Related papers: Kink Moduli Spaces -- Collective Coordinates Recon…
We apply the collective coordinate model framework to describe collisions of a kink and an antikink with nonzero total momentum, i.e., when the solitons possess different velocities. The minimal moduli space with only two coordinates (the…
The moduli space approximation to kink dynamics permits a relativistic generalization if the Derrick scaling parameter is used as a collective coordinate. We develop a perturbative approach to the resulting relativistic moduli space by…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…
In this work, families of kinks are analytically identified in multifield theories with either polynomial or deformed sine-Gordon-type potentials. The underlying procedure not only allows us to obtain analytical solutions for these models,…
Let $(X, \omega)$ be a compact symplectic manifold and $L$ be a Lagrangian submanifold. Suppose $(X, L)$ has a Hamiltonian $S^1$ action with moment map $\mu$. Take an invariant $\omega$-compatible almost complex structure, we consider…
The collective coordinates approximation for the kink/anti-kink scattering in the $1+1$ dimensional $\phi^4$ model is considered and we discuss how the results found in the current literature on the topic can be improved by giving the…
The fractal velocity pattern in symmetric kink-antikink collisions in $\phi^4$ theory is shown to emerge from a dynamical model with two effective moduli, the kink-antikink separation and the internal shape mode amplitude. The shape mode…
Examining the $\phi^{4}$ and $\phi^{8}$ models within a two-dimensional framework in the flat spacetime and embracing a theory with unconventional kinetic terms, one investigates the emergence of kinks/antikinks and double-kinks/antikinks.…
We compare numerical solutions to the full field equations to simplified approaches based on implementing three collective coordinates for kink-antikink interactions within the $\varphi^4$ and $\phi^6$ models in one time and one space…
The moduli space of static finite energy solutions to Ward's integrable chiral model is the space $M_N$ of based rational maps from $\CP^1$ to itself with degree $N$. The Lagrangian of Ward's model gives rise to a K\"ahler metric and a…
Wigner's irreducible positive energy representations of the Poincare group are often used to give additional justifications for the Lagrangian quantization formalism of standard QFT. Here we study another more recent aspect. We explain in…
We analyze the perturbative Relativistic Moduli Space approach, where the amplitudes of the Derrick modes are promoted to collective coordinates. In particular, we analyse the possibility to calculate the critical velocity, i.e., the…
Many moduli spaces are constructed as quotients of group actions; this paper surveys the classical theory, as well as recent progress and applications. We review geometric invariant theory for reductive groups and how it is used to…
Studied are moduli spaces of self dual or anti-self dual connections on noncommutative 4-manifolds, especially deformation quantization of compact spin Riemannian 4-manifolds and their isometry groups have 2-torus subgroup. Then such moduli…
We classify parallelizable noncommutative manifold structures on finite sets of small size in the general formalism of framed quantum manifolds and vielbeins introduced previously. The full moduli space is found for $\le 3$ points, and a…
We obtain a compactness result for various classes of Riemannian metrics in dimension four; in particular our method applies to anti-self-dual metrics, Kahler metrics with constant scalar curvature, and metrics with harmonic curvature. With…
In this manuscript, we aim to classify and characterize the moduli space of homogeneous spin connections and homogeneous SU(2) connections on three-dimensional Riemannian homogeneous spaces. An analysis of the topology of the associated…
Minkowski space, conformal group, compactification, conformal infinity, conformal inversion, light cone at infinity, SU(2,2), SO(4,2), Hodge star operator, Clifford algebra, spinors, twistors, antilinear operators, exterior algebra,…
In this paper, we explored a class of potentials with three minima that support kink solutions exhibiting one long-range tail. We analyzed antikink-kink interactions using an effective Lagrangian based on collective coordinates and compared…
We consider the moduli space, in the sense of Kisin, of finite flat models of a 2-dimensional representation with values in a finite field of the absolute Galois group of a totally ramified extension of $mathbb{Q}_p$. We determine the…