Journal ArticleDOI
Quantum Mechanics on Homogeneous Spaces
H. D. Doebner,J. Tolar +1 more
TLDR
In this paper, a complete description of quantum kinematics on a homogeneous G−space M is presented using imprimitivity systems for G based on M. The quantum system on M is considered (if possible and consistent with this quantization) as kinematic on a G−orbit equivalent to M in some Euclidean space Rn, and a physically justified and mathematically well-defined method of connecting the free Hamiltonian of a quantum system in Rn with an operator proportional to the Laplace−Beltrami operator on M (with the RAbstract:
A complete description of quantum kinematics on a homogeneous G−space M is presented using imprimitivity systems for G based on M. The kinematics on M is considered (if possible and consistent with this quantization) as kinematics on a G−orbit equivalent to M in some Euclidean space Rn. This method gives a physically justified and mathematically well−defined method of connecting the free Hamiltonian of a quantum system in Rn with an operator proportional to the Laplace−Beltrami operator on M (with the Riemannian structure inherited from Rn) which is proposed to be the free Hamiltonian on M.read more
Citations
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Journal ArticleDOI
Bicrossproduct structure of κ-Poincare group and non-commutative geometry
Shahn Majid,Henri Ruegg +1 more
TL;DR: In this paper, the authors show that the κ-deformed Poincare quantum algebra proposed for particle physics has the structure of a Hopf algebra bicrossproduct U(so (1, 3)) T.
Journal ArticleDOI
Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
Shahn Majid,Henri Ruegg +1 more
TL;DR: In this article, it was shown that the deformed Poincar et al. quantum algebra proposed for elementary particle physics has the structure of a Hopf agebra bicrossproduct with a backreaction of the momentum sector on the Lorentz rotations.
Book ChapterDOI
Between classical and quantum
TL;DR: In this article, the authors discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely in the limit h -> 0 of small Planck's constant (in a finite system), and through decoherence and consistent histories.
Journal ArticleDOI
Analytic representations in quantum mechanics
TL;DR: In this article, various Euclidean, hyperbolic and elliptic analytic representations of the harmonic oscillator are discussed and relations among them are discussed, and the general theory that relates the growth of analytic functions with the density of their zeros is applied to Bargmann functions and leads to theorems on the completeness of sequences of Glauber coherent states.
Journal ArticleDOI
Quantum mechanics in a discrete space-time
P. Šťovíček,J. Tolar +1 more
TL;DR: In this paper, a complete description of quantum kinematics in the sense of Mackey and Weyl is presented for the class of systems whose underlying configuration spaces are finite sets equipped with the structure of finite Abelian groups.
References
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Book
Quantum Mechanics and Path Integrals
TL;DR: Au sommaire as discussed by the authors developed the concepts of quantum mechanics with special examples and developed the perturbation method in quantum mechanics and the variational method for probability problems in quantum physics.
Angular Momentum in Quantum Mechanics
TL;DR: In this paper, the angular momentum, one of the most fundamental quantities in all of quantum mechanics, is introduced and a concise introduction to its application in atomic, molecular, and nuclear physics is provided.
Book
Mathematical Foundations of Quantum Mechanics
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.