Unitarity of Dynamical Propagators of Perturbed Klein-Gordon Equations
- 1 March 1968
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 9 (3), 386-396
- https://doi.org/10.1063/1.1664591
Abstract
After discussing the basic notions of quantizations as representations of the Weyl relations, a criterion is established for a symplectic transformation on a classical linear system to be unitarily implementable in the free (zero‐interaction) representation. The result is applied to the temporal propagators of to obtain a condition which is sufficient to ensure that they are unitarily implementable in the free representation of the quantized Klein‐Gordon field of mass m. Necessary conditions are also obtained when K commutes with m2I − Δ. Several examples are discussed, the most interesting of which is that of a mass jump (i.e., K = m′2I), where the results given are fairly complete.
Keywords
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