Related papers: Fractal Theory Space: Spacetime of Noninteger Dime…

Field equations in four order derivatives with respect to time and space coordinates based on modified classic relativistic energy of the fractal theory of time and space are received. It is shown appearing of new spin characteristics and…

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with…

First, let the fractal dimension D=n(integer)+d(decimal), so the fractal dimensional matrix was represented by a usual matrix adds a special decimal row (column). We researched that mathematics, for example, the fractal dimensional linear…

We construct a covariant and gauge-invariant theory describing massive fractons in three spacetime dimensions, based on a symmetric rank-2 tensor field. The model includes a Chern-Simons-like term that plays a dual role: it generates a…

A pedagogical and self-contained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the Weyl-Wigner…

We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display…

In the space and the time with a fractional dimensions the Lorents transformations fulfill only as a good approach and become exact only when dimensions are integer. So the principle of relativity (it is exact when dimensions are integer)…

We consider a matrix space based on the spin degree of freedom, describing both a Hilbert state space, and its corresponding symmetry operators. Under the requirement that the Lorentz symmetry be kept, at given dimension, scalar symmetries,…

The extended Yang-Mills gauge theory in Euclidean space is a renormalizable (by power counting) gauge theory describing a local interacting theory of scalar, vector, and tensor gauge fields (with maximum spin 2). In this article we study…

A very simple field theory in noncommutative phase space X^{M},P^{M} in d+2 dimensions, with a gauge symmetry based on noncommutative u*(1,1), furnishes the foundation for the field theoretic formulation of Two-Time Physics. This leads to a…

We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined…

We propose a new field-theoretic framework for formulating the non-relativistic quantum mechanics of D particles in a Fock space of U(N) Yang-Mills theories with all different N in a unified way. D-particle field operators, creating and…

We propose a model for a power-counting renormalizable field theory living in a fractal spacetime. The action is Lorentz covariant and equipped with a Stieltjes measure. The system flows, even in a classical sense, from an ultraviolet…

Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to…

We construct a family of measures for random fields based on the iterated subdivision of simple geometric shapes (triangles, squares, tetrahedrons) into a finite number of similar shapes. The intent is to construct continuum limits of scale…

It is shown that the $SU(2)$ Yang-Mills theory in $3$-dimensional Riemann-Cartan space-time can be completely reformulated as a gravity-like theory in terms of gauge invariant variables. The resulting Yang-Mills induced equations are found,…

Fracton theories possess exponentially degenerate ground states, excitations with restricted mobility, and nontopological higher-form symmetries. This paper shows that such theories can be defined on arbitrary spatial lattices in three…

Various gauge invariant but non-Yang-Mills dynamical models are discussed: Pr\'ecis of Chern-Simons theory in (2+1)-dimensions and reduction to (1+1)-dimensional B-F theories; gauge theories for (1+1)-dimensional gravity-matter…

We study dipole Chern-Simons theory with and without a cosmological constant in $2+1$ dimensions. We write the theory in a second order formulation and show that this leads to a fracton gauge theory coupled to Aristotelian geometry which…

We study a model of quantum Yang-Mills theory with a finite number of gauge invariant degrees of freedom. The gauge field has only a finite number of degrees of freedom since we assume that space-time is a two dimensional cylinder. We…