Dynamics IX: Interacting fields: non-perturbative aspects

Anthony Duncan

in The Conceptual Framework of Quantum Field Theory

Published in print August 2012 | ISBN: 9780199573264
Published online January 2013 | e-ISBN: 9780191743313 | DOI:
Dynamics IX: Interacting fields: non-perturbative aspects

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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

Chapter.  19937 words.  Illustrated.

Subjects: Mathematical and Statistical Physics

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