Letters in Mathematical Physics

, Volume 103, Issue 2, pp 171–181 | Cite as

Field Diffeomorphisms and the Algebraic Structure of Perturbative Expansions

Article

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.

Mathematics Subject Classification (2010)

81S99 81T99 

Keywords

diffeomorphism invariance Hopf ideals BCFW relations tadpoles renormalization 

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Departments of Physics and of MathematicsHumboldt UniversityBerlinGermany
  2. 2.Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA

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