Related papers: Brackets
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
This note presents an attempt to provide a conceptual framework for variational formulations of classical physics. Variational principles of physics have all a common source in the {\it principle of virtual work} well known in statics of…
We relate classical and quantum Dirac and Nambu brackets. At the classical level, we use the relations between the two brackets to gain some insight into the Jacobi identity for Dirac brackets, among other things. At the quantum level, we…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
In this work, we find the Poisson superalgebras related to schemes of quantization. Initially, we consider the Dirac superbracket in the context of the quantization of constrained systems. Next, we show the existence of a Poisson…
This paper proposes a basic theory on physical reality, and a new foundation for quantum mechanics and classical mechanics. It does not only solve the problem of the arbitrariness on the operator ordering for the quantization procedure, but…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
We review how antiparticles may be introduced in classical relativistic mechanics, and emphasize that many of their paradoxical properties can be more transparently understood in the classical than in the quantum domain.
We introduce and study a class of betweenness algebras-Boolean algebras with binary operators, closely related to ternary frames with a betweenness relation. From various axioms for betweenness, we chose those that are most common, which…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
An acute look at \underbar{basic} facts concerning \underbar{unbounded} subnormal operators is taken here. These operators have the richest structure and are the most exciting among the whole family of beneficiaries of the normal ones.…
The classical beta function B(x; y) is one of the most fundamental special functions, due to its important role in various fields in the mathematical, physical, engineering and statistical sciences. Useful extensions of the classical Beta…
A core level of basic information for physics is identified, based on an analysis of the characteristics of the parameters space, time, mass and charge. At this level, it is found that certain symmetries operate, which can be used to…
Algebras of Logic deal with some algebraic structures, often bounded lattices, considered as models of certain logics, including logic as a domain of order theory. There are well known their importance and applications in social life to…
We describe an $p$-mechanical (see funct-an/9405002 and quant-ph/9610016) brackets which generate quantum (commutator) and classic (Poisson) brackets in corresponding representations of the Heisenberg group. We \emph{do not} use any kind of…
We review the linearization of Poisson brackets and related problems, in the formal, analytic and smooth categories.
Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of…
We revisit the standard axioms of domain theory with emphasis on their relation to the concept of partiality, explain how this idea arises naturally in probability theory and quantum mechanics, and then search for a mathematical setting…
The relation between Poisson brackets in supersymmetric one or two-dimensional sigma-models and derived brackets is summarized.
The theory of large deviations is already the natural language for the statistical physics of equilibrium and non-equilibrium. In the field of disordered systems, the analysis via large deviations is even more useful to describe within a…