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: Artículo publishedVersion
Publicado: 2000
Materias:
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
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_03702693_v481_n1_p129_Fosco_oai
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Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
id I28-R145-paper_03702693_v481_n1_p129_Fosco_oai
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spelling I28-R145-paper_03702693_v481_n1_p129_Fosco_oai2024-08-16 Fosco, C.D. Mazzitelli, F.D. 2000 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. application/pdf http://hdl.handle.net/20.500.12110/paper_03702693_v481_n1_p129_Fosco info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Phys Lett Sect B Nucl Elem Part High-Energy Phys 2000;481(1):129-135 Argentina article atomic particle gravity nuclear physics quantum mechanics Anomalies and symmetries of the regularized action info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_03702693_v481_n1_p129_Fosco_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (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 Artículo
Artículo
publishedVersion
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
publishDate 2000
url http://hdl.handle.net/20.500.12110/paper_03702693_v481_n1_p129_Fosco
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_03702693_v481_n1_p129_Fosco_oai
work_keys_str_mv AT foscocd anomaliesandsymmetriesoftheregularizedaction
AT mazzitellifd anomaliesandsymmetriesoftheregularizedaction
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