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

Abstract

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.

25 pages, 3 figures

References in corpus (4)

• Zeta Functions and the Casimir Energy
• On the ground state energy for a penetrable sphere and for a dielectric ball
• Strongly first order electroweak phase transition induced by primordial hypermagnetic fields
• Dirac fields in the background of a magnetic flux string and spectral boundary conditions

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