Related papers: Brackets
We present a study of constrained mechanical systems and of their quantisation, emphasising the importance of the role played by Poisson brackets in the study of gauge theories.
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
We investigate (pseudo)differential forms in the framework of supergeometry. Definitions, basic properties and Cartan calculus (DeRham differential, Lie derivative, inner product, Hodge operator) are presented; the symplectic supermechanics…
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.
It is shown that physical mechanics for pointlike bodies can be effectively modeled in terms of the action of transformation groups that act as symmetries of the solutions of systems of differential equations that describe the integrability…
Algebraic properties of $n$-place opening operations on a fixed set are described. Conditions under which a Menger algebra of rank $n$ can be represented by $n$-place opening operations are found.
Various aspects of q-differential equations are examined in the contexts of quantum groups and spaces, differential calculi, zero curvature, and Lax-Sato hierarchies. There are many explicit formulas and examples along with some survey…
In the present article, real number representations, that are generalizations of classical positive and alternating representations of numbers, are introduced and investigated. The main metric relation, properties of cylinder sets are…
Paradoxes are a very frequent phenomenon in processes of thought which strive towards the intelectual and cognitive shifts. They occur in all areas of human spiritual activites. What we are interested here in, are the paradoxes in physics.…
The Schouten bracket (or antibracket) plays a central role in the Poisson formalism and the Batalin-Vilkovisky quantization of gauge systems. There are several (in)equivalent ways to realize this concept on jet spaces. In this paper, we…
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
As an analogy of superalgebra of multivector fields with the Schounte bracket, we introduce a non-trivial superbracket on differential forms of manifold. We show properties of this new superalgebra. We extend this superalgebra by adding one…
The derivation of the brackets among coordinates and momenta for classical constrained systems is a necessary step toward their quantization. Here we present a new approach for the determination of the classical brackets which does neither…
We introduce a duality triads` notion. These are dual recurrences as used in dynamical data bases theory completed by a third pertinacious relation. Several representative examples of them are given. q-Gaussian triads as well as Fibonomial…
We introduce orbifolds from the classical point of view, using charts, and present orbifold versions of elementary objects from Algebraic Topology, such as the fundamental group, coverings and Euler characteristic; Differential…
This talk reviews some mathematical and physical ideas related to the notion of dimension. After a brief historical introduction, various modern constructions from fractal geometry, noncommutative geometry, and theoretical physics are…
A new generalization of the classical separate algebraicity theorem is suggested and proved.
The concept of $\Zn$-supermanifold has been recently proposed as a natural generalization of classical ($\Zs$-graded) supergeometry, allowing for more complicated commutativity constraints. Here we continue the study of $\Zn$-supergeometry…
This paper is a survey on arc spaces, a recent topic in algebraic geometry and singularity theory. The geometry of the arc space of an algebraic variety yields several new geometric invariants and brings new light to some classical…