Fermion determinant for general background gauge fields

Details Fermion determinant for general background gauge fields Fermion determinant for general background gauge fields

2003-01-15

arxiv.org/abs/hep-th/0301097v3

Phys.Rev. D67 (2003) 065017

Physics

High Energy Physics

High Energy Physics - Theory

Some typographical errors have now been corrected

Scientific paper

10.1103/PhysRevD.67.065017

An exact representation of the Euclidean fermion determinant in two dimensions for centrally symmetric, finite-ranged Abelian background fields is derived. Input data are the wave function inside the field's range and the scattering phase shift with their momenta rotated to the positive imaginary axis and fixed at the fermion mass for each partial-wave. The determinant's asymptotic limit for strong coupling and small fermion mass for square-integrable, unidirecitonal magnetic fields is shown to depend only on the chiral anomaly. The concept of duality is extended from one to two-variable fields, thereby relating the two-dimensional Euclidean determinant for a class of background magnetic fields to the pair production probability in four dimensions for a related class of electric pulses. Additionally, the ``diamagnetic'' bound on the two-dimensional Euclidean determinant is related to the negative sign of dImS_eff/dm^2 in four dimensions in the strong coupling, small mass limit, where S_eff is the one-loop effective action.

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