Bphz Renormalization of $\Lambda \phi^4$ Field Theory in Curved Space-time

Bunch, T.S.

doi:10.1016/0003-4916(81)90187-1

Bphz Renormalization of $\Lambda \phi^4$ Field Theory in Curved Space-time

T.S. Bunch
(
- Liverpool U.
)

1981

31 pages

Published in:

Annals Phys. 131 (1981) 118-148

DOI:

10.1016/0003-4916(81)90187-1

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Abstract: (Elsevier)

A proof is given to all orders in perturbation theory of the renormalizability of λ φ 4 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.

field theory: scalar
PERTURBATION THEORY
RENORMALIZATION: REGULARIZATION
PROPAGATOR
FEYNMAN GRAPH
MATHEMATICAL METHODS

References(21)

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