Jump to ContentJump to Main Navigation
The Conceptual Framework of Quantum Field Theory$
Users without a subscription are not able to see the full content.

Anthony Duncan

Print publication date: 2012

Print ISBN-13: 9780199573264

Published to Oxford Scholarship Online: January 2013

DOI: 10.1093/acprof:oso/9780199573264.001.0001

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: 20 June 2021

Dynamics IX: Interacting fields: non-perturbative aspects

Dynamics IX: Interacting fields: non-perturbative aspects

(p.374) 11 Dynamics IX: Interacting fields: non-perturbative aspects
The Conceptual Framework of Quantum Field Theory

Anthony Duncan

Oxford University Press

This chapter first explains the nature of the divergence in perturbation theory and then gives examples of different types of non-perturbative phenomena encountered in important field theories in the Standard Model of particle physics. This is followed by discussions of the physics of weakly coupled threshhold bound states; the limitations of perturbation theory in strongly coupled theories; the extent to which perturbation theory can be regarded as determining the exact amplitudes of the theory; and the role of the Borel-summability of the perturbative series. Conventional wisdom holds that perturbative information by itself is virtually useless in non-Borel-summable theories. However, it is shown that in at least one iconic case (the anharmonic ‘double-well’ oscillator) purely perturbative information can be ‘massaged’ to obtain a rigorously convergent sequence of approximants to the amplitudes of a non-Borel theory. The chapter concludes with some remarks on numerical approaches to non-perturbative field theory.

Keywords:   perturbation theory, non-perturbative field theory, quantum field theory, Borel-summability, anharmonic double-well 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 .