Quantum heat traces

Abstract

We study new invariants of elliptic partial differential operators acting on sections of a vector bundle over a closed Riemannian manifold that we call the relativistic heat trace and the quantum heat traces. We obtain some reduction formulas expressing these new invariants in terms of some integral transforms of the usual classical heat trace and compute the asymptotics of these invariants. The coefficients of these asymptotic expansion are determined by the usual heat trace coefficients (which are locally computable) as well as by some new global invariants.

33 pages

References in corpus (3)

• Heat Kernel Approach in Quantum Field Theory
• Green functions of higher-order differential operators
• The Heat Kernel Coefficients to the Matrix Schrödinger Operator

Cited by in corpus (6)

• Hearing the shape of inequivalent spin structures and exotic Dirac operators
• Bogolyubov invariant via relative spectral invariants on manifolds
• Relative Spectral Invariants of Elliptic Operators on Manifolds
• Heat Semigroups on Weyl Algebra
• Virial coefficients expressed by heat kernel coefficients
• Spectral Asymptotics of Elliptic Operators on Manifolds