arXiv subjects

Jesús Muñoz-Díaz

Publications and source records attributed to Jesús Muñoz-Díaz.

6 recordsLinked to original sources

arXiv2019

A mathematical objection to the existence of relativistic mechanical systems of several particles

We will prove that, in general, a system formed by several particles moving along relativistic trajectories can not be described by a mechanical system. The contradiction that leads to the previous assertion is due to the fact that a mechanical system defines a second order differential equation and this, in turn, induces an absolute time that will generally be incompatible with the proper times of the different particles.

math-ph↗

arXiv2018

Newton's Second Law in Field Theory

In this article we present a natural generalization of Newton's Second Law valid in field theory, i.e., when the parameterized curves are replaced by parameterized submanifolds of higher dimension. For it we introduce what we have called the geodesic $k$-vector field, analogous to the ordinary geodesic field and which describes the inertial motions (i.e., evolution in the absence of forces). From this generalized Newton's law, the corresponding Hamilton's canonical equations of field theory (Hamilton-De Donder-Weyl equations) are obtained by a simple procedure. It is shown that solutions of generalized Newton's equation also hold the canonical equations. However, unlike the ordinary case, Newton equations determined by different forces can define equal Hamilton's equations.

math-ph↗

arXiv2018

Flux-variational formulation of relativistic perfect fluids

We give a variational formulation of perfect fluids on a general pseudoriemannian manifold by variating tangent fields according the flux produced by them. In this approach no constraints are needed. As a result, Euler and continuity equations are obtained quite directly.

gr-qc↗

arXiv2016

Primary spectrum of $\mathcal{C}^\infty(M)$ and jets theory

We consider, for each smooth manifold $M$, the set $\mathbb{M}$ comprised by all the primary ideals of $\mathcal{C}^\infty(M)$ which are closed and whose radical is maximal. The classical Lie theory of jets (jets of submanifolds) must be extended to $\mathbb{M}$ in order to have nice functorial properties. We will begin with the purely algebraic notions, referred always to the ring $\mathcal{C}^\infty(M)$. Subsequently it will be introduced the differentiable structures on each jets space of a given type. The theory of contact systems, which generalizes the classical one, has a part purely algebraic and another one which depends on the differentiable structures.

math.DG↗

arXiv2014

On the foundation of Mechanics

This note is an extended version of "A note on the foundations of Mechanics", arXiv: 1404.1321 [math-ph]. A presentation of its contents was given in a talk in memorial homage to the professor Juan B. Sancho Guimerá. For this reason, it was written in spanish language. The matter of the note is a systematic foundation of the most classical part of Mechanics. The content by sections is: 0) Notions and basic results, 1) Conservative systems 2) Time. Time constraints, 3) Proper time. Relativistic forces, 4) Electromagnetic fields, 5) On the Hamilton-Noether Principle, 6) Schrödinger equation.

math-ph↗

arXiv2014

A note on the foundations of mechanics

This short note is intended to review the foundations of mechanics, trying to present them with the greatest mathematical and conceptual clarity. It was attempted to remove most of inessential, even parasitic issues, which can hide the true nature of basic principles. The pursuit of that goal results in an improved understanding of some topics such as constrained systems, the nature of time or the relativistic forces. The Srödinger and Klein-Gordon equations appear as conditions fulfilled by certain types of classical solutions of the field equations although the meaning of quantum equations is not, even remotely, exhausted by these cases. A part of this note comes from previous works.

math-ph↗