of this theory the beam envelope profile of non-centrosymmetric polygonal phase space can be calculated directly. An example is carried out in detail to show the practical application of the theory
Graphene for Expandable Space Structures, Phase I
National Aeronautics and Space Administration — Graphene's tightly bonded impermeable single atomic layer of carbon offers unrivalled potential for lightweight flexible gas barrier applications. Graphene has been...
Universal Space IP Transparent Proxy, Phase II
National Aeronautics and Space Administration — Communications applications are strategically moving toward Internet Protocol-based architectures and technologies. Despite IP's huge potential, (e.g. cost...
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
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.
Quantum mechanics in coherent algebras on phase space
International Nuclear Information System (INIS)
Lesche, B.; Seligman, T.H.
1986-01-01
Quantum mechanics is formulated on a quantum mechanical phase space. The algebra of observables and states is represented by an algebra of functions on phase space that fulfills a certain coherence condition, expressing the quantum mechanical superposition principle. The trace operation is an integration over phase space. In the case where the canonical variables independently run from -infinity to +infinity the formalism reduces to the representation of quantum mechanics by Wigner distributions. However, the notion of coherent algebras allows to apply the formalism to spaces for which the Wigner mapping is not known. Quantum mechanics of a particle in a plane in polar coordinates is discussed as an example. (author)
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
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)
A new type of phase-space path integral
International Nuclear Information System (INIS)
Marinov, M.S.
1991-01-01
Evolution of Wigner's quasi-distribution of a quantum system is represented by means of a path integral in phase space. Instead of the Hamiltonian action, a new functional is present in the integral, and its extrema in the functional space are also given by the classical trajectories. The phase-space paths appear in the integral with real weights, so complex integrals are not necessary. The semiclassical approximation and some applications are discussed briefly. (orig.)
Real-space Berry phases: Skyrmion soccer (invited)
Everschor-Sitte, Karin; Sitte, Matthias
2014-05-01
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.
Real-space Berry phases: Skyrmion soccer (invited)
Energy Technology Data Exchange (ETDEWEB)
Everschor-Sitte, Karin, E-mail: karin@physics.utexas.edu; Sitte, Matthias [The University of Texas at Austin, Department of Physics, 2515 Speedway, Austin, Texas 78712 (United States)
2014-05-07
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.
Real-space Berry phases: Skyrmion soccer (invited)
International Nuclear Information System (INIS)
Everschor-Sitte, Karin; Sitte, Matthias
2014-01-01
Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects
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)
Noncommutative Black Holes at the LHC
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.
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
Modular Actuators for Space Applications, Phase I
National Aeronautics and Space Administration — Rocketstar Robotics is proposing the development of a modern dual drive actuator. Rocketstar has put together numerous modern concepts for modular actuators that...
Deep Space Cryocooler System (DSCS), Phase I
National Aeronautics and Space Administration — As NASA missions continue to extend the horizon beyond near-Earth missions, higher performance systems must evolve to address the challenges of reduced power...
Dimensionally Stable Structural Space Cable, Phase I
National Aeronautics and Space Administration — In response to the need for an affordable exoplanet-analysis science mission, NASA has recently embarked on the ROSES Technology Development for Exoplanet Missions...
Deep Space Cryogenic Power Electronics, Phase I
National Aeronautics and Space Administration — Technology Application, Inc. (TAI) is proposing to demonstrate feasibility of implementing silicon germanium (SiGe) strained-gate technology in the power...
Long Duration Space Shelter Shielding, Phase I
National Aeronautics and Space Administration — Physical Sciences Inc. (PSI) has developed fiber reinforced ceramic composites for radiation shielding that can be used for external walls in long duration manned...
Classification of digital affine noncommutative geometries
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."
Study on a phase space representation of quantum theory
International Nuclear Information System (INIS)
Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.; Raboanary, R.
2013-01-01
A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.
Phase space model for transmission of light beam
International Nuclear Information System (INIS)
Fu Shinian
1989-01-01
Based on Fermat's principle of ray optics, the Hamiltonian of an optical ray is derived by comparison with classical mechanics. A phase space model of light beam is proposed, assuming that the light beam, regarded as a group of rays, can be described by an ellipse in the μ-phase space. Therefore, the transmission of light beam is represented by the phase space matrix transformation. By means of this non-wave formulation, the same results are obtained as those from wave equation such as Kogelnik's ABCD law. As an example of the application on this model, the matching problem of optical cavity is solved
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.
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
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
Holographic complexity and noncommutative gauge theory
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.
Group field theory with noncommutative metric variables.
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.
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/
Constraining the noncommutative spectral action via astrophysical observations.
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.
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
Thermo-Acoustic Convertor for Space Power, Phase II
National Aeronautics and Space Administration — In Phase Sunpower looked at Thermoacoustic Stirling Heat Engines (TASHEs). These ranged from a TASHE which was sized for the heat from a single General Purpose Heat...
Phase space descriptions for simplicial 4D geometries
International Nuclear Information System (INIS)
Dittrich, Bianca; Ryan, James P
2011-01-01
Starting from the canonical phase space for discretized (4D) BF theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection between different versions of Regge calculus and approaches using connection variables, such as loop quantum gravity. We find that on a fixed triangulation the (gauge invariant) phase space associated with loop quantum gravity is genuinely larger than the one for length and even area Regge calculus. Rather, it corresponds to the phase space of area-angle Regge calculus, as defined in [1] (prior to the imposition of gluing constraints, which ensure the metricity of the triangulation). Finally, we show that for a subclass of triangulations one can construct first-class Hamiltonian and diffeomorphism constraints leading to flat 4D spacetimes.
Wigner distribution, partial coherence, and phase-space optics
Bastiaans, M.J.
2009-01-01
The Wigner distribution is presented as a perfect means to treat partially coherent optical signals and their propagation through first-order optical systems from a radiometric and phase-space optical perspective
The Wigner phase-space description of collision processes
International Nuclear Information System (INIS)
Lee, H.W.
1984-01-01
The paper concerns the Wigner distribution function in collision theory. Wigner phase-space description of collision processes; some general consideration on Wigner trajectories; and examples of Wigner trajectories; are all discussed. (U.K.)
Phase-space distributions and orbital angular momentum
Directory of Open Access Journals (Sweden)
Pasquini B.
2014-06-01
Full Text Available We review the concept of Wigner distributions to describe the phase-space distributions of quarks in the nucleon, emphasizing the information encoded in these functions about the quark orbital angular momentum.
Phase space overpopulation at CERN and possible explanations
International Nuclear Information System (INIS)
Pratt, S.
