Heat trace for Laplacian type operators with non-scalar symbols

Abstract

For an elliptic selfadjoint operator $P=-[u^{\mu \nu }{\partial }_{\mu }{\partial }_{\nu }+v^{\nu }{\partial }_{\nu }+w]$ acting on a fiber bundle over a Riemannian manifold, where $u,v^{\mu },w$ are $N\times N$-matrices, we develop a method to compute the heat-trace coefficients $a_r$ which allows to get them by a pure computational machinery. It is exemplified in dimension 4 by the value of $a_1$ written both in terms of $u,v^{\mu },w$ or diffeomorphic and gauge invariants. We also answer to the question: when is it possible to get explicit formulae for $a_r$?

37 pages. v2: misprints corrected, references added, section 5.4 added

References in corpus (2)

• Local momentum space and the vector field
• A note on the heat kernel coefficients for nonminimal operators

Cited by in corpus (4)

• Schwinger--DeWitt expansion for the heat kernel of nonminimal operators in causal theories
• Heat coefficient $a_4$ for nonminimal Laplace type operators
• Effective actions in supersymmetric gauge theories: heat kernels for non-minimal operators
• Heat kernel approach to the one-loop effective action for nonlinear electrodynamics