Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions
We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree-level amplitudes for the transformed fields m...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Netherlands
2016
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| Online Access: | http://hdl.handle.net/1721.1/105502 |
| _version_ | 1826198237107716096 |
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| author | Kreimer, Dirk Velenich, Andrea |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Kreimer, Dirk Velenich, Andrea |
| author_sort | Kreimer, Dirk |
| collection | MIT |
| description | We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree-level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. For the massless field theory these relations continue to hold in loop computations. In the massive field theory the situation is more subtle. A necessary condition for the Feynman rules to respect the maximal ideal and co-ideal defined by the core Hopf algebra of the transformed theory is that upon renormalization all massive tadpole integrals (defined as all integrals independent of the kinematics of external momenta) are mapped to zero. |
| first_indexed | 2024-09-23T11:01:33Z |
| format | Article |
| id | mit-1721.1/105502 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:01:33Z |
| publishDate | 2016 |
| publisher | Springer Netherlands |
| record_format | dspace |
| spelling | mit-1721.1/1055022022-10-01T00:38:19Z Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions Kreimer, Dirk Velenich, Andrea Massachusetts Institute of Technology. Department of Physics Velenich, Andrea We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree-level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. For the massless field theory these relations continue to hold in loop computations. In the massive field theory the situation is more subtle. A necessary condition for the Feynman rules to respect the maximal ideal and co-ideal defined by the core Hopf algebra of the transformed theory is that upon renormalization all massive tadpole integrals (defined as all integrals independent of the kinematics of external momenta) are mapped to zero. National Science Foundation (U.S.) (Grant DMS-0603781) 2016-12-01T20:18:02Z 2016-12-01T20:18:02Z 2012-10 2012-09 2016-08-18T15:20:01Z Article http://purl.org/eprint/type/JournalArticle 0377-9017 1573-0530 http://hdl.handle.net/1721.1/105502 Kreimer, Dirk, and Andrea Velenich. “Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions.” Letters in Mathematical Physics 103, no. 2 (October 17, 2012): 171–181. en http://dx.doi.org/10.1007/s11005-012-0589-y Letters in Mathematical Physics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Science+Business Media Dordrecht application/pdf Springer Netherlands Springer Netherlands |
| spellingShingle | Kreimer, Dirk Velenich, Andrea Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions |
| title | Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions |
| title_full | Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions |
| title_fullStr | Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions |
| title_full_unstemmed | Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions |
| title_short | Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions |
| title_sort | field diffeomorphisms and the algebraic structure of perturbative expansions |
| url | http://hdl.handle.net/1721.1/105502 |
| work_keys_str_mv | AT kreimerdirk fielddiffeomorphismsandthealgebraicstructureofperturbativeexpansions AT velenichandrea fielddiffeomorphismsandthealgebraicstructureofperturbativeexpansions |