1998-01-01
By combining information from correlations from Pb+Pb collisions at CERN, one comes to the conclusion that pionic phase space is significantly overpopulated compared to expectations based on chemical equilibrium. A variety of explanations will be addressed. (author)
Path integrals over phase space, their definition and simple properties
International Nuclear Information System (INIS)
Tarski, J.; Technische Univ. Clausthal, Clausthal-Zellerfeld
1981-10-01
Path integrals over phase space are defined in two ways. Some properties of these integrals are established. These properties concern the technique of integration and the quantization rule isup(-I)deltasub(q) p. (author)
Space-Ready Advanced Imaging System, Phase II
National Aeronautics and Space Administration — In this Phase II effort Toyon will increase the state-of-the-art for video/image systems. This will include digital image compression algorithms as well as system...
Joining Silicon Carbide Components for Space Propulsion, Phase I
National Aeronautics and Space Administration — This SBIR Phase I program will identify the joining materials and demonstrate the processes that are suited for construction of advanced ceramic matrix composite...
Simulating Nonlinear Dynamics of Deployable Space Structures, Phase I
National Aeronautics and Space Administration — To support NASA's vital interest in developing much larger solar array structures over the next 20 years, MotionPort LLC's Phase I SBIR project will strengthen...
An extensive phase space for the potential martian biosphere.
Jones, Eriita G; Lineweaver, Charles H; Clarke, Jonathan D
2011-12-01
We present a comprehensive model of martian pressure-temperature (P-T) phase space and compare it with that of Earth. Martian P-T conditions compatible with liquid water extend to a depth of ∼310 km. We use our phase space model of Mars and of terrestrial life to estimate the depths and extent of the water on Mars that is habitable for terrestrial life. We find an extensive overlap between inhabited terrestrial phase space and martian phase space. The lower martian surface temperatures and shallower martian geotherm suggest that, if there is a hot deep biosphere on Mars, it could extend 7 times deeper than the ∼5 km depth of the hot deep terrestrial biosphere in the crust inhabited by hyperthermophilic chemolithotrophs. This corresponds to ∼3.2% of the volume of present-day Mars being potentially habitable for terrestrial-like life.
Explaining Gibbsean phase space to second year students
International Nuclear Information System (INIS)
Vesely, Franz J
2005-01-01
A new approach to teaching introductory statistical physics is presented. We recommend making extensive use of the fact that even systems with a very few degrees of freedom may display chaotic behaviour. This permits a didactic 'bottom-up' approach, starting out with toy systems whose phase space may be depicted on a screen or blackboard, then proceeding to ever higher dimensions in Gibbsean phase space
Wigner function and Schroedinger equation in phase-space representation
International Nuclear Information System (INIS)
Chruscinski, Dariusz; Mlodawski, Krzysztof
2005-01-01
We discuss a family of quasidistributions (s-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space, they have a completely different interpretation
Controlling quantum interference in phase space with amplitude
Xue, Yinghong; Li, Tingyu; Kasai, Katsuyuki; Okada-Shudo, Yoshiko; Watanabe, Masayoshi; Zhang, Yun
2017-01-01
We experimentally show a quantum interference in phase space by interrogating photon number probabilities (n?=?2, 3, and 4) of a displaced squeezed state, which is generated by an optical parametric amplifier and whose displacement is controlled by amplitude of injected coherent light. It is found that the probabilities exhibit oscillations of interference effect depending upon the amplitude of the controlling light field. This phenomenon is attributed to quantum interference in phase space a...
On quantum mechanical phase-space wave functions
DEFF Research Database (Denmark)
Wlodarz, Joachim J.
1994-01-01
An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...... function. The relationship to the recent results by Torres-Vega and Frederick [J. Chem. Phys. 98, 3103 (1993)] is also discussed....
Elementary particles and emergent phase space
Zenczykowski, Piotr
2014-01-01
The Standard Model of elementary particles, although very successful, contains various elements that are put in by hand. Understanding their origin requires going beyond the model and searching for ""new physics"". The present book elaborates on one particular proposal concerning such physics. While the original conception is 50 years old, it has not lost its appeal over time. Its basic idea is that space - an arena of events treated in the Standard Model as a classical background - is a concept which emerges from a strictly discrete quantum layer in the limit of large quantum numbers. This bo
About the phase space of SL(3) black holes
Energy Technology Data Exchange (ETDEWEB)
Cabo-Bizet, Alejandro [SISSA and INFN, Via Bonomea 265, 34128 Trieste (Italy); Giraldo-Rivera, V.I. [SISSA and INFN, Via Bonomea 265, 34128 Trieste (Italy); ICTP, Strada Costiera 11, 34014 Trieste (Italy)
2015-03-17
In this note we address some issues of recent interest, related to the asymptotic symmetry algebra of higher spin black holes in sl(3,ℝ)×sl(3,ℝ) Chern Simons (CS) formulation. We compute the fixed time Dirac bracket algebra that acts on two different phase spaces. Both of these spaces contain black holes as zero modes. The result for one of these phase spaces is explicitly shown to be isomorphic to W{sub 3}{sup (2)}×W{sub 3}{sup (2)} in first order perturbations.
Using the Phase Space to Design Complexity
DEFF Research Database (Denmark)
Heinrich, Mary Katherine; Ayres, Phil
2016-01-01
Architecture that is responsive, adaptive, or interactive can contain active architectural elements or robotic sensor-actuator systems. The consideration of architectural robotic elements that utilize distributed control and distributed communication allows for self-organization, emergence...... with materializations left by robot swarms or elements, rather than robots' internal states. We detail a case study examination of design methodology using the formation space concept for assessment and decision-making in the design of active architectural artifacts......., and evolution on site in real-time. The potential complexity of behaviors in such architectural robotic systems requires design methodology able to encompass a range of possible outcomes, rather than a single solution. We present an approach of adopting an aspect of complexity science and applying...
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
Coordinate, Momentum and Dispersion operators in Phase space representation
International Nuclear Information System (INIS)
Rakotoson, H.; Raoelina Andriambololona; Ranaivoson, R.T.R.; Raboanary, R.
2017-07-01
The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works. We begin in the introduction section with a recall about the concept of representation of operators on wave function spaces. Then, we show that in the case of the phase space representation the coordinate and momentum operators can be represented either with differential operators or with matrices. The explicit expressions of both the differential operators and matrices representations are established. Multidimensional generalization of the obtained results are performed and phase space representation of dispersion operators are given.
Hamiltonian flow over saddles for exploring molecular phase space structures
Farantos, Stavros C.
2018-03-01
Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue `Modern theoretical chemistry'.
Source reconstruction using phase space beam summation technique
International Nuclear Information System (INIS)
Graubart, Gideon.
