Related papers: Curvature Corrections to Dynamics of Domain Walls

We subject the methodology used to derive the effective dynamics of topological defects to a critical reappraisal, using the two-dimensional kink as an illustrative example. Special care is taken on how the zero modes should be handled in…

The effective action of a (1+2)-dimensional defect is obtained as an expansion in powers of the thickness.Considering non-straight solutions as the zero order term, the corrections to the Nambu action are found to depend on the curvature…

We comment on some calculations concerning the finite-thickness corrections to the (generalized) Nambu action for a curved domain wall in Minkowski space. Contrary to a recent claim in the literature, we find no first order corrections in…

We introduce a systematic method to derive the effective action for domain walls directly from the scalar field theory that gives rise to their solitonic solutions. The effective action for the Goldstone mode, which characterizes the…

Relativistic domain walls are studied in the framework of a polynomial approximation to the field interpolating between different vacua and forming the domain wall. In this approach we can calculate evolution of a core and of a width of the…

In this paper we extend the local scalar curvature rigidity result in [6] to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in…

A relativistic generalisation of a well-known method for approximating the dynamics of topological defects in condensed matter is constructed, and applied to the evolution of domain walls in a cosmological context. It is shown that there…

The purpose of the present paper is to present the main applications of a new method for the determination of the fractal structure of plane curves. It is focused on the inverse problem, that is, given a curve in the plane, find its fractal…

Here is an English summary of the abstract: This research investigates a geometric dynamical mechanism within a specific class of domains that contain a fixed convex core. By using a radial structure that links the boundaries of the core…

The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the…

We derive the effective action for a domain wall with small thickness in curved spacetime and show that, apart from the Nambu term, it includes a contribution proportional to the induced curvature. We then use this action to study the…

I report on some work in progress on the dynamics of extended objects in field theories after a rapid phase transition, as is relevant in the early Universe. An analytic technique, originally introduced to approximate the dynamics of…

It has been observed earlier that, in principle, it is possible to obtain a quantum mechanical interpretation of higher order quantum cosmological models in the spatially homogeneous and isotropic background, if auxiliary variable required…

Canonical methods can be used to construct effective actions from deformed covariance algebras, as implied by quantum-geometry corrections of loop quantum gravity. To this end, classical constructions are extended systematically to…

This paper addresses the question of whether it can be beneficial for an optimization algorithm to follow directions of negative curvature. Although prior work has established convergence results for algorithms that integrate both descent…

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…

We study a series of the Wess-Zumino actions obtained by repeatedly integrating conformal anomalies with respect to the conformal-factor field that appear at higher loops. We show that they arise as physical quantities required to make…

A version of the singular Yamabe problem in bounded domains yields complete conformal metrics with negative constant scalar curvatures. In this paper, we study whether these metrics have negative Ricci curvatures. Affirmatively, we prove…

The recently proposed technique to regularize the divergences of the gravitational action on non-compact space by adding boundary counterterms is studied. We propose prescription for constructing the boundary counterterms which are…

The effects of quantum corrections to a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary are considered in the context of a renormalisation procedure. The renormalisation of the…