Abstract
We give mathematically rigorous results on the quantization of the covariant Klein Gordon field with an external stationary scalar interaction in a stationary curved space-time.
We show how, following Segal, Weinless etc., the problem reduces to finding a “one particle structure” for the corresponding classical system.
Our main result is an existence theorem for such a one-particle structure for a precisely specified class of stationary space-times. Byproducts of our approach are:
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1)
A discussion of when a given “equal-time” surface in a given stationary space-time is Cauchy.
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2)
A modification and extension of the methods of Chernoff [3] for proving the essential self-adjointness of certain partial differential operators.
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Kay, B.S. Linear spin-zero quantum fields in external gravitational and scalar fields. Commun.Math. Phys. 62, 55–70 (1978). https://doi.org/10.1007/BF01940330
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DOI: https://doi.org/10.1007/BF01940330