# Diagram technique for the heat kernel of the covariant Laplace operator

## TL;DR

This paper introduces a diagrammatic method to compute Seeley-DeWitt coefficients for covariant Laplace operators, utilizing combinatorial properties to develop a matrix formalism for arbitrary coefficients.

## Contribution

The paper presents a novel diagram technique and matrix formalism for calculating Seeley-DeWitt coefficients in covariant Laplace operators, advancing computational methods in geometric analysis.

## Key findings

- Developed a diagrammatic approach for coefficient calculation
- Derived a general formula for arbitrary coefficients
- Enhanced computational efficiency for heat kernel analysis

## Abstract

We present a diagram technique used to calculate the Seeley-DeWitt coefficients for a covariant Laplace operator. We use the combinatorial properties of the coefficients to construct a matrix formalism and derive a formula for an arbitrary coefficient.