Related papers: Formalisme de Dirac et surprises mathematiques en …
In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton's formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to…
The concept of gauge invariance can be considered one of the most subtle and useful concept in theoretical physics since it can permit the comprehension of difficult systems in physics with an arbitrary choice of a reference frame at every…
A formalism is presented which allows covariant three-dimensional bound-state equations to be derived systematically from four-dimensional ones without the use of delta-functions. The amplitude for the interaction of a bound state described…
In this article, after introducing a kind of q-deformation in quantum mechanics, first, q-deformed form of Dirac equation in relativistic quantum mechanics is derived. Then three important scat erring problem in physics are studied. All…
This note, in a rather expository manner, serves as a conceptional introduction to the certain underlying mathematical structures encoding the geometric quantization formalism and the construction of Witten's quantum invariants, which is in…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
The nilpotent Dirac formalism has been shown, in previous publications, to generate new physical explanations for aspects of particle physics, with the additional possibility of calculating some of the parameters involved in the Standard…
As a continuation of previous investigations, the formalism used there is extended to the case when an external electric field is present and the covariant formulation is performed again. The equation system obtained allows no restriction…
The Dirac approach to constrained systems can be adapted to construct relativistic invariant theories on a noncommutative (NC) space. As an example, we propose and discuss relativistic invariant NC particle coupled to electromagnetic field…
It is the matter of fact that quantum mechanics operates with notions that are not determined in the frame of the mechanics' formalism. Among them we can call the notion of "wave-particle" (that, however, does not appear in both classical…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
We use the theory of the quantum group $U_q(gl(2,\RR))$ in order to develop a quantum theory of invariants and show a decomposition of invariants into a Gordan-Capelli series. Higher binary forms are introduced on the basis of braided…
Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…
We give an overview of the two different methods that have been introduced in order to describe the dynamics of constrained quantum systems; the symplectic formulation and the metric formulation. The symplectic method extends the work of…
Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since…
The non-Hermitian formalism is used at present in many papers for the description of open quantum systems. A special language developed in this field of physics which makes it difficult for many physicists to follow and to understand the…
La m\'ecanique quantique est une th\'eorie physique contemporaine r\'eput\'ee pour ses d\'efis au sens commun et ses paradoxes. Depuis bient\^ot un si\`ecle, plusieurs interpr\'etations de la th\'eorie ont \'et\'e propos\'ees par les…
In a series of papers, a many-minds interpretation of quantum theory has been developed. The aim in these papers is to present an explicit mathematical formalism which constitutes a complete theory compatible with relativistic quantum field…
The usual treatment of a (first order) classical field theory such as electromagnetism has a little drawback: It has a primary constraint submanifold that arise from the fact that the dynamics is governed by the antisymmetric part of the…