Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions
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11005_2012_Article_589.pdf
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Author(s)
Kreimer, Dirk
Velenich, Andrea
Date Issued
October 2012
Journal
Letters in Mathematical Physics
Publisher
Springer Netherlands
Citation
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.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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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.
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DOI of Published Version
https://doi.org/10.1007/s11005-012-0589-y
