Tunneling between fermionic vacua and the overlap formalism

Details Tunneling between fermionic vacua and the overlap formalism Tunneling between fermionic vacua and the overlap formalism

1996-04-09

arxiv.org/abs/hep-th/9604050v2

Phys.Lett. B385 (1996) 193-197

Physics

High Energy Physics

High Energy Physics - Theory

Reference added. 12 pages, LateX, no figures

Scientific paper

10.1016/0370-2693(96)00852-0

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.

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