Related papers: Le groupe de Lorentz-Einstein comme consequence d'…
We formulate Lorentz covariance of a quantum field theory in terms of covariance of time-ordered products (or other Green's functions). This formulation of Lorentz covariance implies spacelike local commutativity or anticommutativity of…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
Recently it has been advocated [1] that for describing nature within the minimal symmetry requirement, certain subgroups of Lorentz group may play a fundamental role. One such group is E(2) which induces a Lie algebraic Non-Commutative…
Two-photon states produce enough symmetry needed for Dirac's construction of the two-oscillator system which produces the Lie algebra for the O(3,2) space-time symmetry. This O(3,2) group can be contracted to the inhomogeneous Lorentz group…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
We study the orbits of two interacting particles described by a fully relativistic classical mechanical Hamiltonian. We use two sets of initial conditions. In the first set (dynamics 1) the system's center of mass is at rest. In the second…
In special relativity theory the physical quantities are generally expressed as function of the velocity. In the particular case of an extended object, the factor 1/gamma of Lorentz contraction of its length in the direction of motion is…
The classical and quantum evolution of a generic probability distribution is analyzed. To that end, a formalism based on the decomposition of the distribution in terms of its statistical moments is used, which makes explicit the differences…
Measurements transfer information about a system to the apparatus, and then further on -- to observers and (often inadvertently) to the environment. I show that even imperfect copying essential in such situations restricts possible…
The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating…
Usually the generators of a quantum group are assumed to be commutative with the noncommuting coordinates of a quantum plane. We have relaxed the assumption and investigated its consequences. Not only does a two-parameter quantum group…
A Lorentz-covariant system of wave equations is formulated for a quantum-mechanical three-body system in one space dimension, comprised of one photon and two identical massive spin one-half Dirac particles, which can be thought of as two…
Bichon, De Rijdt and Vaes introduced the notion of monoidally equivalent compact quantum groups. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital…
The relation between quantum theory and special relativity is peculiar. On the one hand it is close and essential. Steven Weinberg [1], for example, takes the position that the standard model is an inevitable consequence of the marriage of…
Indistinguishability of particles is normally considered to be an inherently quantum property which cannot be possessed by a classical theory. However, Saunders has argued that this is incorrect, and that classically indistinguishable…
The usual quantum mechanics describes the mass eigenstates. To describe the proper-time eigenstates, a duality theory of the usual quantum mechanics was developed. The time interval is treated as an operator on an equal footing with the…
We enhance the standard formalism of quantum theory to enable events. The concepts of experiment and of measurement are defined. Dynamics is given by Liouville's equation that couples quantum system to a classical one. It implies a unique…
A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action.…
Using the well-known free-field formalism for quantum groups, we demonstrate in case of $A(n)_q$, that quantum group is naturally also a cluster variety. Widely used formulae for mutations are direct consequence of independence of group…
The objective is a foundation of physics from the operationalization of its basic observables. We begin with classical and relativistic kinematics. Seizing on a programmatic proposal by Heinrich Hertz we arrive via quantification of…