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Anomalies in Quantum Field Theory$
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Reinhold A. Bertlmann

Print publication date: 2000

Print ISBN-13: 9780198507628

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198507628.001.0001

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Path integrals, FP method and BRS transformation

Path integrals, FP method and BRS transformation

Chapter:
(p.118) 3 Path integrals, FP method and BRS transformation
Source:
Anomalies in Quantum Field Theory
Author(s):

Reinhold A. Bertlmann

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198507628.003.0003

This chapter explains the path integral formalism, specifically the Faddeev–Popov method for quantizing gauge theories and the BRS transformations. Section 3.1 presents Feynman's idea of formulating quantum mechanics as a sum of particle trajectories (paths). Section 3.2 generalizes this approach to scalar fields with self-interaction and calculates the Green functions in a perturbative way. Section 3.3 introduces the Grassman algebra to define PI for fermionic systes. Sections 3.4 and 3.5 explain the Abelian- and non-Abelian field case, respectively, focusing on the occurrence of the Faddeev–Popov ghosts which play — together with the BRS transformation in Section 3.6 — an important role in the treatment of anomalies.

Keywords:   Faddeev–Popov method, gauge theories, path integral formalism, anomalies

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