Dirac Operator on a disk with global boundary conditions

Abstract

We compute the functional determinant for a Dirac operator in the presence of an Abelian gauge field on a bidimensional disk, under global boundary conditions of the type introduced by Atiyah-Patodi-Singer. We also discuss the connection between our result and the index theorem.

RevTeX, 11 pages. References added

References in corpus (8)

• Zeta function determinant of the Laplace operator on the $D$-dimensional ball
• Local Boundary Conditions for the Dirac Operator and One-Loop Quantum Cosmology
• Spectral Boundary Conditions in One-Loop Quantum Cosmology
• Gauge Theories in a Bag
• Antisymmetric tensor fields on spheres: functional determinants and non--local counterterms
• Heat-kernel coefficients and functional determinants for higher-spin fields on the ball
• Functional determinants on certain domains
• Determinants of Dirac operators with local boundary conditions

Cited by in corpus (10)

• Heat kernel expansion: user's manual
• Quark zero modes in intersecting center vortex gauge fields
• Intersections of thick Center Vortices, Dirac Eigenmodes and Fractional Topological Charge in SU(2) Lattice Gauge Theory
• Dirac fields in the background of a magnetic flux string and spectral boundary conditions
• Casimir energy of massive MIT fermions in a Bohm-Aharonov background
• Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession
• Dirac Operator and Spectral Geometry
• Global boundary conditions for a Dirac operator on the solid torus
• $K$-theoretic computation of the Atiyah(-Patodi)-Singer index of lattice Dirac operators
• Dirac fields in a Bohm-Aharonov background and spectral boundary conditions