Translator Disclaimer
VOL. 3 | 2002 Current Aspects of Deformation Quantization

Abstract

After a short introduction to the program of deformation quantization we indicate why this program is of current interest. One of the reasons is Kontsevich’s generalization of the Moyal product of phase-space functions to the case of general Poisson manifolds. We discuss this generalization, including the graphical calculus for presenting the result. We then illustrate the techniques of deformation quantization for quantum mechanical problems by considering the case of the simple harmonic oscillator. We indicate the relations to more conventional approaches, including the formalisms involving operators in Hilbert space and path integrals. Finally, we sketch some new results for relativistic quantum field theories.

Information

Published: 1 January 2002
First available in Project Euclid: 12 June 2015

zbMATH: 1011.53061
MathSciNet: MR1884853

Digital Object Identifier: 10.7546/giq-3-2002-290-303

Rights: Copyright © 2002 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

PROCEEDINGS ARTICLE
14 PAGES


SHARE
Back to Top