Anomalies and symmetries of the regularized action

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We show that the Pauli-Villars regularized action for a scalar field in a gravitational background in 1 + 1 dimensions has, for any value of the cutoff M, a symmetry which involves non-local transformations of the regulator field plus (local) Weyl transformations of the metric tensor. These transfor...

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Autores principales: Fosco, C.D., Mazzitelli, F.D.
Formato: JOUR
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Argentina
article
atomic particle
gravity
nuclear physics
quantum mechanics
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_03702693_v481_n1_p129_Fosco
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_03702693_v481_n1_p129_Fosco2023-10-03T15:28:49Z Anomalies and symmetries of the regularized action Fosco, C.D. Mazzitelli, F.D. Argentina article atomic particle gravity nuclear physics quantum mechanics We show that the Pauli-Villars regularized action for a scalar field in a gravitational background in 1 + 1 dimensions has, for any value of the cutoff M, a symmetry which involves non-local transformations of the regulator field plus (local) Weyl transformations of the metric tensor. These transformations, an extension to the regularized action of the usual Weyl symmetry transformations of the classical action, lead to a new interpretation of the conformal anomaly in terms of the (non-anomalous) Jacobian for this symmetry. Moreover, the Jacobian is automatically regularized, and yields the correct result when the masses of the regulators tend to infinity. In this limit the transformations, which are non-local on a scale of 1/M, become the usual Weyl transformations of the metric. We also present the example of the chiral anomaly in 1 + 1 dimensions, showing that the Pauli-Villars regularized action has a non-local symmetry. This symmetry is similar to the one of (lattice) Ginsparg-Wilson fermions, with the ultraviolet cutoff playing the role of the inverse of the lattice spacing. (C) 2000 Elsevier Science B.V. Fil:Mazzitelli, F.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_03702693_v481_n1_p129_Fosco
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Argentina
article
atomic particle
gravity
nuclear physics
quantum mechanics
spellingShingle Argentina
article
atomic particle
gravity
nuclear physics
quantum mechanics
Fosco, C.D.
Mazzitelli, F.D.
Anomalies and symmetries of the regularized action
topic_facet Argentina
article
atomic particle
gravity
nuclear physics
quantum mechanics
description We show that the Pauli-Villars regularized action for a scalar field in a gravitational background in 1 + 1 dimensions has, for any value of the cutoff M, a symmetry which involves non-local transformations of the regulator field plus (local) Weyl transformations of the metric tensor. These transformations, an extension to the regularized action of the usual Weyl symmetry transformations of the classical action, lead to a new interpretation of the conformal anomaly in terms of the (non-anomalous) Jacobian for this symmetry. Moreover, the Jacobian is automatically regularized, and yields the correct result when the masses of the regulators tend to infinity. In this limit the transformations, which are non-local on a scale of 1/M, become the usual Weyl transformations of the metric. We also present the example of the chiral anomaly in 1 + 1 dimensions, showing that the Pauli-Villars regularized action has a non-local symmetry. This symmetry is similar to the one of (lattice) Ginsparg-Wilson fermions, with the ultraviolet cutoff playing the role of the inverse of the lattice spacing. (C) 2000 Elsevier Science B.V.
format JOUR
author Fosco, C.D.
Mazzitelli, F.D.
author_facet Fosco, C.D.
Mazzitelli, F.D.
author_sort Fosco, C.D.
title Anomalies and symmetries of the regularized action
title_short Anomalies and symmetries of the regularized action
title_full Anomalies and symmetries of the regularized action
title_fullStr Anomalies and symmetries of the regularized action
title_full_unstemmed Anomalies and symmetries of the regularized action
title_sort anomalies and symmetries of the regularized action
url http://hdl.handle.net/20.500.12110/paper_03702693_v481_n1_p129_Fosco
work_keys_str_mv AT foscocd anomaliesandsymmetriesoftheregularizedaction
AT mazzitellifd anomaliesandsymmetriesoftheregularizedaction
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