The gauge covariance of the quark gap equation is compared for the case of three different quark–gluon vertices: the bare vertex, a Ball–Chiu-like vertex constrained by the corresponding Slavnov–Taylor identity, and a full vertex in...
The gauge equation is a generalization of the conjugacy relation for the Koszul connection to bundle morphisms that are not isomorphisms. The existence of nontrivial solution to this equation, especially when duality is imposed upon related connectio...
It is revealed that the material derivative of a variable in gravity field is its directional derivative, from which and energy/complementary-energy conservations with exterior derivatives, two sets of gauge equations of Newton’s dynamic gravit...
The equations of motion of an isospin-carrying particle in a Yang–Mills and gravitational field were first proposed in 1968 by Kerner, who considered geodesics in a Kaluza–Klein-type framework. Two years later, the flat space Kerner equat...
We consider a simple model for QCD dynamics in which DGLAP integro-differential equation may be solved analytically. This is a gauge model which possesses dominant evolution of gauge boson (gluon) distribution and in which the gauge coupling does not...
In this paper, we study possible mathematical connections of the Clifford algebra with the su(N)-Lie algebra, or in more physical terms the links between space-time symmetry (Lorentz invariance) and internal SU(N) gauge-symmetry for a massive spin on...
The paper presents an application of symmetry approach to finance. This symmetry approach comes from the gauge field theory in Physics. We revise the pricing model of financial derivatives in a financial market in a gauge symmetry view, and rewrite...
This paper investigates an integrable spin system known as the Myrzakulov-XIII (M-XIII) equation through geometric and gauge-theoretic methods. The M-XIII equation, which describes dispersionless dynamics with curvature-induced interactions, is shown...
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In this...
In this paper, we study the Kuralay equations, namely the Kuralay-I equation (K-IE) and the Kuralay-II equation (K-IIE). The integrable motion of space curves induced by these equations is investigated. The gauge equivalence between these two equatio...
Using an analogy between the multi-fractal Schrödinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge,...
An experimental method to measure forces of small magnitude with a strain gauge as a force sensor in the fluid–wall interaction of open water channels is presented. Six uniaxial strain gauges were employed for this purpose, which were embedded...
In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete ga...
Maxwell equations have two types of asymmetries between the electric and magnetic fields. The first asymmetry is the inhomogeneity induced by the absence of magnetic charge sources. The second asymmetry is due to parity. We show how both asymmetries...
We present and amplify some of our previous statements on non-canonical interrelations between the solutions to free Dirac equation (DE) and Klein–Gordon equation (KGE). We demonstrate that all the solutions to the DE (possessing point- or stri...
We investigate the dynamics of vector solitons in a two-component Bose–Einstein condensates governed by the system of Gross–Pitaevskii equations. Using a gauge-transformation approach, we construct a four-soliton solution and analyze thei...
The realization of a BRST cohomology of the 4D topological gauge-affine gravity is established in terms of a superconnection formalism. The identification of fields in the quantized theory occurs directly as is usual in terms of superconnection and i...
Electromagnetically induced transparency (EIT) is well known as a quantum optical phenomenon that permits a normally opaque medium to become transparent due to the quantum interference between transition pathways. This work addresses multi-soliton dy...
We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physi...
We apply extended local hidden-gauge formalism to study meson–meson interactions with the quark constituents ccc¯c¯, ccc¯b¯/c¯c¯cb, ccb¯b¯/c¯c¯bb, bbc¯b¯/b¯b¯cb, and bbb¯...
By employing the combined Bohmian quantum formalism with the U(1) and SU(2) gauge transformations of the non-relativistic wave-function and the relativistic spinor, within the Schrödinger and Dirac quantum pictures of electron motions, the existence...
Thick wall structures involving longitudinal wave are typically utilized in aerospace engineering, nuclear power engineering, precision transmission device design, and pressure vessels design. Consequently, developing sophisticated dynamic models for...
A dualistic structure on a smooth Riemaniann manifold M is a triple (M,g,∇) with g a Riemaniann metric and ∇ an affine connection generally assumed to be torsionless. From g and ∇, dual connection ∇* can be defined. In this wo...
The second-order differential equation for a damped harmonic oscillator can be converted to two coupled first-order equations, with two two-by-two matrices leading to the group Sp(2). It is shown that this oscillator system contains the essential fea...
Einstein's article titled, "The Fundaments of Theoretical Physics", from Science, Washington, D.C., May 24, 1940, is presented in its entirety as it is an outstanding presentation of the history and status of the foundations of theoretical physics as...
