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. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 20 June 2019

Euclidean Path Integrals In Quantum Mechanics

Euclidean Path Integrals In Quantum Mechanics

Chapter:
(p.19) 2 EUCLIDEAN PATH INTEGRALS IN QUANTUM MECHANICS
Source:
Quantum Field Theory and Critical Phenomena
Author(s):

JEAN ZINN-JUSTIN

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198509233.003.0002

This chapter focuses on Quantum Mechanics and Quantum Field Theory in a euclidean formulation. This means that, in general, it discusses the matrix elements of the quantum statistical operator eβH (the density matrix at thermal equilibrium), where H is the hamiltonian and β is the inverse temperature. The chapter begins by first deriving the path integral representation of matrix elements of the quantum statistical operator for hamiltonians of the simple form p 2/2m + V (q). Comparing classical statistical physics in one space dimension and quantum statistical physics of the particle, it introduces statistical correlation functions and discusses their quantum interpretation. It then explicitly calculates the path integral corresponding to a harmonic oscillator in a time-dependent external force. This result can be used to reduce the evaluation of path integrals in the case of analytic potentials to perturbation theory. The chapter shows on a first example that path integrals are especially well suited to the study of the classical limit, by relating a quantum and classical partition function. The appendix explains some general properties of the two-point function, and use the semi-classical approximation of the partition function to derive Bohr–Sommerfeld's quantization condition.

Keywords:   euclidean formation, path integrals, hamiltonians

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 .