Spectral boundary conditions for generalizations of Laplace and Dirac operators

Abstract

Spectral boundary conditions for Laplace-type operators, of interest in string and brane theory, are partly Dirichlet, partly Neumann-type conditions, partitioned by a pseudodifferential projection. We give sufficient conditions for existence of associated heat trace expansions with power and power-log terms. The first log coefficient is a noncommutative residue, vanishing when the smearing function is 1. For Dirac operators with general well-posed spectral boundary conditions, it follows that the zeta function is regular at 0. In the selfadjoint case, the eta function has a simple pole at zero, and the value of zeta as well as the residue of eta at zero are stable under perturbations of the boundary projection of order at most minus the dimension.

38 pages, to appear in Comm. Math. Phys., further references to physics literature included, typos corrected, AMSTeX

References in corpus (3)

• Heat Kernel Approach in Quantum Field Theory
• Spectral branes
• Logarithmic terms in trace expansions of Atiyah-Patodi-Singer problems

Cited by in corpus (10)

• Heat kernel expansion: user's manual
• Dai-Freed theorem and topological phases of matter
• The Dirac system on the Anti-de Sitter Universe
• Analytic Torsion of Z_2-graded Elliptic Complexes
• Casimir effect with non-local boundary conditions
• Three lectures on global boundary conditions and the theory of self--adjoint extensions of the covariant Laplace--Beltrami and Dirac operators on Riemannian manifolds with boundary
• A Feynman-Kac formula for differential forms on manifolds with boundary and applications
• Analytic torsion for twisted de Rham complexes
• Spectral Asymmetry, Zeta Functions and the Noncommutative Residue
• A new proof of the local regularity of the eta invariant of a Dirac operator