相关论文: Old Game, New Rules: Rethinking The Form of Physic…

The application of the theory of scale relativity to microphysics aims at recovering quantum mechanics as a new non-classical mechanics on a non-derivable space-time. This program was already achieved as regards the Schr\"odinger and Klein…

Using a nonlinear Schr\"{o}dinger equation for the wave function of all systems, continuous transitions between quantum and classical motions are demonstrated for (i) the double-slit set up, (ii) the 2D harmonic oscillator and (iii) the…

We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as non-interacting, entangled systems, according to the Page and Wootters approach. We study how…

We establish a duality between the quantum wave vector spectrum and the eigenmodes of the classical Liouvillian dynamics for integrable billiards. Signatures of the classical eigenmodes appear as peaks in the correlation function of the…

Because of the isomorphism ${C \kern -0.1em \ell}_{1,3}(\Bbb{C})\cong{C \kern -0.1em \ell}_{2,3}(\Bbb{R})$, it is possible to complexify the spacetime Clifford algebra ${C \kern -0.1em \ell}_{1,3}(\Bbb{R})$ by adding one additional timelike…

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…

In these notes we introduce the Clifford algebra of a quadratic space using techniques from universal algebra and algebraic theory of quadratic forms. We also define the Clifford, Pin and Spin groups associated to the algebra, and study how…

The most fundamental characteristics of a physical system can often be deduced from its behaviour under discrete symmetry transformations such as time reversal, parity and chirality. Here we review basic symmetry properties of the…

After a summary of a recently proposed new type of instant form of dynamics (the Wigner-covariant rest-frame instant form), the reduced Hamilton equations in the covariant rest-frame Coulomb gauge for the isolated system of N scalar…

The spatially flat and isotropic cosmological model of Brans-Dicke theory with coupling parameter $\omega\neq-3/2$ is quantized by the approach of loop quantum cosmology. An interesting feature of this model is that, although the…

The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein-Gordon-Maxwell…

Schr\"{o}dinger (Nature, v.169, 538 (1952)) noted that the complex matter field in the Klein-Gordon equation can be made real by a gauge transform, although charged fields are believed to require complex functions. Surprisingly, the result…

We obtain by invariance arguments the relativistic and non-relativistic invariant dynamical equations of a classical model of a spinning electron. We apply the formalism to a particular classical model which satisfies Dirac's equation when…

A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…

In this paper we present for the first time a complete description of the Bohm model of the Dirac particle. This result demonstrates again that the common perception that it is not possible to construct a fully relativistic version of the…

Based on the tensor method, a q-analoque of the spin-orbit coupling is introduced in a q-deformed Schroedinger equation, previously derived for a central potential. Analytic expressions for the matrix elemnets of the representation j=l\pm…

This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…

The $D$-dimensional $(\beta, \beta')$-two-parameter deformed algebra introduced by Kempf is generalized to a Lorentz-covariant algebra describing a ($D+1$)-dimensional quantized space-time. In the D=3 and $\beta=0$ case, the latter…

Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac…

The physics of excitons, electron-hole pairs that are bound together by their mutual Coulomb attraction, can to great extent be understood in the framework of the quantum-mechanical hydrogen model. This model has recently been challenged by…