arXiv subjects

Jean Claude Dutailly

Publications and source records attributed to Jean Claude Dutailly.

3 recordsLinked to original sources

arXiv2015

Quantum mechanics revisited (v.3)

The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can be represented in a Hilbert space, that a self-adjoint operator is associated to any observable, that the result of a measure must be the eigen value of the operator and appear with the usual probability. Furthermore an equivalent of the Wigner's theorem holds, which leads to the Schr{ö}dinger equation. These results are based on well known mathematics, and do not involve any specific hypothesis in Physics. They validate and explain the methods currently used, which are made simpler and safer, and open new developments. In the third edition of this paper developments have been added about the estimation of physical anomalies.

math-ph↗

arXiv2014

Mathematics for theoretical physics

This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and intelligible manner.The first part addresses the Foundations (mathematical logic, set theory, categories), the second Algebra (algebraic strucutes, groups, vector spaces tensors, matrices, Clifford algebra). The third Analysis (general topology, measure theory, Banach Spaces, Spectral theory). The fourth Differential Geometry (derivatives, manifolds, tensorial bundle, pseudo-riemannian manifolds, symplectic manifolds). The fifth Lie Algebras, Lie Groups.and representation theory. The sixth Fiber bundles and jets. The last one Functional Analysis (differential operators, distributions, ODE, PDE, variational calculus). Several signficant new results are presented (distributions over vector bundles, functional derivative, spin bundle and manifolds with boundary).

math-ph↗

arXiv2011

Yang Mills model of interacting particles in the classical field theory

The purpose is to study systems of interacting particles in the Generl Relativity context, by the principle of least action using purely classical concepts. The particles are described by a state tensor using a Clifford algebra for the kinematic part. The force fields, including gravitation, are described by connections on principle bundles. A solution has been found to account for individual particles. A more specific model based on scalar products, Dirac operator and chirality is studied in more details. Problems related to symmetries, including the Higgs mechanism, are intoduced. With a comprehensive coverage of topics it can be a useful pedagogical study.

math-ph↗