Based on Newtonian mechanics, in this article, we present a heuristic derivation of the Friedmann equations, providing an intuitive foundation for these fundamental relations in cosmology. Additionally, using the first law of thermodynamics and Euler...
Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric...
In this paper we give a derivation of a system of equations which generalize the London brothers and Ginzburg–Landau systems of equations, to describe the electrodynamics of s-wave superconductors. First, we consider a relativistically covariant theo...
This article is Part I of our series of full papers on a gauge-invariant “linear” perturbation theory on the Schwarzschild background spacetime which was briefly reported in our short papers by the present author in 2021. We first review...
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This work shows that the procedure of deriving the standard...
It has been previously demonstrated that stochastic volatility emerges as the gauge field necessary to restore local symmetry under changes in stock prices in the Black–Scholes (BS) equation. When this occurs, a Merton–Garman-like equatio...
This paper is devoted to developing a more refined mathematical theory for designing the previously proposed membrane deflection-based rain gauges. The differential-integral equations governing the large deflection behavior of the membrane are improv...
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein–Gordon–Maxwell electrodyn...
In the particular configuration of the scalar field k-essence in the Wheeler–DeWitt quantum equation, for some age in the Bianchi type I anisotropic cosmological model, a fractional differential equation for the scalar field arises naturally. T...
A fully relativistically covariant and manifestly gauge-invariant formulation of classical Maxwell electrodynamics is presented, purely in terms of gauge-invariant potentials without entailing any gauge fixing. We show that the inhomogeneous equation...
We extend the three-dimensional noncommutative relations of the position and momentum operators to those in the four dimension. Using the Seiberg-Witten (SW) map, we give the Heisenberg representation of these noncommutative algebras and endow the no...
This is the Part II paper of our series of papers on a gauge-invariant perturbation theory on the Schwarzschild background spacetime. After reviewing our general framework of the gauge-invariant perturbation theory and the proposal of gauge-invariant...
The Lagrangian formalism has provided a powerful and elegant framework for obtaining governing equations for classical and quantum systems. It is based on the concept of action, which involves Lagrangians, whose a priori knowledge is required. There...
We revisit the charge-conjugation operation for the Dirac equation in its chiral representation. A new decomposition of the Dirac spinor field is suggested and achieved by means of projection operators based on charge conjugation, which is discussed...
GeoGauge is a portable instrument for rapid determination of the stiffness and modulus of compacted soil, which can quickly, safely, and nondestructively evaluate the quality of each compacted layer. In order to deeply study the effectiveness of the...
In ultrafast science, the strong-field approximation (SFA) provides a powerful framework to describe high-order harmonic generation (HHG) and related phenomena. Meanwhile, within the current ab initio theoretical framework, the use of nonlocal potent...
The lightcone gauge is a set of what are called the observational coordinates adapted to our past lightcone. We develop this gauge by producing a perturbed spacetime metric that describes the geometry of our past lightcone where observations are usua...
We propose a gauge-invariant formulation of the channel orbital-based time-dependent configuration interaction singles (TDCIS) method [Phys. Rev. A, 74, 043420 (2006)], one of the powerful ab initio methods to investigate electron dynamics in atoms a...
A gauge function for the van der Pol oscillator is constructed and used to perform stability analysis of this system as well as to determine its dynamical states without solving the corresponding equation of motion. Despite previous claims that the o...
Within the framework of noncommutative (NC) deformation of gauge field theory by the angular twist, we first rederive the NC scalar and gauge field model from our previous papers, and then generalize it to the second order in the Seiberg–Witten...
In this paper, Lie symmetries and Noether symmetries along with the corresponding conservation laws are derived for weakly nonlinear dispersive magnetohydrodynamic wave equations, also known as the triple degenerate derivative nonlinear Schrödin...
The Aharonov-Vaidman gauge additively transforms the mean energy of a quantum mechanical system into a weak valued system energy. In this paper, the equation of motion of this weak valued energy is used to provide a mathematical statement of an exten...
For allowable defect analyses, the fracture toughness of materials needs to be accurately predicted. In this regard, a lower fluctuation of fracture toughness can lead to reduction in safety and economic risks. Crack tip opening displacement (CTOD),...
This paper shows how gauge theoretic structures arise in a noncommutative calculus where the derivations are generated by commutators. These patterns include Hamilton’s equations, the structure of the Levi–Civita connection, and generaliz...
Gravity can be formulated as a gauge theory by combining symmetry principles and geometrical methods in a consistent mathematical framework. The gauge approach to gravity leads directly to non-Euclidean, post-Riemannian spacetime geometries, providin...
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