Quantum Theory of Fields in an Expanding Space. I

概要

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In order to deal with the quantum theory of fields in an expanding space relying on a well-defined quantum picture, a device is proposed to join the metric for the expanding space with those for flat space-times and a new time variable is introduced in a suitable manner. In this paper the quantization of the electromagnetic field is mainly discussed in the whole region defined by the joined metrics. If the physical component of vector potential is quantized, there appears some peculiar feature, which serves to destroy the macroscopic causality based on a particle image, in the four-dimensional commutation function according to the manner of joining two adjacent metrics. The appearance of such a peculiar feature has an intimate connection with that of an abnormal transformation function like the one in van Hove's model. On the other hand, the quantization of original vector potential does not lead to such difficulties. It is concluded that the quantization of the electromagnetic field should be carried out in terms of the original vector potential, but not its physical component.
理論物理学刊行会の論文
1964-06-25