An extension of the Faddeev–Jackiw technique to fields in curved spacetimes
The Legendre transformation on singular Lagrangians, e.g. Lagrangians representing gauge theories, fails due to the presence of constraints. The Faddeev–Jackiw technique, which offers an alternative to that of Dirac, is a symplectic approach to calculating a Hamiltonian paired with a well-defined in...
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| Format: | Article |
| Language: | en_US |
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IOP Publishing
2015
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| Online Access: | http://hdl.handle.net/1721.1/98016 https://orcid.org/0000-0002-6742-4532 https://orcid.org/0000-0003-2480-5973 |
| _version_ | 1826188944393371648 |
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| author | Bertschinger, Edmund Prescod-Weinstein, Chanda |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Bertschinger, Edmund Prescod-Weinstein, Chanda |
| author_sort | Bertschinger, Edmund |
| collection | MIT |
| description | The Legendre transformation on singular Lagrangians, e.g. Lagrangians representing gauge theories, fails due to the presence of constraints. The Faddeev–Jackiw technique, which offers an alternative to that of Dirac, is a symplectic approach to calculating a Hamiltonian paired with a well-defined initial value problem when working with a singular Lagrangian. This phase space coordinate reduction was generalized by Barcelos-Neto and Wotzasek to simplify its application. We present an extension of the Faddeev–Jackiw technique for constraint reduction in gauge field theories and non-gauge field theories that are coupled to a curved spacetime that is described by general relativity. A major difference from previous formulations is that we do not explicitly construct the symplectic matrix, as that is not necessary. We find that the technique is a useful tool that avoids some of the subtle complications of the Dirac approach to constraints. We apply this formulation to the Ginzburg–Landau action and provide a calculation of its Hamiltonian and Poisson brackets in a curved spacetime. |
| first_indexed | 2024-09-23T08:07:26Z |
| format | Article |
| id | mit-1721.1/98016 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T08:07:26Z |
| publishDate | 2015 |
| publisher | IOP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/980162022-09-30T07:39:25Z An extension of the Faddeev–Jackiw technique to fields in curved spacetimes Bertschinger, Edmund Prescod-Weinstein, Chanda Massachusetts Institute of Technology. Department of Physics MIT Kavli Institute for Astrophysics and Space Research Prescod-Weinstein, Chanda Bertschinger, Edmund The Legendre transformation on singular Lagrangians, e.g. Lagrangians representing gauge theories, fails due to the presence of constraints. The Faddeev–Jackiw technique, which offers an alternative to that of Dirac, is a symplectic approach to calculating a Hamiltonian paired with a well-defined initial value problem when working with a singular Lagrangian. This phase space coordinate reduction was generalized by Barcelos-Neto and Wotzasek to simplify its application. We present an extension of the Faddeev–Jackiw technique for constraint reduction in gauge field theories and non-gauge field theories that are coupled to a curved spacetime that is described by general relativity. A major difference from previous formulations is that we do not explicitly construct the symplectic matrix, as that is not necessary. We find that the technique is a useful tool that avoids some of the subtle complications of the Dirac approach to constraints. We apply this formulation to the Ginzburg–Landau action and provide a calculation of its Hamiltonian and Poisson brackets in a curved spacetime. Massachusetts Institute of Technology. Dr. Martin Luther King, Jr. Visiting Professors and Scholars Program 2015-08-04T18:48:49Z 2015-08-04T18:48:49Z 2015-03 2014-12 Article http://purl.org/eprint/type/JournalArticle 0264-9381 1361-6382 http://hdl.handle.net/1721.1/98016 Prescod-Weinstein, C., and Edmund Bertschinger. “An Extension of the Faddeev–Jackiw Technique to Fields in Curved Spacetimes.” Classical and Quantum Gravity 32, no. 7 (March 17, 2015): 075011. https://orcid.org/0000-0002-6742-4532 https://orcid.org/0000-0003-2480-5973 en_US http://dx.doi.org/10.1088/0264-9381/32/7/075011 Classical and Quantum Gravity Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf IOP Publishing arXiv |
| spellingShingle | Bertschinger, Edmund Prescod-Weinstein, Chanda An extension of the Faddeev–Jackiw technique to fields in curved spacetimes |
| title | An extension of the Faddeev–Jackiw technique to fields in curved spacetimes |
| title_full | An extension of the Faddeev–Jackiw technique to fields in curved spacetimes |
| title_fullStr | An extension of the Faddeev–Jackiw technique to fields in curved spacetimes |
| title_full_unstemmed | An extension of the Faddeev–Jackiw technique to fields in curved spacetimes |
| title_short | An extension of the Faddeev–Jackiw technique to fields in curved spacetimes |
| title_sort | extension of the faddeev jackiw technique to fields in curved spacetimes |
| url | http://hdl.handle.net/1721.1/98016 https://orcid.org/0000-0002-6742-4532 https://orcid.org/0000-0003-2480-5973 |
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