Related papers: A Note on Functional Integral over the Local Gauge…

In the absence of Gribov complications, the modified gauge fixing in gauge theory $ \int{\cal D}A_{\mu}\{\exp[-S_{YM}(A_{\mu})-\int f(A_{\mu})dx] /\int{\cal D}g\exp[-\int f(A_{\mu}^{g})dx]\}$ for example, $f(A_{\mu})=(1/2)(A_{\mu})^{2}$, is…

The issue of local gauge invariance in the simplicial lattice formulation of gravity is examined. We exhibit explicitly, both in the weak field expansion about flat space, and subsequently for arbitrarily triangulated background manifolds,…

We find that sometimes the usual definition of functional integration over the gauge group through limiting process may have internal difficulties.

Let $\mu$ be the Haar measure of a unimodular locally compact group $G$ and $m (G)$ as the infimum of the volumes of all open subgroups of $G$. The main result of this paper is that \begin{align*} \int_{G}^{} f \circ \left( \phi_1 * \phi_2…

In 4D compact U(1) lattice gauge theory with a monopole term added to the Wilson action we first reveal some properties of a third phase region at negative $\beta$. Then at some larger values of the monopole coupling $\lambda$ by a…

We add to the literature the following observation. If $\mu$ is a singular measure on $\mathbb{R}^n$ which assigns measure zero to every porous set and $f:\mathbb{R}^n\rightarrow\mathbb{R}$ is a Lipschitz function which is…

We classify locally finite joinings with respect to the Burger-Roblin measure for the action of a horospherical subgroup $U$ on $\Gamma \backslash G$, where $G = \operatorname{SO}(n,1)^\circ$ and $\Gamma$ is a convex cocompact and Zariski…

We introduce local iterated function systems and present some of their basic properties. A new class of local attractors of local iterated function systems, namely local fractal functions, is constructed. We derive formulas so that these…

Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…

Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set…

In this paper, we prove the fractional Hardy inequality on polarisable metric measure spaces. The integral Hardy inequality for $1<p\leq q<\infty$ is playing a key role in the proof. Moreover, we also prove the fractional Hardy-Sobolev type…

Critical properties of the compact three-dimensional U(1) lattice gauge theory are explored at finite temperatures on an asymmetric lattice. For vanishing value of the spatial gauge coupling one obtains an effective two-dimensional spin…

Suppose $G$ is a locally solid lattice group. It is known that there are non-equivalent classes of bounded homomorphisms on $G$ which have topological structures. In this paper, our attempt is to assign lattice structures on them. More…

In this paper, we study functional and geometric inequalities on complete Finsler measure spaces under the condition that the weighted Ricci curvature ${\rm Ric}_\infty$ has a lower bound. We first obtain some local uniform Poincar\'{e}…

If ${\mathcal C}\simeq 2^{\mathbb N}$ denotes the Cantor set realized as the infinite product of two-point groups, then a folklore result says the Cantor map from ${\mathcal C}$ into $[0,1]$ sends Haar measure to Lebesgue measure on the…

Haar measure is a fundamental structure in harmonic analysis on locally compact groups. Its existence reflects the compatibility between topology and the associative algebraic structure of groups. In this paper we propose a framework for…

Davydov, Moldavskaya, and Zitikis introduced local indices for quantifying the lack of convexity of a \(C^2\) function by measuring the nuclear-norm distance of its Hessian from the cone of positive semidefinite matrices. This paper…

This article provides a concise introduction to the theory of Haar measures on locally compact Hausdorff groups. We cover the necessary preliminaries on topological groups and measure theory, the Haar correspondence, unimodularity and Haar…

We study gauge fixing via the standard local extremization algorithm for 2-dimensional $U(1)$. On a lattice with spherical topology $S^2$ where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in…

The Wilson action for Euclidean lattice gauge theory defines a positive-definite transfer matrix that corresponds to a unitary lattice gauge theory time-evolution operator if analytically continued to real time. Hoshina, Fujii, and Kikukawa…