In general coordinate invariant gravity theories whose Lagrangians contain arbitrarily high order derivative fields, the Noether currents for global translation and Nakanishi’s IOSp(8|8) choral symmetry containing BRS as its member are constructed. We generally show that each of these currents, a suitable linear combination equations motion can be brought into form Maxwell-type field equation p...

The aim of this article is to classify completely integrable systems of the following form ut = u3 + f(u, v, u1, v1, u2, v2, ), vt = g(u, v, u1, v1). Here, ui = ∂u/∂x, ut = ∂u/∂t. The popular symmetry approach to the classification of integrable partial differential systems requires large calculations. That is why we applied the simpler ”Chinese” method that deals with canonical conserved densi...

This paper investigates the geometry of compact stellar objects via Noether symmetry strategy in framework curvature-matter coupled gravity. For this purpose, we assume specific model theory to evaluate equations, generators and corresponding conserved parameters. We use parameters examine some fascinating attributes for suitable values It is analyzed that depend on quantities find obtained sol...

We consider a cosmological model in Friedmann--Lema\^{\i}tre--Robertson--Walker background space with an ideal gas defined Weyl Integrable gravity. In the Einstein-Weyl theory scalar field is introduced geometric way. Furthermore, and interact gravitational Action Integral. we introduce potential term for show that equations admit minisuperspace description. Noether's theorem applied constraint...

-In this paper we study the interplay between dynamical systems geometrical theory and computational calculus of dynamical systems. The viewpoint is geometric and we also compute and characterize objects of dynamical significance, in order to understanding the mathematical properties observed in numerical computation for dynamical models arising in mathematics, science and engineering. We use a...

We study a classical many-particle system with an external control represented by a time-dependent extensive parameter in a Lagrangian. We show that thermodynamic entropy of the system is uniquely characterized as the Noether invariant associated with a symmetry for an infinitesimal nonuniform time translation t→t+ηℏβ, where η is a small parameter, ℏ is the Planck constant, β is the inverse tem...

The tetrad gauge invariant theory of the free Dirac field in two special moving charts of the de Sitter spacetime is investigated pointing out the operators that commute with the Dirac one. These are the generators of the symmetry transformations corresponding to isometries that give rise to conserved quantities according to the Noether theorem. With their help the plane wave spinor solutions o...

This paper has two main objectives: (a) Discuss the formal analogy between some important symmetry–invariance arguments used in physics, probability and statistics. Specifically, we will focus on Noether theorems in physics, maximum entropy principle in probability theory, and de Finetti type theorems in Bayesian statistics. (b) Discuss the epistemological and ontological implications of these ...

Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We examine the local conformal invariance (Weyl invariance) in tensor-scalar theories used in recently proposed con...