Noncommutative Dymanics

We propose a new wiew on the structure of quantum mechanics and postulate a q-deformed algebra of observables. We find equations of motion for this system, which guarantee a unitary time developement. We solve this equations for simple models. We write this formalism in terms of twisted deRham complex.Comment: 8 pages, LaTeX, KFT UL 9/9

Quantum Braided Poincar\'E Group

A new deformation of the of the Poincar\'e group and of the Minkowski space-time is given. From the mathematical point of view this deformation is rather quantum-braided group. Global and local structure of this quantum-braided Poincar\'e group is investigated. A kind of ``quantum metrics'' is introduced in the $q$-Minkowski space.Comment: LaTeX (A4), 11pp., KFT UL 7/9

Superluminal Phenomena and the Quantum Preferred Frame

Motivated by a number of recent experiments, we discuss in this paper a speculative but physically admissible form and solutions of effective Maxwell-like equations describing propagation of electromagnetic field in a medium which ``feels'' a quantum preferred frame.Comment: 4 pages, REVTeX 3.1, one sentence modified, references update

Tachyonic neutrinos?

It is shown that tachyons are associated with unitary representations of Poincare mappings induced from SO(2) little group instead of SO(2,1) one. This allows us to treat more seriously possibility that neutrinos are fermionic tachyons according to the present experimental data.Comment: 8 pp., RevTeX (AmSsymb removed, due to reported troubles with processing

Einstein-Podolsky-Rosen Correlations of Spin Measurements in Two Moving Inertial Frames

The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum-mechanics formulated in the absolute synchronization framework. The results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical system in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin opeartor with proper transformation properties under the action of the Lorentz group. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum-mechanical preferred frame.Comment: RevTeX 4, 9 pp., 2 figures; published versio

Quantization of the tachyonic field

A consistent quantization scheme for imaginary-mass field is proposed. It is related to an appriopriate choice of the synchronization procedure (definition of time), which guarantee an absolute causality. In that formulation a possible existence of field exctitations (tachyons) distinguish an inertial frame (tachyon privileged frame of reference) via spontaneous breaking of the so called synchronization group.Comment: 17pp., RevTeX 3.0, KFT UL 2/94; eq. (29) and minor misprints correcte

"Meta" relativity: Against special relativity?

We introduce a Lorentz-covariant description of tachyons, free of inconsistencies. Our approach is based on an appropriate extension of the special relativity beyond the light barrier, owing to the freedom of synchronization of distant clocks.Comment: 14 pages, 4 figure

Two-Dimensional Quantum Poincar\'E Group

Quantum Poincar\'e-Weyl group in two dimensional quantum Minkowski space-time is considered and an appriopriate relativistic kinematics is investigated. It is claimed that a consistent approach to the above questions demands a kind of a ``quantum geometry'' in the $q$-deformed space-time.Comment: LaTeX (A4 style), 6pp, KFT UL 5/9

The Preferred Frame and Poincare Symmetry

In this paper we describe a covariant canonical formalism for a free time-like (massive) as well as space-like (tachyonic) particle in the framework of nonstandard synchronization scheme. In this scheme one is able to introduce absolute causality without breaking the Poincar\'e invariance.Comment: LaTeX file, 7 pp., no figure

Groups and nonlinear dynamical systems. Dynamics on the SU(2) group

An abstract Newton-like equation on a general Lie algebra is introduced such that orbits of the Lie-group action are attracting set. This equation generates the nonlinear dynamical system satisfied by the group parameters having an attractor coinciding with the orbit. The periodic solutions of the abstract equation on a Lie algebra are discussed. The particular case of the SU(2) group is investigated. The resulting nonlinear second-order dynamical system in $R^3$ as well as its constrained version referring to the generalized spherical pendulum are shown to exhibit global Hopf bifurcation.Comment: 22 pages LaTeX, uses espart.sty and equation.st