Related papers: Little-used Mathematical Structures in Quantum Mec…
Based on empirical evidence, quantum systems appear to be strictly linear and gauge invariant. This work uses concise mathematics to show that quantum eigenvalue equations on a one dimensional ring can either be gauge invariant or have a…
In relativistic quantum mechanics, elementary particles are described by irreducible unitary representations of the Poincare group. The same applies to the center-of-mass kinematics of a multi-particle system that is not subject to external…
We discuss some basic properties of Lie group representations in rigged Hilbert spaces. In particular, we show that a differentiable representation in a rigged Hilbert space may be obtained as the projective limit of a family of continuous…
Multidimensional contractions of irreducible representations of the Cayley-Klein unitary algebras in the Gel'fand-Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method…
The quantum mechanics of one degree of freedom exhibiting the exact conformal SL(2,R) symmetry is presented. The starting point is the classification of the unitary irreducible representations of the SL(2,R) group (or, to some extent, its…
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can…
It is shown that the independence of the continuum hypothesis points to the unique definite status of the set of intermediate cardinality: the intermediate set exists only as a subset of continuum. This latent status is a consequence of…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
Entanglement is often regarded as an inherently quantum feature. We show that this does not have to be the case: under restricted operational access, classical correlations can appear nonseparable when expressed in the formalism of quantum…
A new infinite family of examples of finite non-bicolorable configurations of rays in Hilbert space is described. Such configurations appear in the analysis of quantum mechanics in terms of Bell's inequalities and Kochen-Specker theorem and…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
We show an example of benign non-separability in an apparently separable system consisting of $n$ free non-correlated quantum particles, solitonic solutions to the nonlinear phase modification of the Schr\"{o}dinger equation proposed…
Quantum superposition says that any physical system simultaneously exists in all of its possible states, the number of which is exponential in the number of entities composing the system. The strength of presence of each possible state in…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
Despite their inextricable quantum mechanical nature, events at a high energy particle collider experiment typically have very few unambiguous quantum signatures, due the type of data and the manner in which they are collected. We present a…
We study unitary representations of semidirect products of a compact quantum group with a finite group. We give a classification of all irreducible unitary representations, a description of the conjugate representation of irreducible…
We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation ($U$) of a finite group ($G$), whenever $U \otimes U^c$ is simply reducible (with…
For quantum mechanics on a lattice the position (``particle number'') operator and the quasi-momentum (``phase'') operator obey canonical commutation relations (CCR) only on a dense set of the Hilbert space. We compare exact numerical…
We consider some examples of quantum super-integrable systems and the associated nonlinear extensions of Lie algebras. The intimate relationship between super-integrability and exact solvability is illustrated. Eigenfunctions are…
I discuss different formulations of the relativistic few-body problem with an emphasis on how they are related. I first discuss the implications of some of the differences with non-relativistic quantum mechanics. Then I point out that the…