1990-10-01
In this work, the phase-space beam summation technique (PSBS), is applied to back propagation and inverse source problems. The PSBS expresses the field as a superposition of shifted and tilted beams. This phase space spectrum of beams is matched to the source distribution via an amplitude function which expresses the local spectrum of the source function in terms of a local Fourier transform. In this work, the emphasis is on the phase space processing of the data, on the information content of this data and on the back propagation scheme. More work is still required to combine this back propagation approach in a full, multi experiment inverse scattering scheme. It is shown that the phase space distribution of the data, computed via the local spectrum transform, is localized along lines that define the local arrival direction of the wave data. We explore how the choice of the beam width affects the compactification of this distribution, and derive criteria for choosing a window that optimizes this distribution. It should be emphasized that compact distribution implies fewer beams in the back propagation scheme and therefore higher numerical efficiency and better physical insight. Furthermore it is shown how the local information property of the phase space representation can be used to improve the performance of this simple back propagation problem, in particular with regard to axial resolution; the distance to the source can be determined by back propagating only the large angle phase space beams that focus on the source. The information concerning transverse distribution of the source, on the other hand, is contained in the axial phase space region and can therefore be determined by the corresponding back propagating beams. Because of the global nature of the plane waves propagators the conventional plane wave back propagation scheme does not have the same 'focusing' property, and therefore suffers from lack of information localization and axial resolution. The
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
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.
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
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
Quantum de Finetti theorem in phase-space representation
International Nuclear Information System (INIS)
Leverrier, Anthony; Cerf, Nicolas J.
2009-01-01
The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).
Phase space treatment of optical beams
International Nuclear Information System (INIS)
Nemes, G.; Teodorescu, I.E.; Nemes, M.
1984-01-01
The lecture reveals the possibility of treating optical beams and systems using the PS concept. In the first part some well-known concepts and results of charged particle optics are applied to optical beam and systems. Attention is paid to the PSE concept as to beina a beam invariant according to Liouville's theorem. In the second part some simple optical sources, their PSE and their transforms through simple optical elements are theoretically presented. An experimental method and a device for PSE measurements are presented in the third part. In the fourth part the main problems of the linear system theory which were applied to electrical circuits in the time (or freo.uency) domain and to optical systems in the bidimensional space of spatial coordinates (or spatial frequencies) are applied to stigmatic optical systems in the bidimensional PS (spatial coordinate, angle). Some examples of applying PS concepts in optics are presented in the fifth part. The lecture is mainly based on original results some of them being previously unpublished. (authors)
Phase space eigenfunctions of multidimensional quadratic Hamiltonians
International Nuclear Information System (INIS)
Dodonov, V.V.; Man'ko, V.I.
1986-01-01
We obtain the explicit expressions for phace space eigenfunctions (PSE),i.e. Weyl's symbols of dyadic operators like vertical stroken> ,vertical strokem>, being the solution of the Schroedinger equation with the Hamiltonian which is a quite arbitrary multidimensional quadratic form of the operators of Cartesian coordinates and conjugated to them momenta with time-dependent coefficients. It is shown that for an arbitrary quadratic Hamiltonian one can always construct the set of completely factorized PSE which are products of N factors, each factor being dependent only on two arguments for nnot=m and on a single argument for n=m. These arguments are nothing but constants of motion of the correspondent classical system. PSE are expressed in terms of the associated Laguerre polynomials in the case of a discrete spectrum and in terms of the Airy functions in the continuous spectrum case. Three examples are considered: a harmonic oscillator with a time-dependent frequency, a charged particle in a nonstationary uniform magnetic field, and a particle in a time-dependent uniform potential field. (orig.)
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.
Intelligent Monte Carlo phase-space division and importance estimation
International Nuclear Information System (INIS)
Booth, T.E.
1989-01-01
Two years ago, a quasi-deterministic method (QD) for obtaining the Monte Carlo importance function was reported. Since then, a number of very complex problems have been solved with the aid of QD. Not only does QD estimate the importance far faster than the (weight window) generator currently in MCNP, QD requires almost no user intervention in contrast to the generator. However, both the generator and QD require the user to divide the phase-space into importance regions. That is, both methods will estimate the importance of a phase-space region, but the user must define the regions. In practice this is tedious and time consuming, and many users are not particularly good at defining sensible importance regions. To make full use of the fat that QD is capable of getting good importance estimates in tens of thousands of phase-space regions relatively easily, some automatic method for dividing the phase space will be useful and perhaps essential. This paper describes recent progress toward an automatic and intelligent phase-space divider
Prime divisors and noncommutative valuation theory
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...
Diffeomorphisms as symplectomorphisms in history phase space: Bosonic string model
International Nuclear Information System (INIS)
Kouletsis, I.; Kuchar, K.V.
2002-01-01
The structure of the history phase space G of a covariant field system and its history group (in the sense of Isham and Linden) is analyzed on an example of a bosonic string. The history space G includes the time map T from the spacetime manifold (the two-sheet) Y to a one-dimensional time manifold T as one of its configuration variables. A canonical history action is posited on G such that its restriction to the configuration history space yields the familiar Polyakov action. The standard Dirac-ADM action is shown to be identical with the canonical history action, the only difference being that the underlying action is expressed in two different coordinate charts on G. The canonical history action encompasses all individual Dirac-ADM actions corresponding to different choices T of foliating Y. The history Poisson brackets of spacetime fields on G induce the ordinary Poisson brackets of spatial fields in the instantaneous phase space G 0 of the Dirac-ADM formalism. The canonical history action is manifestly invariant both under spacetime diffeomorphisms Diff Y and temporal diffeomorphisms Diff T. Both of these diffeomorphisms are explicitly represented by symplectomorphisms on the history phase space G. The resulting classical history phase space formalism is offered as a starting point for projection operator quantization and consistent histories interpretation of the bosonic string model
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
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)
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.
Phase-space evolution of x-ray coherence in phase-sensitive imaging.
Wu, Xizeng; Liu, Hong
2008-08-01
X-ray coherence evolution in the imaging process plays a key role for x-ray phase-sensitive imaging. In this work we present a phase-space formulation for the phase-sensitive imaging. The theory is reformulated in terms of the cross-spectral density and associated Wigner distribution. The phase-space formulation enables an explicit and quantitative account of partial coherence effects on phase-sensitive imaging. The presented formulas for x-ray spectral density at the detector can be used for performing accurate phase retrieval and optimizing the phase-contrast visibility. The concept of phase-space shearing length derived from this phase-space formulation clarifies the spatial coherence requirement for phase-sensitive imaging with incoherent sources. The theory has been applied to x-ray Talbot interferometric imaging as well. The peak coherence condition derived reveals new insights into three-grating-based Talbot-interferometric imaging and gratings-based x-ray dark-field imaging.
Secondary beam line phase space measurement and modeling at LAMPF
International Nuclear Information System (INIS)
Floyd, R.; Harrison, J.; Macek, R.; Sanders, G.
