Schwinger--DeWitt expansion for the heat kernel of nonminimal operators in causal theories

Abstract

We suggest a systematic calculational scheme for heat kernels of covariant nonminimal operators in causal theories whose characteristic surfaces are null with respect to a generic metric. The calculational formalism is based on a pseudodifferential operator calculus which allows one to build a linear operator map from the heat kernel of the minimal operator to the nonminimal one. This map is realized as a local expansion in powers of spacetime curvature, dimensional background fields, and their covariant derivatives with the coefficients -- the functions of the Synge world function and its derivatives. Finiteness of these functions, determined by multiple proper time integrals, is achieved by a special subtraction procedure which is an important part of the calculational scheme. We illustrate this technique on the examples of the vector Proca model and the vector field operator with a nondegenerate principal symbol. We also discuss smoothness properties of heat kernels of nonminimal operators in connection with the nondegenerate nature of their operator symbols.

15 pages. Subsection 8.1 containing the lowest nontrivial order of perturbation theory for a nonminimal vector field operator with a generic potential term is added, along with Section 9 where commutator algebra of the generic order is presented explicitly. Typos are corrected

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Cited by in corpus (6)

• Functorial properties of Schwinger-DeWitt expansion and Mellin-Barnes representation
• Heat kernel of non-minimal second-order operators
• Quantizing non-projectable Hořava gravity with Lagrangian path integral
• Heat kernel approach to the one-loop effective action for nonlinear electrodynamics
• Pseudodifferential calculus in Schwinger--DeWitt formalism: UV and IR parts
• Conformal gauge theory of vector-spinors and spin-3/2 particles