Related papers: Gauge-invariance in cellular automata
Gauge-invariance is a mathematical concept that has profound implications in Physics---as it provides the justification of the fundamental interactions. It was recently adapted to the Cellular Automaton (CA) framework, in a restricted case.…
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…
We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by a random noise, and the notion of strongly stochastically…
"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…
Gauge invariance, a core principle in electrodynamics, has two separate meanings. One concept treats the photon as the gauge particle for electrodynamics. It is based on symmetries of the Lagrangian, and requires no mention of electric or…
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…
This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or…
Gauge invariance was discovered in the development of classical electromagnetism and was required when the latter was formulated in terms of the scalar and vector potentials. It is now considered to be a fundamental principle of nature,…
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…
In this paper we discuss how the gauge principle can be applied to classical-mechanics models with finite degrees of freedom. The local invariance of a model is understood as its invariance under the action of a matrix Lie group of…
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…
The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell's equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from…
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…
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…
In particle physics, the fundamental forces are subject to symmetries called gauge invariance. It is a redundancy in the mathematical description of any physical system. In this article I will demonstrate that the transformer architecture…
Gauge invariance in discrete dynamical systems and its connection with quantization are considered. For a complete description of gauge symmetries of a system we construct explicitly a class of groups unifying in a natural way the space and…
Previous analyses on the gauge invariance of the action for a generally covariant system are generalized. It is shown that if the action principle is properly improved, there is as much gauge freedom at the endpoints for an arbitrary gauge…
For gauge theory, the matrix element for any physical process is independent of the gauge used. Since this is a formal statement and examples are known where gauge invariance is violated, for any specific process this gauge invariance needs…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…