1979-01-01
Hardware and software have been developed for precision on-line measurement and fitting of secondary beam line phase space parameters. A system consisting of three MWPC planes for measuring particle trajectories, in coincidence with a time-of-flight telescope and a range telescope for particle identification, has been interfaced to a computer. Software has been developed for on-line track reconstruction, application of experimental cuts, and fitting of two-dimensional phase space ellipses for each particle species. The measured distributions have been found to agree well with the predictions of the Monte Carlo program DECAY TURTLE. The fitted phase space ellipses are a useful input to optimization routines, such as TRANSPORT, used to search for superior tunes. Application of this system to the LAMPF Stopped Muon Channel is described
Augmenting Phase Space Quantization to Introduce Additional Physical Effects
Robbins, Matthew P. G.
Quantum mechanics can be done using classical phase space functions and a star product. The state of the system is described by a quasi-probability distribution. A classical system can be quantized in phase space in different ways with different quasi-probability distributions and star products. A transition differential operator relates different phase space quantizations. The objective of this thesis is to introduce additional physical effects into the process of quantization by using the transition operator. As prototypical examples, we first look at the coarse-graining of the Wigner function and the damped simple harmonic oscillator. By generalizing the transition operator and star product to also be functions of the position and momentum, we show that additional physical features beyond damping and coarse-graining can be introduced into a quantum system, including the generalized uncertainty principle of quantum gravity phenomenology, driving forces, and decoherence.
Phase space view of quantum mechanical systems and Fisher information
International Nuclear Information System (INIS)
Nagy, Á.
2016-01-01
Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Phase space view of quantum mechanical systems and Fisher information
Energy Technology Data Exchange (ETDEWEB)
Nagy, Á., E-mail: anagy@madget.atomki.hu
2016-06-17
Highlights: • Phase-space Fisher information coming from the canonical distribution is derived for the ground state of quantum mechanical systems. • Quantum mechanical phase-space Fisher information contains an extra term due to the position dependence of the temperature. • A complete analogy to the classical case is demonstrated for the linear harmonic oscillator. - Abstract: Pennini and Plastino showed that the form of the Fisher information generated by the canonical distribution function reflects the intrinsic structure of classical mechanics. Now, a quantum mechanical generalization of the Pennini–Plastino theory is presented based on the thermodynamical transcription of the density functional theory. Comparing to the classical case, the phase-space Fisher information contains an extra term due to the position dependence of the temperature. However, for the special case of constant temperature, the expression derived bears resemblance to the classical one. A complete analogy to the classical case is demonstrated for the linear harmonic oscillator.
Quantum phase space with a basis of Wannier functions
Fang, Yuan; Wu, Fan; Wu, Biao
2018-02-01
A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn’s method and Löwdin method such that each Wannier function is localized at a Planck cell. With these Wannier functions one can map a wave function unitarily onto phase space. Various examples are used to illustrate our method and compare it to Wigner function. The advantage of our method is that it can smooth out the oscillations in wave functions without losing any information and is potentially a better tool in studying quantum-classical correspondence. In addition, we point out that our method can be used for time-frequency analysis of signals.
Grassmann phase space methods for fermions. II. Field theory
Energy Technology Data Exchange (ETDEWEB)
Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)
2017-02-15
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.
Grassmann phase space methods for fermions. II. Field theory
International Nuclear Information System (INIS)
Dalton, B.J.; Jeffers, J.; Barnett, S.M.
2017-01-01
In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.
Quantum phase space points for Wigner functions in finite-dimensional spaces
Luis Aina, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas.
Quantum phase space points for Wigner functions in finite-dimensional spaces
International Nuclear Information System (INIS)
Luis, Alfredo
2004-01-01
We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas
Multiplexed phase-space imaging for 3D fluorescence microscopy.
Liu, Hsiou-Yuan; Zhong, Jingshan; Waller, Laura
2017-06-26
Optical phase-space functions describe spatial and angular information simultaneously; examples of optical phase-space functions include light fields in ray optics and Wigner functions in wave optics. Measurement of phase-space enables digital refocusing, aberration removal and 3D reconstruction. High-resolution capture of 4D phase-space datasets is, however, challenging. Previous scanning approaches are slow, light inefficient and do not achieve diffraction-limited resolution. Here, we propose a multiplexed method that solves these problems. We use a spatial light modulator (SLM) in the pupil plane of a microscope in order to sequentially pattern multiplexed coded apertures while capturing images in real space. Then, we reconstruct the 3D fluorescence distribution of our sample by solving an inverse problem via regularized least squares with a proximal accelerated gradient descent solver. We experimentally reconstruct a 101 Megavoxel 3D volume (1010×510×500µm with NA 0.4), demonstrating improved acquisition time, light throughput and resolution compared to scanning aperture methods. Our flexible patterning scheme further allows sparsity in the sample to be exploited for reduced data capture.
Incomplete Detection of Nonclassical Phase-Space Distributions
Bohmann, M.; Tiedau, J.; Bartley, T.; Sperling, J.; Silberhorn, C.; Vogel, W.
2018-02-01
We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.
Neutron guide geometries for homogeneous phase space volume transformation
International Nuclear Information System (INIS)
Stüßer, N.; Bartkowiak, M.; Hofmann, T.
2014-01-01
We extend geometries for recently developed optical guide systems that perform homogeneous phase space volume transformations on neutron beams. These modules allow rotating beam directions and can simultaneously compress or expand the beam cross-section. Guide systems combining these modules offer the possibility to optimize ballistic guides with and without direct view on the source and beam splitters. All systems are designed for monochromatic beams with a given divergence. The case of multispectral beams with wavelength-dependent divergence distributions is addressed as well. - Highlights: • Form invariant volume transformation in phase space. • Geometrical approach. • Ballistic guide, beam splitter, beam bender
Neutron guide geometries for homogeneous phase space volume transformation
Energy Technology Data Exchange (ETDEWEB)
Stüßer, N., E-mail: stuesser@helmholtz-berlin.de; Bartkowiak, M.; Hofmann, T.
2014-06-01
We extend geometries for recently developed optical guide systems that perform homogeneous phase space volume transformations on neutron beams. These modules allow rotating beam directions and can simultaneously compress or expand the beam cross-section. Guide systems combining these modules offer the possibility to optimize ballistic guides with and without direct view on the source and beam splitters. All systems are designed for monochromatic beams with a given divergence. The case of multispectral beams with wavelength-dependent divergence distributions is addressed as well. - Highlights: • Form invariant volume transformation in phase space. • Geometrical approach. • Ballistic guide, beam splitter, beam bender.
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.
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)
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
Relativistic algebraic spinors and quantum motions in phase space
International Nuclear Information System (INIS)
Holland, P.R.
