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The Conceptual Framework of Quantum Field Theory$
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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

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Dynamics IX: Interacting fields: non-perturbative aspects

Dynamics IX: Interacting fields: non-perturbative aspects

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

Anthony Duncan

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199573264.003.0011

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

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