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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: February 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

(p.118) 3 Path integrals, FP method and BRS transformation
Anomalies in Quantum Field Theory

Reinhold A. Bertlmann

Oxford University Press

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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