1986-01-01
Following suggestions of Schonberg and Bohm, we study the tensorial phase space representation of the Dirac and Feynman-Gell-Mann equations in terms of the complex Dirac algebra C 4 , a Jordan-Wigner algebra G 4 , and Wigner transformations. To do this we solve the problem of the conditions under which elements in C 4 generate minimal ideals, and extend this to G 4 . This yields the linear theory of Dirac spin spaces and tensor representations of Dirac spinors, and the spin-1/2 wave equations are represented through fermionic state vectors in a higher space as a set of interconnected tensor relations
Grassmann phase space theory and the Jaynes–Cummings model
International Nuclear Information System (INIS)
Dalton, B.J.; Garraway, B.M.; Jeffers, J.; Barnett, S.M.
2013-01-01
The Jaynes–Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes–Cummings model based on expanding the state vector in terms of products of atomic and n-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects. In quantum optics however, the behaviour of the bosonic quantum EM field is often treated using phase space methods, where the bosonic mode annihilation and creation operators are represented by c-number phase space variables, with the density operator represented by a distribution function of these variables. Fokker–Planck equations for the distribution function are obtained, and either used directly to determine quantities of experimental interest or used to develop c-number Langevin equations for stochastic versions of the phase space variables from which experimental quantities are obtained as stochastic averages. Phase space methods have also been developed to include atomic systems, with the atomic spin operators being represented by c-number phase space variables, and distribution functions involving these variables and those for any bosonic modes being shown to satisfy Fokker–Planck equations from which c-number Langevin equations are
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
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
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
Frame transforms, star products and quantum mechanics on phase space
International Nuclear Information System (INIS)
Aniello, P; Marmo, G; Man'ko, V I
2008-01-01
Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G x G. These transforms have remarkable properties. In particular, their ranges are reproducing kernel Hilbert spaces endowed with a suitable 'star product' which mimics, at the level of functions, the original product of operators. A 'phase space formulation' of quantum mechanics relying on the frame transforms introduced in the present paper, and the link of these maps with both the Wigner transform and the wavelet transform are discussed
International Nuclear Information System (INIS)
Pons, Josep M
2003-01-01
Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms being projectable to phase space, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of general relativity, or other generally covariant theories, only closes as a soft algebra and not as a Lie algebra. The deep relationship between these two issues is clarified. In particular, we see that the second one may be understood as a side effect of the procedure to solve the first. It is explicitly shown how the adoption of specific metric-dependent diffeomorphisms, as a way to achieve projectability, causes the algebra of gauge generators (constraints) in phase space not to be a Lie algebra -with structure constants - but a soft algebra - with structure functions
International Nuclear Information System (INIS)
Henggeler, W.; Boehm, M.
2003-11-01
Both reports - part I by Wolfgang Henggeler and part II by Martin Boehm - serve as a comprehensive basis for the realisation of a PST (phase-space transformation) instrument coupled either to cold or ultra-cold neutrons, respectively. This publication accidentally coincides with the 200 th birthday of the Austrian physicist C.A. Doppler who discovered the principle (i.e., the effect denoted later by his name) giving rise to the phase-space transformation described in the present work. (author)
On phase-space representations of quantum mechanics using ...
Indian Academy of Sciences (India)
2016-07-16
Jul 16, 2016 ... (2016) 87: 27 c Indian Academy of Sciences ..... converted to the language of the phase-space, and in .... as Husimi function, a name given in recognition of the work of .... the equations only differ from each other in the sign.
Deformation quantization: Quantum mechanics lives and works in phase space
Directory of Open Access Journals (Sweden)
Zachos Cosmas K.
2014-01-01
A sampling of such intriguing techniques and methods has already been published in C. K. Zachos, Int Jou Mod Phys A17 297-316 (2002, and T. L. Curtright, D. B. Fairlie, and C. K. Zachos, A Concise Treatise on Quantum Mechanics in Phase Space, (Imperial Press & World Scientific, 2014.
Lattice quantum phase space and Yang-Baxter equation
International Nuclear Information System (INIS)
Djemai, A.E.F.
1995-04-01
In this work, we show that it is possible to construct the quantum group which preserves the quantum symplectic structure introduced in the context of the matrix Hamiltonian formalism. We also study the braiding existing behind the lattice quantum phase space, and present another type of non-trivial solution to the resulting Yang-Baxter equation. (author). 20 refs, 1 fig
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the ...
Quantum dynamics via a time propagator in Wigner's phase space
DEFF Research Database (Denmark)
Grønager, Michael; Henriksen, Niels Engholm
1995-01-01
We derive an expression for a short-time phase space propagator. We use it in a new propagation scheme and demonstrate that it works for a Morse potential. The propagation scheme is used to propagate classical distributions which do not obey the Heisenberg uncertainty principle. It is shown that ...... as a part of the sampling function. ©1995 American Institute of Physics....
Phase-Space Models of Solitary Electron Hoies
DEFF Research Database (Denmark)
Lynov, Jens-Peter; Michelsen, Poul; Pécseli, Hans
1985-01-01
Two different phase-space models of solitary electron holes are investigated and compared with results from computer simulations of an actual laboratory experiment, carried out in a strongly magnetized, cylindrical plasma column. In the two models, the velocity distribution of the electrons...
Phase space overpopulation at CERN and possible explanations
International Nuclear Information System (INIS)
Pratt, S.
1999-01-01
Complete text of publication follows. By combining information from correlations from Pb+Pb collisions at CERN, one comes to the conclusion that pionic phase space is significantly overpopulated compared to expectations based on chemical equilibrium. A variety of explanations will be addressed. (author)
Quantum Potential and Symmetries in Extended Phase Space
Directory of Open Access Journals (Sweden)
Sadollah Nasiri
2006-06-01
Full Text Available The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space. It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation. The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one. The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation.
Phase-space exploration in nuclear giant resonance decay
International Nuclear Information System (INIS)
Drozdz, S.; Nishizaki, S.; Wambach, J.; Speth, J.
1995-01-01
The rate of phase-space exploration in the decay of isovector and isoscalar giant quadrupole resonances in 40 Ca is analyzed. The study is based on the time dependence of the survival probability and of the spectrum of generalized entropies evaluated in the space of one-particle--one-hole (1p-1h) and 2p-2h states. Three different cases for the level distribution of 2p-2h background states, corresponding to (a) high degeneracy, (b) classically regular motion, and (c) classically chaotic motion, are studied. In the latter case the isovector excitation evolves almost statistically while the isoscalar excitation remains largely localized, even though it penetrates the whole available phase space
Quantum Hamiltonian differential geometry: how does quantization affect space?
International Nuclear Information System (INIS)
Aldrovandi, R.
