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Quantum Field Theory and Critical Phenomena$
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Jean Zinn-Justin

Print publication date: 2002

Print ISBN-13: 9780198509233

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198509233.001.0001

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Unstable Vacua In Quantum Field Theory

Unstable Vacua In Quantum Field Theory

Quantum Field Theory and Critical Phenomena


Oxford University Press

This chapter begins with a semi-classical study of barrier penetration in quantum field theory, generalizing the methods explained in quantum mechanics. It has been shown that in quantum mechanics barrier penetration is associated with classical motion in imaginary time; it is thus natural here to consider quantum field theory in its euclidean formulation. In the functional representation of field theory barrier penetration in the semi-classical limit is also related to finite action solutions (instantons) of the classical field equations. The chapter first tries to characterize such solutions. It then explains how to evaluate the instanton contributions at leading order, the main new problem arising from UV divergences.

Keywords:   quantum field theory, barrier penetration, instantons

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