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Path Integrals and Quantum Anomalies$
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Kazuo Fujikawa and Hiroshi Suzuki

Print publication date: 2004

Print ISBN-13: 9780198529132

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198529132.001.0001

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QUANTUM THEORY OF PHOTONS AND THE PHASE OPERATOR

QUANTUM THEORY OF PHOTONS AND THE PHASE OPERATOR

Chapter:
(p.31) 3 QUANTUM THEORY OF PHOTONS AND THE PHASE OPERATOR
Source:
Path Integrals and Quantum Anomalies
Author(s):

Kazuo Fujikawa

Hiroshi Suzuki

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198529132.003.0003

This chapter presents the essence of the quantization of the electromagnetic field and its path integral representation. The electromagnetic field is the simplest example of a gauge field, and its quantization nicely illustrates the technical problems associated with the quantization of gauge fields in general. The problem associated with the phase operator of the photon, which appears as a result of quantizing the electromagnetic field, is then discussed. This problem is analysed based on the notion of index and the postulate of positive definite Hilbert space. It is argued that this problem of the phase operator is closely related, in technical terms, to the chiral anomaly.

Keywords:   quantization, electromagnetic field, path integral representation, gauge field, index

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