M. Dütsch

Causal construction of Yang-Mills theories. - II

SummaryPure 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.

Scalar QED revisited

SummaryScalar 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.

Gauge invariance in finite QED

SummaryGauge invariance is discussed in the causal approach to QED. It is proven that the iterative construction of theS-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.

Gauge invariance of massless QED

Abstract A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.

Interacting fields in finite QED

SummaryIn the framework of the causal approach to QED, interacting fields are introduced by functional differentiation of theS-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.

On gauge invariance of Yang-Mills theories with matter fields

SummaryWe 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 theCg-identities (C-number identities expressing gauge invariance) is completed. We attach importance to the correct treatment of the degenerate terms and to theCg-identities with external matter legs. Moreover, the compatibility of allCg-identities withP-, T-, C-invariance and pseudo-unitarity is shown.

The vertex function and adiabatic limit in finite QED

The vertex function is computed in the cutoff-free causal formulation of QED. By normalization at zero momentum, difficulties with the infrared problem are avoided. The latter is studied in the course of the adiabatic limit, where the spacetime switching function goes to one. This allows the authors to keep the photon mass always equal to zero. They prove that the adiabatic limit exists in the inclusive cross section.

The infrared problem and adiabatic switching

The infrared problem of QED is investigated by means of adiabatic switching of the interaction. The authors prove in lowest-order perturbation theory that the adiabatic limit of the inclusive cross section is independent of the switching function, provided four polarizations of soft bremsstrahlung are taken into account before the limit. This gives the possibility of simulating charged asymptotic states in a Fock space consisting only of free fields. Finally, they show that no (finite) charge renormalization is necessary in order to fix the physical charge. This turns out to be a consequence of the Ward identity.

Axial Anomalies in Massless Finite QED.

SummaryThe 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.

Axial anomalies in finite QED

Abstract The triangle graphs with axial vector coupling are investigated in the casual approach to QED. Since this approach does not require ultraviolet regularization the question of axial current conservation can be unambiguously discussed. The anomaly appears in the process of distribution splitting. Particular attention is paid to the case of massless fermions.