Related papers: Bessel Process and Conformal Quantum Mechanics
We point out a possible complementation of the basic equations of quantum mechanics in the presence of gravity. This complementation is suggested by the well-known fact that quantum mechanics can be equivalently formulated in the position…
In this paper we present a new algebraic structure (a super hyperbolic system in our terminology) for finite quantum systems, which is a generalization of the usual one in the two-level system. It fits into the so-called generalized Pauli…
Severe methodological and numerical problems of the traditional quantum mechanical approach to the description of molecular systems are outlined. To overcome these, a simple alternative to the Born-Oppenheimer approximation is presented on…
A motivation is given for expressing classical mechanics in terms of diagonal projection matrices and diagonal density matrices. Then quantum mechanics is seen to be a simple generalization in which one replaces the diagonal real matrices…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
We discuss the $q$ deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in Quantum Mechanics. We show that the $q$-deformation parameter labels the Weyl systems in Quantum Mechanics and the unitarily…
A number of issues related to measurement show that self-consistency is lacking in quantum mechanics as this theory has been generally understood. Each issue is presented as a point in this paper. Each point can be resolved by incorporating…
We consider the hypothesis that quantum mechanics is an approximation to another, cosmological theory, accurate only for the description of subsystems of the universe. Quantum theory is then to be derived from the cosmological theory by…
The q-Laguerre polynomials correspond to an indetermined moment problem. For explicit discrete non-N-extremal measures corresponding to Ramanujan's ${}_1\psi_1$-summation we complement the orthogonal q-Laguerre polynomials into an explicit…
A modified version of relational quantum mechanics is developed based on the three following ideas. An observer can develop an internally consistent description of the universe but it will, of necessity, differ in particulars from the…
We propose novel numerical method of modelling Bose-Einstein correlations (BEC) observed among identical (bosonic) particles produced in multiparticle production reactions. We argue that the most natural approach is to work directly in the…
A new possible version of multisimultaneous causality is proposed, and real experiments allowing us to decide between this view and quantum mechanical retrocausation are further discussed. The interest of testing quantum mechanics against…
One-to-one reversible automata are introduced. Their applicability to a modelling of the quantum mechanical measurement process is discussed.
A new version of hidden variables theory founded on the generalisation of world's geometry is proposed. The quantum-mechanical motion as the motion in some "inner space", which has a structure of the integrable Weyl space is examined.…
We study the logarithmic conformal field theories in which conformal weights are continuous subset of real numbers. A general relation between the correlators consisting of logarithmic fields and those consisting of ordinary conformal…
We explore the group theoretical underpinning of noncommutative quantum mechanics for a system moving on the two-dimensional plane. We show that the pertinent groups for the system are the two-fold central extension of the Galilei group in…
Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group. Any linear representation of a finite…
In this continuation paper the theory is further extended to reveal the connection between its formal aparatus, dealing with microscopic quantities, and the formal aparatus of thermodynamics, related to macroscopic properties of large…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
We derive a precise link between series expansions of Gaussian random vectors in a Banach space and Parseval frames in their reproducing kernel Hilbert space. The results are applied to pathwise continuous Gaussian processes and a new…