Related papers: Differential algebra and mathematical physics

A differential version of the classical Weil descent is established in all characteristics. It yields a theory of differential restriction of scalars for differential varieties over finite differential field extensions. This theory is then…

Differential geometry may be generalized to allow infinitesimals to any order. The purpose of the present contribution is to show that the theory so developed expands received geometrical ideas in an interesting way, rich in potential for…

Second-order superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the non-linear partial differential equations employed in current methods become unmanageable. Here we propose…

A characteristic feature of differential-algebraic equations is that one needs to find derivatives of some of their equations with respect to time, as part of so called index reduction or regularisation, to prepare them for numerical…

Secondary Calculus is a formal replacement for differential calculus on the space of solutions of a system of possibly non-linear partial differential equations and it is essentially due to Alexandre M. Vinogradov and his collaborators.…

A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one…

In this paper, we define the semi-symmetric metric connection on the algebra of differential forms. We compute some special semi-symmetric metric connections and their curvature tensor and their Ricci tensor on the algebra of differential…

A rigorous mathematical theory of dimensional analysis, systematically accounting for the use of physical quantities in science and engineering, perhaps surprisingly, was not developed until relatively recently. We claim that this has…

A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…

Many important theories in modern physics can be stated using differential geometry. Symplectic geometry is the natural framework to deal with autonomous Hamiltonian mechanics. This admits several generalizations for nonautonomous systems,…

This paper introduces a notion of differential forms on closed, potentially fractal, subsets of Euclidean space by defining pointwise cotangent spaces using the restriction of $C^1$ functions to this set. Aspects of cohomology are…

In the book, I considered differential equations of order $1$ over Banach $D$\Hyph algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. I considered examples of…

We consider the algebra of N x N matrices as a reduced quantum plane on which a finite-dimensional quantum group H acts. This quantum group is a quotient of U_q(sl(2,C)), q being an N-th root of unity. Most of the time we shall take N=3; in…

A non-traditional approach to the discretization of differential-geometrical connections was suggested by the authors in 1997. At the same time we started studying first order difference ``black and white triangle operators (equations)'' on…

In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…

(This short article is a continuation of a longer, review work, in the same volume of Proceedings, by Ashtekar, Marolf and Mour\~ao [gr-qc/9403042]. All the details and other results are to be found in joint papers of the author with Abhay…

The aim of this article is to highlight the interest to apply Differential Geometry and Mechanics concepts to chaotic dynamical systems study. Thus, the local metric properties of curvature and torsion will directly provide the analytical…

The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…

We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…

A geometric approach is used to study the Abel first order differential equation of the first kind. The approach is based on the recently developed theory of quasi-Lie systems which allows us to characterise some particular examples of…