Heat kernel for antisymmetric tensor field on a disk

TL;DR

This paper develops a method to simplify boundary conditions for antisymmetric tensor fields on a disk, expressing the heat kernel in terms of scalar kernels and confirming previous scaling results.

Contribution

Introduces a reduction technique for mixed boundary conditions to pure ones, specifically applied to rank-two tensors on a four-dimensional disk.

Findings

Heat kernel expressed via scalar heat kernels

Scaling behavior $(0)$ matches previous results

Method applicable to antisymmetric tensor fields

Abstract

We suggest a method of reduction of mixed absolute and relative boundary conditions to pure ones. The case of rank two tensor is studied in detail. For four-dimensional disk the corresponding heat kernel is expressed in terms of scalar heat kernels. The result for scaling behavior $\zeta (0)$ agrees with previous calculations.