BPHZ renormalization of λφ4 field theory in curved spacetime |
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Authors: | TS Bunch |
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Institution: | Department of Applied Mathematics and Theoretical Physics, University of Liverpool, P.O. Box 147, Liverpool L69 3BX, England |
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Abstract: | A proof is given to all orders in perturbation theory of the renormalizability of λφ4 field theory in curved spacetime. The proof is based on the BPHZ definition of a renormalized Feynman integrand and uses dimensional regularization to ensure that products of Feynman propagators are well-defined distributions. The explicit structure of the pole terms in the Feynman integrand is obtained using a local momentum space representation of the Feynman propagator and is shown to be of a form which can be cancelled by counterterms in the scalar field Lagrangian. The proof given is, technically, only valid for metrics which have been analytically continued to Euclidean (++++) signature. |
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