1993-01-01
Quantum phase space is given a description which entirely parallels the usual presentation of Classical Phase Space. A particular Schwinger unitary operator basis, in which the expansion of each operator is its own Weyl expression, is specially convenient for the purpose. The quantum Hamiltonian structure obtains from the classical structure by the conversion of the classical pointwise product of dynamical quantities into the noncommutative star product of Wigner functions. The main qualitative difference in the general structure is that, in the quantum case, the inverse symplectic matrix is not simply antisymmetric. This difference leads to the presence of braiding in the backstage of Quantum Mechanics. (author)
Review on two-phase flow instabilities in narrow spaces
International Nuclear Information System (INIS)
Tadrist, L.
2007-01-01
Instabilities in two-phase flow have been studied since the 1950s. These phenomena may appear in power generation and heat transfer systems where two-phase flow is involved. Because of thermal management in small size systems, micro-fluidics plays an important role. Typical processes must be considered when the channel hydraulic diameter becomes very small. In this paper, a brief review of two-phase flow instabilities encountered in channels having hydraulic diameters greater than 10 mm are presented. The main instability types are discussed according to the existing experimental results and models. The second part of the paper examines two-phase flow instabilities in narrow spaces. Pool and flow boiling cases are considered. Experiments as well as theoretical models existing in the literature are examined. It was found that several experimental works evidenced these instabilities meanwhile only limited theoretical developments exist in the literature. In the last part of the paper an interpretation of the two-phase flow instabilities linked to narrow spaces are presented. This approach is based on characteristic time scales of the two-phase flow and bubble growth in the capillaries
Independence and totalness of subspaces in phase space methods
Vourdas, A.
2018-04-01
The concepts of independence and totalness of subspaces are introduced in the context of quasi-probability distributions in phase space, for quantum systems with finite-dimensional Hilbert space. It is shown that due to the non-distributivity of the lattice of subspaces, there are various levels of independence, from pairwise independence up to (full) independence. Pairwise totalness, totalness and other intermediate concepts are also introduced, which roughly express that the subspaces overlap strongly among themselves, and they cover the full Hilbert space. A duality between independence and totalness, that involves orthocomplementation (logical NOT operation), is discussed. Another approach to independence is also studied, using Rota's formalism on independent partitions of the Hilbert space. This is used to define informational independence, which is proved to be equivalent to independence. As an application, the pentagram (used in discussions on contextuality) is analysed using these concepts.
Key-space analysis of double random phase encryption technique
Monaghan, David S.; Gopinathan, Unnikrishnan; Naughton, Thomas J.; Sheridan, John T.
2007-09-01
We perform a numerical analysis on the double random phase encryption/decryption technique. The key-space of an encryption technique is the set of possible keys that can be used to encode data using that technique. In the case of a strong encryption scheme, many keys must be tried in any brute-force attack on that technique. Traditionally, designers of optical image encryption systems demonstrate only how a small number of arbitrary keys cannot decrypt a chosen encrypted image in their system. However, this type of demonstration does not discuss the properties of the key-space nor refute the feasibility of an efficient brute-force attack. To clarify these issues we present a key-space analysis of the technique. For a range of problem instances we plot the distribution of decryption errors in the key-space indicating the lack of feasibility of a simple brute-force attack.
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
From stochastic phase-space evolution to brownian motion in collective space
Energy Technology Data Exchange (ETDEWEB)
Benhassine, B. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France)); Farine, M. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France) Ecole Navale, Lamveoc-Loulmic, 29 Brest-Naval (France)); Hernandez, E.S. (Dept. de Fisica - Facultad de Ciencias Exactas y Naturales, Univ. de Buenos Aires (Argentina)); Idier, D. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France)); Remaud, B. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France)); Sebille, F. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France))
1994-01-24
Within the framework of stochastic transport equations in phase space, we study the dynamics of fluctuations on collective variables in homogeneous fermion systems. The transport coefficients are formally deduced in the relaxation-time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations: respectively, the BUU/Landau-Vlasov equation for the average phase-space trajectories and the equations for the averages and dispersions of the observables. Independently, we derive the general covariance matrix of phase-space fluctuations and then by projection, the dispersion on collective variables at equilibrium. Detailed numerical applications of the formalism are given; they show that the dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy, whatever is its degree of thermalization. (orig.)
From stochastic phase-space evolution to brownian motion in collective space
International Nuclear Information System (INIS)
Benhassine, B.; Farine, M.; Hernandez, E.S.; Idier, D.; Remaud, B.; Sebille, F.
1994-01-01
Within the framework of stochastic transport equations in phase space, we study the dynamics of fluctuations on collective variables in homogeneous fermion systems. The transport coefficients are formally deduced in the relaxation-time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations: respectively, the BUU/Landau-Vlasov equation for the average phase-space trajectories and the equations for the averages and dispersions of the observables. Independently, we derive the general covariance matrix of phase-space fluctuations and then by projection, the dispersion on collective variables at equilibrium. Detailed numerical applications of the formalism are given; they show that the dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy, whatever is its degree of thermalization. (orig.)
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.
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.)
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.
Probabilistic Q-function distributions in fermionic phase-space
International Nuclear Information System (INIS)
Rosales-Zárate, Laura E C; Drummond, P D
2015-01-01
We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used Grassmann methods that do not give probabilities. The fermionic Q-function obtained here is constructed using normally ordered Gaussian operators, which include both non-interacting thermal density matrices and BCS states. We prove that the Q-function exists for any density matrix, is real and positive, and has moments that correspond to Fermi operator moments. It is defined on a finite symmetric phase-space equivalent to the space of real, antisymmetric matrices. This has the natural SO(2M) symmetry expected for Majorana fermion operators. We show that there is a physical interpretation of the Q-function: it is the relative probability for observing a given Gaussian density matrix. The distribution has a uniform probability across the space at infinite temperature, while for pure states it has a maximum value on the phase-space boundary. The advantage of probabilistic representations is that they can be used for computational sampling without a sign problem. (fast track communication)
Kinetic solvers with adaptive mesh in phase space
Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.
2013-12-01
An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a “tree of trees” (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.
From stochastic phase space evolution to Brownian motion in collective space
International Nuclear Information System (INIS)
Benhassine, B.; Farine, M.; Hernandez, E.S.; Idier, D.; Remaud, B.; Sebille, F.
1993-01-01
Within the framework of stochastic transport equations in phase space, the dynamics of fluctuations on collective variables in homogeneous fermion systems is studied. The transport coefficients are formally deduced in the relaxation time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations. Independently, the general covariance matrix of phase space fluctuations and the dispersion on collective variables at equilibrium are derived. Detailed numerical applications show that dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy whatever is its degree of thermalization. (authors). 16 refs., 12 figs
TRANSVERSE PHASE SPACE PAINTING FOR SNS ACCUMULATOR RING INJECTION.
