Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly
We show the equivalence between Fujikawa’s method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for an O(N) symmetric scalar field theory. Fujikawa’s method leads to a sum of terms, each one superficially in on...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Advances in High Energy Physics |
| Online Access: | http://dx.doi.org/10.1155/2016/2809290 |
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| author | Chris L. Lin Carlos R. Ordóñez |
| author_facet | Chris L. Lin Carlos R. Ordóñez |
| author_sort | Chris L. Lin |
| collection | DOAJ |
| description | We show the equivalence between Fujikawa’s method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for an O(N) symmetric scalar field theory. Fujikawa’s method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to scale-dependence of the couplings, whereas, in terms of the effective action, the anomaly is the result of the breakdown of Noether’s theorem due to explicit symmetry breaking terms of the effective potential. |
| format | Article |
| id | doaj-art-10ea958e1b1447ab9f84216ad8f908ad |
| institution | Kabale University |
| issn | 1687-7357 1687-7365 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in High Energy Physics |
| spelling | doaj-art-10ea958e1b1447ab9f84216ad8f908ad2025-02-03T06:12:10ZengWileyAdvances in High Energy Physics1687-73571687-73652016-01-01201610.1155/2016/28092902809290Relationship between Fujikawa’s Method and the Background Field Method for the Scale AnomalyChris L. Lin0Carlos R. Ordóñez1Department of Physics, University of Houston, Houston, TX 77204-5005, USADepartment of Physics, University of Houston, Houston, TX 77204-5005, USAWe show the equivalence between Fujikawa’s method for calculating the scale anomaly and the diagrammatic approach to calculating the effective potential via the background field method, for an O(N) symmetric scalar field theory. Fujikawa’s method leads to a sum of terms, each one superficially in one-to-one correspondence with a vacuum diagram of the 1-loop expansion. From the viewpoint of the classical action, the anomaly results in a breakdown of the Ward identities due to scale-dependence of the couplings, whereas, in terms of the effective action, the anomaly is the result of the breakdown of Noether’s theorem due to explicit symmetry breaking terms of the effective potential.http://dx.doi.org/10.1155/2016/2809290 |
| spellingShingle | Chris L. Lin Carlos R. Ordóñez Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly Advances in High Energy Physics |
| title | Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly |
| title_full | Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly |
| title_fullStr | Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly |
| title_full_unstemmed | Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly |
| title_short | Relationship between Fujikawa’s Method and the Background Field Method for the Scale Anomaly |
| title_sort | relationship between fujikawa s method and the background field method for the scale anomaly |
| url | http://dx.doi.org/10.1155/2016/2809290 |
| work_keys_str_mv | AT chrisllin relationshipbetweenfujikawasmethodandthebackgroundfieldmethodforthescaleanomaly AT carlosrordonez relationshipbetweenfujikawasmethodandthebackgroundfieldmethodforthescaleanomaly |