Relationship between causality, in a classical relativistic field theory, and Lorentz invariance, in the corresponding quantum theory, for a massive spin-one field in external potentials
For reasons of calculational simplicity, a massive spin-one field, interacting with external potentials, is described in terms of the Stulckelberg formalism (Helv. Phys. Acta.; 11: 299-328 (1938)). Some points, concerning necessary and sufficient conditions for the classical theory to be causal, in the sense of Velo and Zwanziger (Phys. Rev.; 186; 1337-41 (1969) and Phys. Rev.; 188: 2218-22 (1969)), are clarified. It is then shown that with a simple restriction on the type of interaction considered, the classical theory is causal, in the above sense, if and only if the corresponding quantum theory is Lorentz invariant, in that the S operator in the interaction picture is normal independent. Incidental in this demonstration is the result that the characteristic and Lee-- Yang determinants share the same form. It is indicated how this result generalizes to interactions between Stuckelberg, Klein-- Gordon and electromagnetic fields; and the validity of the result, in the more usual vector formalism, is established. (auth)
- Research Organization:
- Univ. of Durham, Eng.
- NSA Number:
- NSA-29-019953
- OSTI ID:
- 4353776
- Journal Information:
- J. Phys., A (London), v. 6, no. 12, pp. 1935-1942, Other Information: Orig. Receipt Date: 30-JUN-74; Bib. Info. Source: UK (United Kingdom (sent to DOE from))
- Country of Publication:
- United Kingdom
- Language:
- English
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