Search

We continue the investigation of quantied Yang-Mills theories coupled to matter fields in the framework of causal perturbation theory. In this approach, which goes back to Epstein and Glaser, one works with free fields throughout, so that all expressions are mathematically well defined. The general proof of the Cg-identities ( C-number identities expressing gauge invariance) is completed. We attach importance to the correct treatment of the degenerate terms and to the Cg-identities with external matter legs. Moreover, the compatibility of all Cg-identities with P-, T-, C-invariance and pseudo-unitarity is shown. [ABSTRACT FROM AUTHOR]

We prove perturbative unitarity of the S-matrix on the physical Hilbert space for Yang-Mills theories with matter fields in the causal approach. Here unitarity is a direct consequence of gauge invariance. To establish the latter, we prove the C-number identities for gauge invariance (Cg-identities). [ABSTRACT FROM AUTHOR]

The investigation of quantized Yang-Mills theories by means of causal perturbation theory is continued. We give a comprehensive discussion of the C-number identities which express gauge invariance of the non-Abelian theory (Cg-identities). Having proven these identities for distributions with two external legs in a previous paper, we derive all identities for 3-legs and 4-legs here as a consequence of gauge invariance. Their proof by suitable normalization in the causal construction is considered in part IV of this series. [ABSTRACT FROM AUTHOR]

The investigation of pure quantized Yang-Mills theories by means of causal perturbation theory is continued. We prove (re)normalizability and study gauge invariance by introducing additional couplings between Yang-Mills and ghost fields. Then, gauge invariance can be expressed by a large but finite set of identities between C-number distributions, analogous to the Ward-Takahashi identities. We work with free fields throughout, so that all expressions are mathematically well-defined. [ABSTRACT FROM AUTHOR]

Pure quantized Yang-Mills theories are constructed by causalperturbation theory. We study operator gauge transformations which lead in a natural way to the introduction of ghost fields. Considering fermionic as well as bosonic ghosts, we find that only the former save gauge invariance in second order. We work with free quantum fields throughout, so that all expressions are mathematically well defined. [ABSTRACT FROM AUTHOR]

Scalar QED is investigated in the framework of causal perturbation theory. This approach which is ultraviolet finite differs from the conventional formalism because the inductive construction starts from the simple first-order interaction, without the term quadratic in the electromagnetic potential. The latter appears in the process of distribution splitting as a consequence of gauge invariance. In this way normalizability, gauge invariance and unitarity can be rigorously proven. [ABSTRACT FROM AUTHOR]

The triangle graphs with vector and axial vector couplings are investigated in the causal approach to massless QED. Since this approach does not require ultraviolet regularization the question of axial current conservation can be unambiguously discussed. Moreover, the case of massless fermions causes no serious problem. The anomaly appears in the process of distribution splitting. [ABSTRACT FROM AUTHOR]

Gauge invariance is discussed in the causal approach to QED. It is proven that the iterative construction of the S-matrix by the method of Epstein and Glaser can be carried out in such a way that perturbative gauge invariance holds true. The proof rests on a careful analysis of the process of distribution splitting. In case of nontrivial distribution splitting gauge invariance implies the Ward-Takahashi identities. [ABSTRACT FROM AUTHOR]

In the framework of the causal approach to QED, interacting fields are introduced by functional differentiation of the S-matrix. The properties of these field operators are studied in detail. It is shown that appropriately defined quantum versions of the Dirac and wave equations hold true. As a by-product, the correct operator products for QED are obtained. [ABSTRACT FROM AUTHOR]

Copyright of Il Nuovo Cimento: A is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)