Anomalies and symmetries of the regularized action
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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paper:paper_03702693_v481_n1_p129_Fosco2023-06-08T15:36:37Z Anomalies and symmetries of the regularized action Mazzitelli, Francisco Diego 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. 2000 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03702693_v481_n1_p129_Fosco 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) |
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Argentina article atomic particle gravity nuclear physics quantum mechanics |
| spellingShingle |
Argentina article atomic particle gravity nuclear physics quantum mechanics Mazzitelli, Francisco Diego 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. |
| author |
Mazzitelli, Francisco Diego |
| author_facet |
Mazzitelli, Francisco Diego |
| author_sort |
Mazzitelli, Francisco Diego |
| 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 |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03702693_v481_n1_p129_Fosco http://hdl.handle.net/20.500.12110/paper_03702693_v481_n1_p129_Fosco |
| work_keys_str_mv |
AT mazzitellifranciscodiego anomaliesandsymmetriesoftheregularizedaction |
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1768542365910302720 |