Tunneling between fermionic vacua and the overlap formalism

Abstract

The probability amplitude for tunneling between the Dirac vacua corresponding to different signs of a parity breaking fermionic mass $M$ in $2+1$ dimensions is studied, making contact with the continuum overlap formulation for chiral determinants. It is shown that the transition probability in the limit when $M\to \infty$ corresponds, via the overlap formalism, to the squared modulus of a chiral determinant in two Euclidean dimensions. The transition probabilities corresponding to two particular examples: fermions on a torus with twisted boundary conditions, and fermions on a disk in the presence of an external constant magnetic field are evaluated.

Reference added. 12 pages, LateX, no figures

References in corpus (4)

• A Method for Simulating Chiral Fermions on the Lattice
• A construction of lattice chiral gauge theories
• Chiral Fermions on the Lattice
• Determinant of twisted chiral Dirac Operator on the Lattice

Cited by in corpus (1)

• Chiral zero modes on the domain-wall model in 4+1 dimensions