Energy Technology Data Exchange (ETDEWEB)
BEEBE-WANG,J.; LEE,Y.Y.; RAPARIA,D.; WEI,J.
1999-03-29
The result of investigation and comparison of a series of transverse phase space painting schemes for the injection of SNS accumulator ring [1] is reported. In this computer simulation study, the focus is on the creation of closed orbit bumps that give desired distributions at the target. Space charge effects such as tune shift, emittance growth and beam losses are considered. The results of pseudo end-to-end simulations from the injection to the target through the accumulator ring and Ring to Target Beam Transfer (RTBT) system [2] are presented and discussed.
Identifying phase-space boundaries with Voronoi tessellations
International Nuclear Information System (INIS)
Debnath, Dipsikha; Matchev, Konstantin T.; Gainer, James S.; Kilic, Can; Yang, Yuan-Pao; Kim, Doojin
2016-01-01
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis. (orig.)
Identifying phase-space boundaries with Voronoi tessellations
Energy Technology Data Exchange (ETDEWEB)
Debnath, Dipsikha; Matchev, Konstantin T. [University of Florida, Physics Department, Gainesville, FL (United States); Gainer, James S. [University of Hawaii, Department of Physics and Astronomy, Honolulu, HI (United States); Kilic, Can; Yang, Yuan-Pao [The University of Texas at Austin, Theory Group, Department of Physics and Texas Cosmology Center, Austin, TX (United States); Kim, Doojin [University of Florida, Physics Department, Gainesville, FL (United States); CERN, Theory Division, Geneva 23 (Switzerland)
2016-11-15
Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis. (orig.)
Quantum dynamical time evolutions as stochastic flows on phase space
International Nuclear Information System (INIS)
Combe, P.; Rodriguez, R.; Guerra, F.; Sirigue, M.; Sirigue-Collin, M.
1984-01-01
We are mainly interested in describing the time development of the Wigner functions by means of stochastic processes. In the second section we recall the main properties of the Wigner functions as well as those of their Fourier transform. In the next one we derive the evolution equation of these functions for a class of Hamiltonians and we give a probabilistic expression for the solution of these equations by means of a stochastic flow in phase space which reminds of the classical flows. In the last section we remark that the previously defined flow can be extended to the bounded continuous functions on phase space and that this flow conserves the cone generated by the Wigner functions. (orig./HSI)
Correlation dimension and phase space contraction via extreme value theory
Faranda, Davide; Vaienti, Sandro
2018-04-01
We show how to obtain theoretical and numerical estimates of correlation dimension and phase space contraction by using the extreme value theory. The maxima of suitable observables sampled along the trajectory of a chaotic dynamical system converge asymptotically to classical extreme value laws where: (i) the inverse of the scale parameter gives the correlation dimension and (ii) the extremal index is associated with the rate of phase space contraction for backward iteration, which in dimension 1 and 2, is closely related to the positive Lyapunov exponent and in higher dimensions is related to the metric entropy. We call it the Dynamical Extremal Index. Numerical estimates are straightforward to obtain as they imply just a simple fit to a univariate distribution. Numerical tests range from low dimensional maps, to generalized Henon maps and climate data. The estimates of the indicators are particularly robust even with relatively short time series.
A device for automated phase space measurement of ion beams
International Nuclear Information System (INIS)
Lukas, J.; Priller, A.; Steier, P.
2007-01-01
Equipment for automated phase-space measurements was developed at the VERA Lab. The measurement of the beam's intensity distribution, as well as its relative position with respect to the reference orbit is performed at two locations along the beam line. The device basically consists of moveable slits and a beam profile monitor, which are both coordinated and controlled by an embedded controller. The operating system of the controller is based on Linux with real-time extension. It controls the movement of the slits and records the data synchronized to the movement of the beam profile monitor. The data is sent via TCP/IP to the data acquisition system of VERA where visualization takes place. The duration of one phase space measurement is less than 10 s, which allows for using the device during routine beam tuning
Lin, Chao; Shen, Xueju; Li, Zengyan
2013-07-01
The key space of phase encryption algorithm using discrete random phase mask is investigated by numerical simulation in this paper. Random phase mask with finite and discrete phase levels is considered as the core component in most practical optical encryption architectures. The key space analysis is based on the design criteria of discrete random phase mask. The role of random amplitude mask and random phase mask in optical encryption system is identified from the perspective of confusion and diffusion. The properties of discrete random phase mask in a practical double random phase encoding scheme working in both amplitude encoding (AE) and phase encoding (PE) modes are comparably analyzed. The key space of random phase encryption algorithm is evaluated considering both the encryption quality and the brute-force attack resistibility. A method for enlarging the key space of phase encryption algorithm is also proposed to enhance the security of optical phase encryption techniques.
Torus as phase space: Weyl quantization, dequantization, and Wigner formalism
Energy Technology Data Exchange (ETDEWEB)
Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it [Dipartimento di Matematica, Università di Bari, I-70125 Bari (Italy)
2016-08-15
The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.
The Helmholtz Hierarchy: Phase Space Statistics of Cold Dark Matter
Tassev, Svetlin
2010-01-01
We present a new formalism to study large-scale structure in the universe. The result is a hierarchy (which we call the "Helmholtz Hierarchy") of equations describing the phase space statistics of cold dark matter (CDM). The hierarchy features a physical ordering parameter which interpolates between the Zel'dovich approximation and fully-fledged gravitational interactions. The results incorporate the effects of stream crossing. We show that the Helmholtz hierarchy is self-consistent and obeys...
Phase space analysis of some interacting Chaplygin gas models
Energy Technology Data Exchange (ETDEWEB)
Khurshudyan, M. [Academy of Sciences of Armenia, Institute for Physical Research, Ashtarak (Armenia); Tomsk State University of Control Systems and Radioelectronics, Laboratory for Theoretical Cosmology, Tomsk (Russian Federation); Tomsk State Pedagogical University, Department of Theoretical Physics, Tomsk (Russian Federation); Myrzakulov, R. [Eurasian National University, Eurasian International Center for Theoretical Physics, Astana (Kazakhstan)
2017-02-15
In this paper we discuss a phase space analysis of various interacting Chaplygin gas models in general relativity. Linear and nonlinear sign changeable interactions are considered. For each case appropriate late time attractors of field equations are found. The Chaplygin gas is one of the dark fluids actively considered in modern cosmology due to the fact that it is a joint model of dark energy and dark matter. (orig.)
A geometric view on BRST extension of the phase space
International Nuclear Information System (INIS)
Kyuldjiev, A.
