Lectures on the mass of topological solitons

Abstract

In this series of lectures a method is developed to compute one-loop shifts to classical masses of kinks, multi-component kinks, and self-dual vortices. Canonical quantization is used to show that the mass shift induced by one-loop quantum fluctuations is the trace of the square root of the differential operator governing these fluctuations. Standard mathematical techniques are used to deal with some powers of pseudo-differential operators. Ultraviolet divergences are tamed by using generalized zeta function regularization methods and, then performing zero-point energy and mass renormalizations.

arXiv comment99 pages. Lecture notes on three two-hour lectures given by JMG during the third week of July 2005 in the Department of Physics of the Universidade Federal de Paraiba (Joao Pessoa, Brazil)

References in corpus (11)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• On the ground state energy for a penetrable sphere and for a dielectric ball
• Anomaly and quantum corrections to solitons in two-dimensional theories with minimal supersymmetry
• Degenerate Domain Wall Solutions in Supersymmetric Theories
• Energy, Central Charge, and the BPS Bound for 1+1 Dimensional Supersymmetric Solitons
• Nonvanishing quantum corrections to the mass and central charge of the N=2 vortex and BPS saturation
• Quantum corrections to the mass of the supersymmetric vortex
• One-loop correction to classical masses of quantum kink families
• Fermionic Vacuum Energy from a Nielsen-Olesen Vortex
• Quantum oscillations of self-dual Abrikosov-Nielsen-Olesen vortices
• Quantization of supersymmetric solitons

Cited by in corpus (13)

• Two-Loop Scalar Kinks
• One-loop kink mass shifts: a computational approach
• One loop corrections to the mass of self-dual semi-local planar topological solitons
• Quantum corrections to the noncommutative kink
• Well-Defined Quantum Soliton Masses Without Supersymmetry
• Dissecting zero modes and bound states on BPS vortices in Ginzburg-Landau superconductors
• Kink fluctuation asymptotics and zero modes
• A new simple class of superpotentials in SUSY Quantum Mechanics
• Quantum fluctuations around low-dimensional topological defects
• On the semiclassical mass of ${\mathbb{S}}^2$-kinks
• Quantum aspects of a noncommutative supersymmetric kink
• One-loop fluctuations of semi-local self-dual vortices
• Quantum scalar fields in the half-line. A heat kernel/zeta function approach