Vacuum Energy of Quantum Fields in Classical Background Configurations

Abstract

The ground state energy of a quantum field in the background of classical field configurations is considered. The subject of the ground state energy in framework of the quantum field theory is explained. The short review of calculation methods (generalized zeta function and heat kernel expansion) and their mathematical foundations is given. We use the zeta-functional regularization and express the ground state energy as an integral involving the Jost function of a two dimensional scattering problem.We perform the renormalization by subtracting the contributions from first several heat kernel coefficients. The ground state energy is presented as a convergent expression suited for numerical evaluation. The investigation for three models has been carried out: scalar quantum field on the background of scalar string with rectangular shape, spinor vacuum polarized by magnetic string of the similar shape and spinor vacuum interacting with the Nielsen-Olesen vortex. Using the uniform asymptotic expansion of the special functions entering the Jost function we are also able to calculate higher order heat kernel coefficients. Several features of vacuum energy have been investigated numerically. We discuss corresponding numerical results.

151 pages, 82 citations, 23 figures, 3 tables, mathematical appendix

References in corpus (24)

• Semilocal and Electroweak Strings
• Casimir Effect on the Worldline
• Casimir energies for massive fields in the bag
• Vacuum instability in external fields
• Casimir energy in the MIT bag model
• On the ground state energy for a penetrable sphere and for a dielectric ball
• Heat kernels and zeta-function regularization for the mass of the supersymmetric kink
• Vacuum energy in a spherically symmetric background field
• Heat trace asymptotics with transmittal boundary conditions and quantum brane-world scenario
• The ground state energy of a spinor field in the background of a finite radius flux tube
• An Exact QED_{3+1} Effective Action
• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• Fermion-induced quantum action of vortex systems
• Quantum corrections to the mass of the supersymmetric vortex
• Fermionic Vacuum Energy from a Nielsen-Olesen Vortex
• Heat Kernel Expansions for Distributional Backgrounds
• Center-Vortex Solutions of the Yang-Mills Effective Action in Three and Four Dimensions
• Dirac fields in the background of a magnetic flux string and spectral boundary conditions
• The Dirac Sea Contribution To The Energy Of An Electroweak String
• On the Vacuum energy of a Color Magnetic Vortex
• Casimir energy of massive MIT fermions in a Bohm-Aharonov background
• Vacuum energy in the presence of a magnetic string with delta function profile
• Dependence of the vacuum energy on spherically symmetric background fields
• Strong magnetic field asymptotic behaviour for the fermion-induced effective energy in the presence of a magnetic flux tube