Correlations around an interface

Abstract

We compute one-loop correlation functions for the fluctuations of an interface using a field theory model. We obtain them from Feynman diagrams drawn with a propagator which is the inverse of the Hamiltonian of a Pöschl-Teller problem. We derive an expression for the propagator in terms of elementary functions, show that it corresponds to the usual spectral sum, and use it to calculate quantities such as the surface tension and interface profile in two and three spatial dimensions. The three-dimensional quantities are rederived in a simple, unified manner, whereas those in two dimensions extend the existing literature, and are applicable to thin films. In addition, we compute the one-loop self-energy, which may be extracted from experiment, or from Monte Carlo simulations. Our results may be applied in various scenarios, which include fluctuations around topological defects in cosmology, supersymmetric domain walls, Z(N) bubbles in QCD, domain walls in magnetic systems, interfaces separating Bose-Einstein condensates, and interfaces in binary liquid mixtures.

One-loop results for kink and domain wall profiles at zero and finite temperature

“…However, we can reliably cover the onset of the melting of kinks and in this way provide benchmarks for more daring approximations and approaches. Systematic calculations of one-loop corrections to kink profiles and domain walls at zero and finite temperature have been carried out before by several authors [25][26][27][28][29]. Our results are in agreement with those once the differences in the renormalization schemes are taken into account.…”

“…As has been shown in Ref. [29], this apparent discrepancy was due to having compared two versions of a zero-momentum renormalization scheme. The zero-momentum scheme considered in Refs.…”

“…[30,31] renormalizes the derivative of the two-point function with respect to momentum to one, while the scheme in Refs. [25,29] does not introduce nontrivial wave-function renormalization, which is possible at one-loop order. Taking this difference into account resolves this issue.…”

Quantum kink and its excitations

“…In string theory, D-branes are analogous to topological defects. There has been widespread interest in the excitation spectra of topological defects, although mostly as a calculational tool for finding perturbative corrections to the mass of the defect [5,6,7,8,9,10,11]. However, excitations themselves are of physical interest [12,13,14].…”

Semiclassical approximation for the partition function in QFT

“…Even in quantum field theories, where one has to deal with partial differential equations, there are relevant examples [4][5][6] where the semiclassical propagator can be obtained using elementary methods [7].…”