skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Note on quantum Minkowski space

Abstract

In this work, some interesting details about quantum Minkowski space and quantum Lorentz group structures are revealed. The task is accomplished by generalizing an approach adopted in a previous work where quantum rotation group and quantum Euclidean space structures have been investigated. The generalized method is based on a mapping relating the q-spinors (precisely the tensor product of dotted and undotted fondamental q-spinors) to Minkowski q-vectors. As a result of this mapping, the quantum analog of Minkowski space is constructed (with a definite metric). Also, the matrix representation of the quantum Lorentz group is determined together with its corresponding q-deformed orthogonality relation.

Authors:
 [1];  [2]
  1. Laboratoire de Physique Theorique, Universite de Tlemcen, Tlemcen (Algeria)
  2. Laboratoire de Physique Theorique, Universite d'Oran Es-senia, 31100 Oran (Algeria)
Publication Date:
OSTI Identifier:
21254149
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 78; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.78.064068; (c) 2008 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EUCLIDEAN SPACE; LORENTZ GROUPS; MINKOWSKI SPACE; QUANTUM MECHANICS; ROTATION; SPINORS

Citation Formats

Bentalha, Z., and Tahiri, M. Note on quantum Minkowski space. United States: N. p., 2008. Web. doi:10.1103/PHYSREVD.78.064068.
Bentalha, Z., & Tahiri, M. Note on quantum Minkowski space. United States. doi:10.1103/PHYSREVD.78.064068.
Bentalha, Z., and Tahiri, M. 2008. "Note on quantum Minkowski space". United States. doi:10.1103/PHYSREVD.78.064068.
@article{osti_21254149,
title = {Note on quantum Minkowski space},
author = {Bentalha, Z. and Tahiri, M.},
abstractNote = {In this work, some interesting details about quantum Minkowski space and quantum Lorentz group structures are revealed. The task is accomplished by generalizing an approach adopted in a previous work where quantum rotation group and quantum Euclidean space structures have been investigated. The generalized method is based on a mapping relating the q-spinors (precisely the tensor product of dotted and undotted fondamental q-spinors) to Minkowski q-vectors. As a result of this mapping, the quantum analog of Minkowski space is constructed (with a definite metric). Also, the matrix representation of the quantum Lorentz group is determined together with its corresponding q-deformed orthogonality relation.},
doi = {10.1103/PHYSREVD.78.064068},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 78,
place = {United States},
year = 2008,
month = 9
}
  • The differential calculus on {ital n}-dimensional ({ital n}{ge}3) quantum Minkowski space covariant with respect to left action of {kappa}-Poincar{acute e} group is constructed and its uniqueness is shown. {copyright} {ital 1996 American Institute of Physics.}
  • We formulate finite-temperature quantum field theories in Minkowski space (real time) using Feynman path integrals. We show that at non-zero temperature a new field arises which plays the role of a ghost field and is necessary for unambiguous Feynman rules. Consequently, the finite-temperature Lagrangian is different from the zero-temperature one and a new, discrete Z/sub 2/ symmetry arises. We discuss the functional formalism and spontaneous symmetry breakdown at finite temperature and also the possibility of spontaneous breakdown of the (thermal) Z/sub 2/ symmetry.
  • The proof of the decoupling theorem of quantum field theory given earlier (E. B. Manoukian, J. Math. Phys. 26, 1065 (1985)) in Minkowski space, in the distributional sense, for theories involving particles with vanishingly small masses as well is extended under more general conditions, thus being applicable to a larger class of graphs. All subtractions of renormalization are carried out at the origin of momentum space with the degree of divergence of a subtraction coinciding with the dimensionality of the corresponding subdiagram.
  • Noncommutative differential calculus on quantum Minkowski space is not separated with respect to the standard generators, in the sense that partial derivatives of functions of a single generator can depend on all other generators. It is shown that this problem can be overcome by a separation of variables. We study the action of the universal L-matrix, appearing in the coproduct of partial derivatives, on generators. Powers of the resulting quantum Minkowski algebra valued matrices are calculated. This leads to a nonlinear coordinate transformation which essentially separates the calculus. A compact formula for general derivatives is obtained in form of amore » chain rule with partial Jackson derivatives. It is applied to the massive quantum Klein-Gordon equation by reducing it to an ordinary q-difference equation. The rest state solution can be expressed in terms of a product of q-exponential functions in the separated variables.« less