相关论文: The classical Bertrand-Darboux problem

We present a panoramic view on various attempts to "solve" the problems of quantum measurement and macro-objectivation, i.e. of the transition from a probabilistic quantum mechanic microscopic world to a deterministic classical macroscopic…

Classical relativistic system of point particles coupled with an electromagnetic field is considered in the three-dimensional representation. The gauge freedom connected with the chronometrical invariance of the four-dimensional description…

We consider a 3-parametric linear deformation of the Poisson brackets in classical mechanics. This deformation can be thought of as the classical limit of dynamics in so-called "quantized spaces". Our main result is a description of the…

We study some Diophantine problems related to triangles with two given integral sides. We solve two problems posed by Zolt\'an Bertalan and we also provide some generalization.

Alternative versions of the Klein-Gordon and Dirac equations in a curved spacetime are got by applying directly the classical-quantum correspondence.

The problem of time, considered as a problem in the usual physical context, is reflected in relation with the paper by Kauffman and Smolin (gr-qc/9703026). It is shown that the problem is a misposed problem in the sense that it was raised…

In this work we discuss the deformed relativistic wave equations, namely the Klein--Gordon and Dirac equations in a Doubly Special Relativity scenario. We employ what we call a geometric approach, based on the geometry of a curved momentum…

Even though it has been almost a century since quantum mechanics planted roots, the field has its share of unresolved problems. It could be the result of a wrong mathematical structure providing inadequate understanding of the quantum…

It is shown that the squared operation of the Dirac equation which is widely applied may create new solutions and moreover may change the inner nature of original equation. Some illustrating examples are considered as well.

The time irreversibility problem is the dichotomy of the reversible microscopic dynamics and the irreversible macroscopic physics. This problem was considered by Boltzmann, Poincar\'e, Bogolyubov and many other authors and though some…

We define B\"acklund--Darboux transformations in Sato's Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on…

We are familiar with Dirac equation in flat space by which we can investigate the behaviour of half-integral spin particle. With the introduction of general relativistic effects the form of the Dirac equation will be modified. For the cases…

The mathematical foundations of relativistic quantum mechanics is largely based upon the discovery of the Pauli and Dirac matrices. An algebra which lies at an even more fundamental level is the geometric Clifford algebra with metric…

We review origins and main properties of the most important bracket operations appearing canonically in differential geometry and mathematical physics in the classical, as well as the supergeometric setting. The review is supplemented by a…

We derive the probabilities of measurement results from Schroedinger's equation plus a definition of macroscopic as a particular kind of thermodynamic limit. Bohr's insight that a measurement apparatus must be classical in nature and…

This paper is a study of the relationship between two constructions associated with Cartan geometries, both of which involve Lie algebroids: the Cartan algebroid, due to [Blaom A.D., Trans. Amer. Math. Soc. 358 (2006), 3651-3671], and…

The reasons which restrict opportunities of classical mechanics at the description of nonequilibrium systems are discussed. The way of overcoming of the key restrictions is offered. This way is based on an opportunity of representation of…

The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…

In 1931 Elie Cartan constructed a geometry which was rarely considered. Cartan proposed a way to define an infinitesimal metric $ds$ starting from a variational problem on hypersurfaces in an $n$-dimensional manifold $\mathcal{M}$. This…

Contrary to the widespread belief, the problem of the emergence of classical mechanics from quantum mechanics is still open. In spite of many results on the $\h \to 0$ asymptotics, it is not yet clear how to explain within standard quantum…