Related papers: Non-Abelian Gauge-Invariant Cellular Automata
Gauge-invariance is a fundamental concept in Physics -- known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of…
Gauge-invariance is a fundamental concept in physics---known to provide the mathematical justification for all four fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts, directly in…
Gauge symmetries play a fundamental role in Physics, as they provide a mathematical justification for the fundamental forces. Usually, one starts from a non-interactive theory which governs `matter', and features a global symmetry. One then…
The purpose of this paper is to investigate the gauge symmetry of classical field theories in integral formalism. A gauge invariant theory is defined in terms of the invariance of the physical observables under the coordinate…
The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every…
An algorithm is described to convert Lorentz and gauge invariant expressions in non--Abelian gauge theories with matter into a standard form, consisting of a linear combination of basis invariants. This algorithm is needed for computer…
The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension…
"Physical theories of fundamental significance tend to be gauge theories. These are theories in which the physical system being dealt with is described by more variables than there are physically independent degree of freedom. The…
A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.
Lattice gauge theories are fundamental to such distinct fields as particle physics, condensed matter or quantum information theory. The recent progress in the control of artificial quantum systems already allows for studying Abelian lattice…
The role of the gauge invariance in noncommutative field theory is discussed. A basic introduction to noncommutative geometry and noncommutative field theory is given. Background invariant formulation of Wilson lines is proposed. Duality…
A particular form of non-linear $\sigma$-model, having a global gauge invariance, is studied. The detailed discussion on current algebra structures reveals the non-abelian nature of the invariance, with {\it{field dependent structure…
We give an introductory account of the recently identified gauge invariance of the equilibrium statistical mechanics of classical many-body systems [J. M\"uller et al., Phys. Rev. Lett. Phys. Rev. Lett. 133, 217101 (2024)]. The gauge…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
Physical systems may couple to other systems through variables that are not gauge invariant. When we split a gauge system into two subsystems, the gauge-invariant variables of the two subsystems have less information than the gauge…
We start by reviewing the concept of gauge invariance in quantum mechanics, for Abelian and Non-Ableian cases. Then we idescribe how the various gauge potential and field can be associated with the geometrical phase acquired by a quantum…
We study the properties of a non-abelian gauge theory subjected to a gauge invariant constraint given by the classical equations of motion. The constraint is not imposed by hand, but appears naturally when we study a particular type of…
This work studies the relationship between gauge-invariant and non gauge-invariant abelian vector models. Following a technique introduced by Harada and Tsutsui, we show that the Proca and the Chiral Schwinger models may both be viewed as…
We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by…
Generalized non-autonomous linear celullar automata are systems of linear difference equations with many variables that can be seen as convolution equations in a discrete group. We study those systems from the stand point of the Galois…