A Hamiltonian Approach to the Heat Kernel of a SubLaplacian on S(2n+1)

TL;DR

This paper derives the heat kernel for the Cauchy-Riemann subLaplacian on odd-dimensional spheres using a Hamiltonian approach, showing parallels with classical elliptic heat kernel methods.

Contribution

It introduces a Hamiltonian method to obtain the heat kernel for a subelliptic operator, extending classical techniques to subLaplacians on spheres.

Findings

Heat kernel derived using Hamiltonian approach

Method parallels classical elliptic heat kernel derivation

Supports applicability of Hamiltonian methods to subelliptic operators

Abstract

The heat kernel for the Cauchy-Riemann subLaplacian on S(2n+1) is derived in a manner which is completely analogous to the classical derivation of elliptic heat kernels. This suggests that the classical hamiltonian construction of elliptic heat kernels, with appropriate modifications, does yield heat kernels for subelliptic operators.