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

Multi-Instantons In Quantum Mechanics

Multi-Instantons In Quantum Mechanics

Quantum Field Theory and Critical Phenomena


Oxford University Press

The concepts of multi-instanton configurations and contributions are non-trivial because classical equations are non-linear and thus in general a linear combination of solutions is not a solution. However, in the limit in which all instantons are largely separated, such configurations render the action almost stationary because each instanton solution differs from a constant solution only by exponentially small corrections at large distances (in a field theory this is only true if the theory is massive). This chapter examines in the context of Quantum Mechanics the significance of such multi-instanton quasi-solutions. Sections 43.1, 43.2, studies explicitly two examples which we have already considered in Chapter 41: the double-well potential and the periodic cosine potential. It then discusses general potentials with degenerate minima. It also calculates the large order behaviour in the case of the O(ν) symmetric anharmonic oscillator.

Keywords:   double-well potential, periodic cosine potential, symmetric anharmonic oscillator

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 .