UNITARITY OF DYNAMICAL PROPAGATORS OF PERTURBED KLEIN-GORDON EQUATIONS

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 □φ = m2φ + Kφ 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.