Anomalies in finite amplitudes: Two-dimensional single axial-vector triangle

An explicit and detailed investigation about the two-dimensional single axial-vector (AVV) triangle is performed. Such a perturbative amplitude is related to the anomalous axial-vector (AV) one through contractions with external momenta. Given this fact, before considering such a triangle we must gi...

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Bibliographic Details
Published in:Physical review. D, Particles, fields, gravitation, and cosmology Particles, fields, gravitation, and cosmology, 2012-04, Vol.85 (8), Article 085007
Main Authors: Battistel, O. A., Fonseca, M. V. S., Dallabona, G.
Format: Article
Language:English
Subjects:
Amplitudes
Anomalies
Cosmology
Gravitation
Mathematical analysis
Regularization
Strategy
Triangles
Two dimensional
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Summary:An explicit and detailed investigation about the two-dimensional single axial-vector (AVV) triangle is performed. Such a perturbative amplitude is related to the anomalous axial-vector (AV) one through contractions with external momenta. Given this fact, before considering such a triangle we must give a clear point of view for the AV amplitude. Such a point of view is constructed within the context of an alternative strategy to handle the divergences typical of perturbative solutions of quantum field theory. In this procedure all amplitudes in all theories, formulated in odd and even space-time dimensions, renormalizable or not, are treated in an absolutely identical way. The ambiguities are automatically eliminated and the symmetry relations preserved. The well-known divergent anomalous amplitudes are correctly described, in a predictive scenario. After performing, in a very detailed way, all the calculations involved we conclude that the same phenomenon occurring in the AV amplitude is also present in the finite AVV triangle. The conclusion gives support to the thesis that the phenomenon is present in all pseudoamplitudes in a chain where the divergent AV one is only the most simple structure. The same must occur in all even space-time dimensions. In particular, the single and triple four-dimensional box amplitudes must exhibit anomalies too. A conclusive investigation is allowed due to the special features of the adopted procedure where regularization is completely avoided and an adequate systematization for the finite parts is introduced.
ISSN:1550-7998
1550-2368
DOI:10.1103/PhysRevD.85.085007