Renormalization for a Scalar Field in an External Scalar Potential
The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functiona...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-02-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/3/54 |
| _version_ | 1798040511910510592 |
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| author | Stephen A. Fulling Thomas E. Settlemyre Kimball A. Milton |
| author_facet | Stephen A. Fulling Thomas E. Settlemyre Kimball A. Milton |
| author_sort | Stephen A. Fulling |
| collection | DOAJ |
| description | The Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here, this is demonstrated in detail for two different models of the field-potential coupling. There is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully-interacting quantum field theories; these terms are finite, but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply-rising smooth potential. |
| first_indexed | 2024-04-11T22:08:40Z |
| format | Article |
| id | doaj.art-1b80d9c39019416e85724cacb7be7227 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T22:08:40Z |
| publishDate | 2018-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1b80d9c39019416e85724cacb7be72272022-12-22T04:00:37ZengMDPI AGSymmetry2073-89942018-02-011035410.3390/sym10030054sym10030054Renormalization for a Scalar Field in an External Scalar PotentialStephen A. Fulling0Thomas E. Settlemyre1Kimball A. Milton2Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USADepartment of Mathematics, Texas A&M University, College Station, TX 77843-3368, USAH. L. Dodge Department of Physics & Astronomy, University of Oklahoma, Norman, OK 73019, USAThe Pauli–Villars regularization procedure confirms and sharpens the conclusions reached previously by covariant point splitting. The divergences in the stress tensor of a quantized scalar field interacting with a static scalar potential are isolated into a three-parameter local, covariant functional of the background potential. These divergences can be naturally absorbed into coupling constants of the potential, regarded as a dynamical object in its own right; here, this is demonstrated in detail for two different models of the field-potential coupling. There is a residual dependence on the logarithm of the potential, reminiscent of the renormalization group in fully-interacting quantum field theories; these terms are finite, but numerically dependent on an arbitrary mass or length parameter, which is purely a matter of convention. This work is one step in a program to elucidate boundary divergences by replacing a sharp boundary by a steeply-rising smooth potential.http://www.mdpi.com/2073-8994/10/3/54vacuum energyrenormalizationPauli–Villarspoint splittingboundarypotentialscalar field |
| spellingShingle | Stephen A. Fulling Thomas E. Settlemyre Kimball A. Milton Renormalization for a Scalar Field in an External Scalar Potential Symmetry vacuum energy renormalization Pauli–Villars point splitting boundary potential scalar field |
| title | Renormalization for a Scalar Field in an External Scalar Potential |
| title_full | Renormalization for a Scalar Field in an External Scalar Potential |
| title_fullStr | Renormalization for a Scalar Field in an External Scalar Potential |
| title_full_unstemmed | Renormalization for a Scalar Field in an External Scalar Potential |
| title_short | Renormalization for a Scalar Field in an External Scalar Potential |
| title_sort | renormalization for a scalar field in an external scalar potential |
| topic | vacuum energy renormalization Pauli–Villars point splitting boundary potential scalar field |
| url | http://www.mdpi.com/2073-8994/10/3/54 |
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