1994-11-01
The role of complex polarizations is emphasized as providing coordinate-free approach to creation and annihilation operators needed for particle interpretation. With their help a proposition is made for explanation of BRST extension of the phase space due to fixing to zero the number of particles corresponding to constraint functions. The procedure treats the case when no group action is assumed and does not require any form of supersymmetry. (author). 19 refs
Quantum-deformed geometry on phase-space
International Nuclear Information System (INIS)
Gozzi, E.; Reuter, M.
1992-12-01
In this paper we extend the standard Moyal formalism to the tangent and cotangent bundle of the phase-space of any hamiltonian mechanical system. In this manner we build the quantum analog of the classical hamiltonian vector-field of time evolution and its associated Lie-derivative. We also use this extended Moyal formalism to develop a quantum analog of the Cartan calculus on symplectic manifolds. (orig.)
Braiding transformation, entanglement swapping, and Berry phase in entanglement space
International Nuclear Information System (INIS)
Chen Jingling; Ge Molin; Xue Kang
2007-01-01
We show that braiding transformation is a natural approach to describe quantum entanglement by using the unitary braiding operators to realize entanglement swapping and generate the Greenberger-Horne-Zeilinger states as well as the linear cluster states. A Hamiltonian is constructed from the unitary R i,i+1 (θ,φ) matrix, where φ=ωt is time-dependent while θ is time-independent. This in turn allows us to investigate the Berry phase in the entanglement space
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
2017-02-22
Feb 22, 2017 ... i.e., ρ(θ,q ,p |q,p,t) is a measure of the interference effects associated ... an oscillating electric field, when the initial state is cho- sen as a .... The conclusive effect is that. A±(q,p,t) ...... wave functions ±(q,p,t) stem from the time depen- dence of ..... define a two-dimensional cell in phase space, which is centred ...
Quantum tomography, phase-space observables and generalized Markov kernels
International Nuclear Information System (INIS)
Pellonpaeae, Juha-Pekka
2009-01-01
We construct a generalized Markov kernel which transforms the observable associated with the homodyne tomography into a covariant phase-space observable with a regular kernel state. Illustrative examples are given in the cases of a 'Schroedinger cat' kernel state and the Cahill-Glauber s-parametrized distributions. Also we consider an example of a kernel state when the generalized Markov kernel cannot be constructed.
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
Computational commutative and non-commutative algebraic geometry
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.
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.
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)
Zonal-flow dynamics from a phase-space perspective
Ruiz, D. E.; Parker, J. B.; Shi, E. L.; Dodin, I. Y.
2017-10-01
The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics (GO) limit. Here we present a new theory that captures both of these effects, while still treating DW quanta (``driftons'') as particles in phase space. In this theory, the drifton dynamics is described by an equation of the Wigner-Moyal type, which is analogous to the phase-space formulation of quantum mechanics. The ``Hamiltonian'' and the ``dissipative'' parts of the DW-ZF interactions are clearly identified. Moreover, this theory can be interpreted as a phase-space representation of the second-order cumulant expansion (CE2). In the GO limit, this formulation features additional terms missing in the traditional WKE that ensure conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the traditional WKE. Numerical simulations are presented to illustrate the importance of these additional terms. Supported by the U.S. DOE through Contract Nos. DE-AC02-09CH11466 and DE-AC52-07NA27344, by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.
Incorporating space charge in the transverse phase-space matching and tomography at PITZ
Energy Technology Data Exchange (ETDEWEB)
Kourkafas, Georgios
2015-11-15
The ever-expanding achievements in the field of particle accelerators push their specifications to very demanding levels. The performance of many modern applications depends on their ability to be operated with high bunch charges confined in small volumes. However, the consequence of increased intensity is strong space-charge forces, which perplex the beam manipulation and undermine the beam quality. As a result, reliable methods are needed to control and measure the accelerated particles under these extraordinary conditions. The phase space tomography is a diagnostic technique which can reveal details of the transverse beam parameters for a wide range of intensities and energies, with minimal influence from the machine instabilities, in a quasi non-destructive way. The accuracy of this method relies on the precise knowledge and control of the particle dynamics under the influence of space charge in different stages of the measurement. On the one hand, the matching of the beam to the measurement's design transverse parameters requires a procedure which efficiently compensates the effects of space charge. Depending on the structure of the magnetic lattice, different aspects of these effects prevail, therefore different strategies have to be developed. On the other hand, the impact of the space-charge forces on the phase-space transformations during the data acquisition has to be included in the model which is used for the tomographic reconstruction. The aim of this thesis is to provide and test time-efficient solutions for the incorporation of space charge in the transverse beam matching and phase space tomography.
Incorporating space charge in the transverse phase-space matching and tomography at PITZ
International Nuclear Information System (INIS)
Kourkafas, Georgios
2015-11-01
The ever-expanding achievements in the field of particle accelerators push their specifications to very demanding levels. The performance of many modern applications depends on their ability to be operated with high bunch charges confined in small volumes. However, the consequence of increased intensity is strong space-charge forces, which perplex the beam manipulation and undermine the beam quality. As a result, reliable methods are needed to control and measure the accelerated particles under these extraordinary conditions. The phase space tomography is a diagnostic technique which can reveal details of the transverse beam parameters for a wide range of intensities and energies, with minimal influence from the machine instabilities, in a quasi non-destructive way. The accuracy of this method relies on the precise knowledge and control of the particle dynamics under the influence of space charge in different stages of the measurement. On the one hand, the matching of the beam to the measurement's design transverse parameters requires a procedure which efficiently compensates the effects of space charge. Depending on the structure of the magnetic lattice, different aspects of these effects prevail, therefore different strategies have to be developed. On the other hand, the impact of the space-charge forces on the phase-space transformations during the data acquisition has to be included in the model which is used for the tomographic reconstruction. The aim of this thesis is to provide and test time-efficient solutions for the incorporation of space charge in the transverse beam matching and phase space tomography.
Momentum-space cigar geometry in topological phases
Palumbo, Giandomenico
2018-01-01
In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of three-dimensional topological insulators in class AII, which are described by a massive Dirac Hamiltonian and characterized by an half-integer Chern number. The gap is induced by introducing a magnetic perturbation, such as an external Zeeman field or a ferromagnet on the surface. The quantum Bures metric acquires a central role in our discussion and identifies a cigar geometry. We first derive the Chern number from the cigar geometry and we then show that the quantum metric can be seen as a solution of two-dimensional non-Abelian BF theory in momentum space. The gauge connection for this model is associated to the Maxwell algebra, which takes into account the Lorentz symmetries related to the Dirac theory and the momentum-space magnetic translations connected to the magnetic perturbation. The Witten black-hole metric is a solution of this gauge theory and coincides with the Bures metric. This allows us to calculate the corresponding momentum-space entanglement entropy that surprisingly carries information about the real-space conformal field theory describing the defect lines that can be created on the gapped boundary.
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)
((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)
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
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.)
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.)
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.