Gauge invariance, the vertex function, and the magnitude of the renormalization constants of quantum electrodynamics
By means of the Gupta-Bleuler formalism for quantum electrodynamics, it is proved that the regularized secondorder vertex function, in the limit of high momentumtransfer P2, on the mass shell, is given by gamma μC log P22 rather than gamma . This proves that the assumption of G. Kallen that the renormalized vertex function tends to Z1γμ in the above limit, is not valid to second order in the Feynman gauge. Since the Kallen formalism is the proper renormalization of the Feynman gauge, this indicates that Kallen's assumption is not valid in the Kallen gauge. The failure of this assumption would invalidate Kallen's proof that a completely finite theory of quantum electrodynamics cannot be formulated in a consistent way. A valid operator gauge-transformation that reproduces the Landau transformations for the propagators was formulated. The operator gauge-transformation introduces a set of noninter acting scalar fields in a Hilbert space that has an indefinite metric. In theories that do not have a Ward identity, the high-momentum limit of the renormalized vertex function was sometimes taken as the definition of Z1. It is shown that this is not correct for the vector meson, but that it may be valid for the pseudoscalar meson, when these mesons interact with a spinor field.
- Research Organization:
- New York Univ., New York
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-18-002609
- OSTI ID:
- 4147831
- Journal Information:
- Nuovo Cimento, Vol. 29, Issue 5; Other Information: Orig. Receipt Date: 31-DEC-64; ISSN 0029-6341
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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