A Diffeomorphism-Invariant Cut-Off Regularization of the Determinant of a Scalar Particle in a Euclidean Gravitational Field

Details A Diffeomorphism-Invariant Cut-Off Regularization of the Determinant of a Scalar Particle in a Euclidean Gravitational Field A Diffeomorphism-Invariant Cut-Off Regularization of the Determinant of a Scalar Particle in a Euclidean Gravitational Field

1997-06-27

arxiv.org/abs/hep-th/9706205v1

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, LaTeX

Scientific paper

Continuing the thrust of our recent work, but with an important new idea, we find a cut-off regularization of the determinant of a scalar particle in a classical Euclidean gravitational field. The field is assumed asymptotically flat, and the regularization is diffeomorphism-invariant under coordinate changes that are the identity at infinity. The scalar field is expanded in term of variables that depend on the gravitational field, with wavelet localization of each variable. A renormalization group structure is thus automatically present. A similar construction is carried out for the determinant of a scalar field in a background Yang-Mills field.

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