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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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Symmetries III: Global symmetries in field theory

Symmetries III: Global symmetries in field theory

(p.487) 14 Symmetries III: Global symmetries in field theory
The Conceptual Framework of Quantum Field Theory

Anthony Duncan

Oxford University Press

This chapter examines the role of global symmetries in local quantum field theories. It shows that exact global symmetries are rare — indeed, if we take gravitational effects into account, probably non-existent. Nevertheless, approximate global symmetries play an enormously important role in modern field theory. The appearance of massless Goldstone particles once an exact global symmetry is spontaneously broken is of enormous importance in modern field theory, and proof of the Goldstone theorem embodying this phenomenon is given. Dynamical aspects of spontaneous symmetry-breaking (SSB) are examined, and it is shown that the essence of SSB resides in the energetics of the theory in the infrared (i.e., at long distances).

Keywords:   global symmetry, local quantum field theory, Goldston particles, Goldston theorem, spontaneous symmetry-breaking

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