• DOI:10.1143/PTP.52.1929
• Corpus ID: 120369911

The Lehmann-Symanzik-Zimmermann Formalism for Manifestly Covariant Quantum Electrodynamics

@article{Nakanishi1974TheLF,
  title={The Lehmann-Symanzik-Zimmermann Formalism for Manifestly Covariant Quantum Electrodynamics},
  author={Noboru Nakanishi},
  journal={Progress of Theoretical Physics},
  year={1974},
  volume={52},
  pages={1929-1945}
}

• N. Nakanishi
• Published 1 December 1974
• Physics
• Progress of Theoretical Physics

/~Zimmermann formalism is presented for manifestly covariant quantum electrodynamics involving, a gauge parameter a. Contrary to Kiilll5n's assertion, it is shown that one can consistently formulate the asymptotic condition for the electromagnetic field and construct the Fock space of asymptotic states. Except for the case of Feynman gauge (a=1), the formalism ,is somewhat complicated because of the presence of dipole ghosts, but , emphasis is laid on the very existence of a consistent formalism. The complete­ ness relation for the asymptotic states, is presented so that the generalized unitarity relation can be written down. Indefinite-metric' theory of a massive vector field is briefly discussed. § I. Introduction More than twenty years ago, Kallen1> pointed out that electromagnetic field A" (x) in the Gupta-Bleuler formalism2> could not satisfy the asymptotic condition in the sense of Yang and Feldman.3> Ind~ed, he showed that if A"(x) ~A~n(x) as x0~ -oo and if A~(x) satisfies the Feynman-gauge free-field commutation 'relation