Spectral geometry of symplectic spinors

TL;DR

This paper explores the spectral geometry of symplectic spinors, focusing on Dirac operators, defining a distance function, and analyzing heat trace asymptotics to deepen understanding of their geometric properties.

Contribution

It introduces the spectral geometry framework for symplectic spinors, including the definition of a distance function and computation of heat trace asymptotics, expanding the mathematical understanding of these operators.

Findings

Defined a new distance function for symplectic spinors

Computed heat trace asymptotics for Dirac operators on symplectic spinors

Enhanced understanding of the geometric properties of symplectic spinor bundles

Abstract

Symplectic spinors form an infinite-rank vector bundle. Dirac operators on this bundle were constructed recently by K.~Habermann. Here we study the spectral geometry aspects of these operators. In particular, we define the associated distance function and compute the heat trace asymptotics.