p-Mechanics as a Physical Theory. An Introduction

Details p-Mechanics as a Physical Theory. An Introduction p-Mechanics as a Physical Theory. An Introduction

2002-12-17

arxiv.org/abs/quant-ph/0212101v3

Journal of Physics A: Mathematical and General, 2004, volume 37, issue 1, pages 183 - 204

Physics

Quantum Physics

LaTeX2e (amsart), 22 pages, 4 PS illustrations, v2 & v3 contain minor changes

Scientific paper

10.1088/0305-4470/37/1/013

The paper provides an introduction into p-mechanics, which is a consistent physical theory suitable for a simultaneous description of classical and quantum mechanics. p-Mechanics naturally provides a common ground for several different approaches to quantisation (geometric, Weyl, coherent states, Berezin, deformation, Moyal, etc.) and has a potential for expansions into field and string theories. The backbone of p-mechanics is solely the representation theory of the Heisenberg group. Keywords: Classical mechanics, quantum mechanics, Moyal brackets, Poisson brackets, commutator, Heisenberg group, orbit method, deformation quantisation, symplectic group, representation theory, metaplectic representation, Berezin quantisation, Weyl quantisation, Segal--Bargmann--Fock space, coherent states, wavelet transform, contextual interpretation, string theory, field theory.

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