Generalized Zeta Functions and One-loop Corrections to Quantum Kink Masses

Abstract

A method for describing the quantum kink states in the semi-classical limit of several (1+1)-dimensional field theoretical models is developed. We use the generalized zeta function regularization method to compute the one-loop quantum correction to the masses of the kink in the sine-Gordon and cubic sinh-Gordon models and another two $\mathrm{P}(\varphi {)}_2$ systems with polynomial self-interactions.

29 pages, 4 figures; version to appear in Nucl. Phys. B

Cited by in corpus (35)

• Heat kernel expansion: user's manual
• Heat kernels and zeta-function regularization for the mass of the supersymmetric kink
• Deformed defects for scalar fields with polynomial interactions
• One-loop correction to classical masses of quantum kink families
• Kink dynamics in a system of two coupled scalar fields in two space-time dimensions
• A new renormalization approach to the Dirichlet Casimir effect for ϕ^4 theory in (1+1) dimensions
• The Dirichlet Casimir effect for ${\varphi }^4$ theory in (3+1) dimensions: A new renormalization approach
• Vacuum Polarization Energy for General Backgrounds in One Space Dimension
• Quantum oscillations of self-dual Abrikosov-Nielsen-Olesen vortices
• On a family of (1+1)-dimensional scalar field theory models: kinks, stability, one-loop mass shifts
• Radiative Correction to the Dirichlet Casimir Energy for $\lambda {\varphi }^4$ Theory in Two Spatial Dimensions
• Quantum-induced interactions in the moduli space of degenerate BPS domain walls
• One-loop kink mass shifts: a computational approach
• Emerging Translational Variance: Vacuum Polarization Energy of the ${\varphi }^6$ kink
• One loop corrections to the mass of self-dual semi-local planar topological solitons
• BPS and non-BPS kinks in a massive non-linear S^2-sigma model
• Quantum corrections to the noncommutative kink
• Kinks in the Hartree approximation
• On domain walls in a Ginzburg-Landau non-linear S^2-sigma model
• Kink fluctuation asymptotics and zero modes
• Quantum magnetic flux lines, BPS vortex zero modes, and one-loop string tension shifts
• Quantum corrections to static solutions of Nahm equation and Sin-Gordon models via generalized zeta-function
• Domain walls in a non-linear ${\mathbb{S}}^2$-sigma model with homogeneous quartic polynomial potential
• Stability Equation and Two-Component Eigenmode for Domain Walls in a Scalar Potential Model
• On self-gravitating kinks in two-dimensional pseudo-riemannian universes
• One-loop mass shift formula for kinks and self-dual vortices
• On the semiclassical mass of ${\mathbb{S}}^2$-kinks
• One-loop fluctuations of semi-local self-dual vortices
• Quantum corrections to vortex masses and energies
• A note on one-loop soliton quantum mass corrections
• Vacuum Polarization Energy of a Proca Soliton
• Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay
• One-loop quantum cosmological correction to the gravitational constant using the kink solution in de Sitter universe
• Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay
• One-loop quantum cosmological correction to the gravitational constant in the closed Friedmann-Robertson-Walker universe