The ground state energy of a spinor field in the background of a finite radius flux tube

Details The ground state energy of a spinor field in the background of a finite radius flux tube The ground state energy of a spinor field in the background of a finite radius flux tube

1998-12-07

arxiv.org/abs/hep-th/9812060v1

Phys.Rev.D60:105019,1999

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 3 figures

Scientific paper

10.1103/PhysRevD.60.105019

We develop a formalism for the calculation of the ground state energy of a spinor field in the background of a cylindrically symmetric magnetic field. The energy is expressed in terms of the Jost function of the associated scattering problem. Uniform asymptotic expansions needed are obtained from the Lippmann-Schwinger equation. The general results derived are applied to the background of a finite radius flux tube with a homogeneous magnetic field inside and the ground state energy is calculated numerically as a function of the radius and the flux. It turns out to be negative, remaining smaller by a factor of $\alpha$ than the classical energy of the background except for very small values of the radius which are outside the range of applicability of QED.

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