The two-loop radiative corrections to the divergence of the axial-vector current are analyzed in the context of spinor electrodynamics. It is found that the arbitrariness that occurs in the relevant Feynrnan diagrams due to the appearance of surface terms associated with linearly divergent integrals is sufficient to ensure that at two-loop order the Ward identity can be satisfied, irrespective of how the divergences that occur are parametrized. This indicates that the Adler-Bardeen theorem is satisfied.

The anomaly in the supercurrent amplitude S,, is analyzed to one-loop order for A; = 1 supersymmetry in the Wess-Zumino gauge within the framework of preregularization, in which loopmomentum-routing ambiguities percolate into shift-of-integration-variable surface terms peculiar to exactly four space-time dimensions. We find the supercurrent anomaly to be a consequence of the inability of such ambiguities (within a demonstrably finite set of quantum corrections) to absorb violations of gauge invariance ( q v S p ,~O ) and supersymmetry (dtS,,ra.Sf 0 ) simultaneously, a feature quite similar to the inability of VVA-triangle ambiguities to absorb violations of gauge invariance and the axial-vector-current Ward identity simultaneously. We also find that if gauge invariance is preserved, the contribution to the supercurrent anomaly obtained from O ( g 2 ) quantum corrections to the supercurrent involves no infrared or ultraviolet infinities and resides in 3.S rather than y.S. This last result is a consequence of maintaining exactly four space-time dimensions, as is necessary for momentum-routing ambiguities to appear at all in the quantum corrections. The connection between our results and similar results obtained from an Adler-Rosenberg symmetry argument is examined in detail.Loop-momentum-routing ambiguities, which percolate into shift-of-integration-variable surface terms in 4 (but not 4 -E ) may be used to uphold Ward identities (i.e., "preregularize") in non-dimensionallycontinued perturbative calculation^.^ Anomalies manifest themselves in perturbation theory when such ambiguities prove insufficiently general to enforce the full set of Lagrangian symmetries. A textbook example is provided by the chiral anomaly, associated with the current divergences at vertices of the VVA-triangle graph and crossgraph.Contractions of vertex momenta into these graphs yield finite shift-of-integration-variable surface terms from which the anomalous component of the axial-vector current may be obtained.' In his pedagogical review article of 1970, Adler avoids explicit parametrization of ultraviolet infinities while showing how an anomalous contribution to the axial-vector-current Ward identity would vanish (using standard four-dimensional Dirac algebra) if naive shifts of the integration variable were permitted in four-dimensional Feynman integrals.6 However, the retention of shift-of-integration-variable surface terms in Adler's analysis does not automatically lead to the usual chiral anomaly. Rather, one finds that ambiguities in how one chooses to label the internal loop momenta percolate into vector and axial-vector current divergences. These ambiguities have been examined in an earlier paper,7 in which the following results were obtained.( 1 ) Vector and axial-vector current divergences (i.e., a.V,a.A) do not require explicit parametrization of ultraviolet or infrared infinities. Rather, one-loop quantum corrections to 8.V and a.A are manifestly finite, though ambiguous as a result of surface terms sensitive to the routing ...

We describe and investigate the applicability of a recently proposed preregularization procedure in which arbitrary shift-of-integration-variable surface terms (in four dimensions) arising from loop-mementum ambiguities are constrained to absorb any contributions to unrenormalized Feynman amplitudes that violate Ward-Takahashi-Slavnov-Taylor (WTST) identities appropriate to the theory under consideration. Anomalies in WTST identities are shown to be the result of having insufficient arbitrariness in the loop momenta to accommodate the full set of Lagrangian symmetries. We demonstrate the utility of our procedure by analyzing the chiral anomaly in even dimensions, the supercurrent anomaly in N = 1 super Yang-Mills theory, and by calculations in quantum electrodynamics and Yang-Mills theory. We argue that the preregularization procedure should be particularly well suited to supersymmetric theories as a regularization-independent means of upholding super-WTST identities.Nous Ctudions l'applicabilitk d'une prockdure de preregularisation proposke rkcemment, dans laquelle des termes de surface (en quatre dimensions) dus a des decalages de variables d'intkgration provenant d'ambiguites boucle-impulsion sont contraints 5 absorber toutes les contributions aux amplitudes de Feynman non renormalisees qui violent les identitks Ward-TakahashiSlavnov-Taylor (WTST) approprikes a la thkorie considkree. On montre que les anomalies dans les identitks WTST sont le rksultat d'une insuffisance d'arbitraire, dans les boucles-impulsions, qui empkche d'accommoder au complet l'ensemble des symCtries du lagrangien. Nous dkmontrons 1'utilitC de notre prockdure en analysant l'anomalie chirale en nombre pair de dimensions, l'anomalie de supercourant en thkorie super-Yang-Mills N = 1, ainsi que par des calculs en EDQ et en thtorie Yang-Mills. Nous indiquons ainsi que le prockdure de prC-regularisation devrait ktre particulikrement bien adaptCe aux thCories supersymCtriques, comme support independant de la rkgularisation des identitts super-WTST.[Traduit par le journal]Can.

The one-loop effective Lagrangian in scalar electrodynamics is computed using an expansion to second order in the external electromagnetic field and a WKB-type approximation. Quantum fluctuations of both the scalar and vector fields about background scalar and electromagnetic fields are considered.

The technique of operator regularization is applied to the Weinberg-Salam model. By directly regulating operators that arise in the course of evaluating path integrals in the background-field formalism, we preserve all symmetries of the theory. An expansion due to Schwinger is employed to compute amplitudes perturbatively, thereby avoiding Feynman diagrams. No explicitly divergent quantities arise in this approach. The general features of the method are outlined with particular attention paid to the problem of simultaneously regulating functions of an operator A and inverse functions upon which A itself depends. Specific application is made to computation of the one-loop contribution to the muon-photon vertex in the Weinberg-Salam model in the limit of zero momentum transfer to the photon.La technique de rigularisation des optrateurs est appliquie au modkle Weinberg-Salam. En rkgularisant directement les opirateurs qui apparaissent au cours de I'tvaluation des inttgrales de parcours dans le formalisme de champ exttrieur, on preserve toutes les symttries de la theorie. Un dtveloppement dQ a Schwinger est employe pour calculer les amplitudes par perturbations, Cvitant ainsi les diagrammes de Feynman. Aucune quantitt explicitement divergente n'apparait dans cette approche. On prtsente dans leurs grandes lignes les caractkristiques gCntrales de la methode en accordant une attention particulikre au problkme de la rtgularisation simultante des fonctions d'un opirateur A et des fonctions inverses dont A lui-m&me dCpend. Une application sptcifique est faite au calcul de la contribution 3 une boucle au vertex muon-photon dans le mod& Weinberg-Salam, a la limite de transfert nu1 d'impulsation au photon.Can. J. Phys. 65, 1082 (1987) [Traduit par la revue]