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Local momentum space and two-loop renormalizability of λφ 4 field theory in curved space-time

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Abstract

A generalization is given of some previous work in which a momentum space representation for the Feynman propagator,G(x, y), of a scalar field in an arbitrary curved space-time was obtained. The pointsx andy are allowed to vary in a normal neighborhood of an arbitrary fixed pointz which is taken as an origin of normal coordinates and the representation is obtained by Fourier transformation in the coordinate differencex α-y α. The generality of this representation enables it to be applied to the evaluation of the divergences in any Feynman graph. As an example, the third-order (two-loop) corrections to the four-point function of λø4 field theory are shown to be renormalizable in curved space-time.

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References

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Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, Liverpool University, P.O. Box 147, L69 3BX, Liverpool, England

    T. S. Bunch

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  1. T. S. Bunch
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Bunch, T.S. Local momentum space and two-loop renormalizability of λφ 4 field theory in curved space-time. Gen Relat Gravit 13, 711–723 (1981). https://doi.org/10.1007/BF00759414

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