QUANTUM THEORY OF PHOTONS AND THE PHASE OPERATOR
QUANTUM THEORY OF PHOTONS AND THE PHASE OPERATOR
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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