One-Loop Quantum Energy Densities of Domain Wall Field Configurations

Abstract

We discuss a simple procedure for computing one-loop quantum energies of any static field configuration that depends non-trivially on only a single spatial coordinate. We specifically focus on domain wall-type field configurations that connect two distinct minima of the effective potential, and may or may not be the solutions of classical field equations. We avoid the conventional summation of zero-point energies, and instead exploit the relation between functional determinants and solutions of associated differential equations. This approach allows ultraviolet divergences to be easily isolated and extracted using any convenient regularization scheme. Two examples are considered: two-dimensional ${\varphi }^4$ theory, and three-dimensional scalar electrodynamics with spontaneous symmetry breaking at the one-loop level.

RevTex, 29 pages, 1 figure, minor corrections, references added

References in corpus (1)

• Effective Energy Approach to Collectively Quantized Systems

Cited by in corpus (21)

• Electroweak Bubble Nucleation, Nonperturbatively
• Two Higgs doublet dynamics at the electroweak phase transition: a non-perturbative study
• Quantum Energies of Interfaces
• One-loop surface tensions of (supersymmetric) kink domain walls from dimensional regularization
• Higher-Order Corrections to the Bubble-Nucleation Rate at Finite Temperature
• The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction
• Vacuum Polarization Energy for General Backgrounds in One Space Dimension
• Quantum Corrections to Soliton Energies
• Quantum Mass and Central Charge of Supersymmetric Monopoles - Anomalies, current renormalization, and surface terms
• Quantum-induced interactions in the moduli space of degenerate BPS domain walls
• Emerging Translational Variance: Vacuum Polarization Energy of the ${\varphi }^6$ kink
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Thermal and Quantum Fluctuations around Domain Walls
• Spectral Methods for Coupled Channels with a Mass Gap
• One-loop results for kink and domain wall profiles at zero and finite temperature
• Boundary Terms in Supergravity and Supersymmetry
• Comment on `One Loop Renormalization of Soliton Quantum Mass Corrections in 1+1 Dimensional Scalar Field Theory Models' (Phys. Lett. B542 (2002) 282 [hep-th/0206047])
• Correlations around an interface
• A supersymmetric exotic field theory in (1+1) dimensions. One loop soliton quantum mass corrections
• A note on one-loop soliton quantum mass corrections
• Simplified Vacuum Energy Expressions for Radial Backgrounds and Domain Walls