Seeley–DeWitt coefficients

Summary

The Seeley–DeWitt coefficients are the coefficients $a_k(x)$ of the small-time asymptotic expansion of the heat kernel of a Laplace-type operator on the diagonal. They are local invariants: each is a universal polynomial in the curvature, the endomorphism part of the operator, and their covariant derivatives. Their integrals are spectral invariants, and in index theory and quantum field theory they compute indices, anomalies and divergences. For the scalar Laplacian they are the coefficients of the Minakshisundaram–Pleijel expansion.