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 (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 26 January 2021

Algebraic Preliminaries

Algebraic Preliminaries

Quantum Field Theory and Critical Phenomena


Oxford University Press

This chapter reviews algebraic identities about gaussian integrals, in particular Wick's theorem, a result also relevant for gaussian probability distributions. It discusses the steepest descent method, which reduces a certain type of integrals to gaussian expectation values. It then defines and discusses a few properties of dierentiation and integration in a Grassmann, that is, antisymmetric algebra, relevant for theories with fermion particles. In particular, gaussian integrals are calculated and general integrals are again reduced to gaussian expectation values. The chapter also recalls the concept of Legendre transformation, generating functional, functional dierentiation and the algebraic defiition of the determinant of an operator.

Keywords:   gaussian integrals, steepest descent method, Grassmann algebra, antisymmetric algebra, Legendre transformation

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 .