Jump to ContentJump to Main Navigation
Quantum Field Theory and Critical Phenomena$
Users without a subscription are not able to see the full content.

Jean Zinn-Justin

Print publication date: 2002

Print ISBN-13: 9780198509233

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509233.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 13 October 2019

Path And Functional Integrals In Quantum Statistical Physics

Path And Functional Integrals In Quantum Statistical Physics

Chapter:
(p.83) 5 PATH AND FUNCTIONAL INTEGRALS IN QUANTUM STATISTICAL PHYSICS
Source:
Quantum Field Theory and Critical Phenomena
Author(s):

JEAN ZINN-JUSTIN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509233.003.0005

Hamiltonians in quantum mechanics can be expressed in terms of creation and annihilation operators, instead of the more usual position and momentum operators, a method well adapted to the study of perturbed harmonic oscillators. In the holomorphic formalism these operators act by multiplication and differentiation on a vector space of analytic functions. Alternatively, they can also be represented by kernels, functions of complex variables which in the classical limit correspond to a complex parametrization of phase space. To this formalism corresponds a path integral representation of the statistical operator (the density matrix at thermal equilibrium) where paths belong to complex spaces instead of the more usual position-momentum phase space. Its construction provides a useful introduction to the construction of the path integral for fermion degrees of freedom. Both formalisms can then be generalized to a quantum gas of Bose or Fermi particles in the grand canonical formulation. A functional integral representation of quantum partition functions can be derived, a topic discussed in the second part of the chapter. Finally, these formalisms allow the construction of the functional integral representation of the scattering S-matrix in quantum field theory shown in Chapters 6 and 8.

Keywords:   quantum mechanics, holomorphic formalism, functional integrals, Bose particles, Fermi particles

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .