Multi-loop zeta function regularization and spectral cutoff in curved spacetime |
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Authors: | Adel Bilal Frank Ferrari |
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Affiliation: | 1. Centre National de la Recherche Scientifique, Laboratoire de Physique Théorique de l?École Normale Supérieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France;2. Service de Physique Théorique et Mathématique, Université Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, B-1050 Bruxelles, Belgium |
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Abstract: | We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard zeta function regularization at one loop and, on the other hand, a natural generalization of this method to higher loops. In particular, to any Feynman diagram is associated a generalized meromorphic zeta function. For the one-loop vacuum diagram, it is directly related to the usual spectral zeta function. To any loop order, the renormalized amplitudes can be read off from the pole structure of the generalized zeta functions. We focus on scalar field theories and illustrate the general formalism by explicit calculations at one-loop and two-loop orders, including a two-loop evaluation of the conformal anomaly. |
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Keywords: | Zeta function regularization Quantum field theory in curved spacetime Higher loops in curved spacetime Spectral cutoff regularization Conformal anomaly |
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