Fermion determinant for general background gauge fields

Abstract

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.

arXiv commentSome typographical errors have now been corrected

References in corpus (11)

• On the QED Effective Action in Time Dependent Electric Backgrounds
• Borel Summation of the Derivative Expansion and Effective Actions
• Topological Charge and The Spectrum of Exactly Massless Fermions on the Lattice
• QED in inhomogeneous magnetic fields
• Fermionic Determinant of the Massive Schwinger Model
• Some remarks on the Ginsparg-Wilson fermion
• Fermion Determinants in Static, Inhomogeneous Magnetic Fields
• Fermion Determinants
• Mass zeros in the one-loop effective actions of QED in 1+1 and 3+1 dimensions
• Chiral limit of the two-dimensional fermionic determinant in a general magnetic field
• Bound states for Overlap and Fixed Point Actions close to the chiral limit

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• Evidence for mass zeros of the fermionic determinant in four-dimensional quantum electrodynamics
• The Derivative Expansion at Small Mass for the Spinor Effective Action
• Monopole Decay in a Variable External Field
• Full mass range analysis of the QED effective action for an O(2)xO(3) symmetric field
• Strong magnetic field asymptotic behaviour for the fermion-induced effective energy in the presence of a magnetic flux tube
• Fermion Determinants: Some Recent Analytic Results