Related papers: The Symmetry Groups of Noncommutative Quantum Mech…
A hidden gauge theory structure of quantum mechanics which is invisible in its conventional formulation is uncovered. Quantum mechanics is shown to be equivalent to a certain Yang-Mills theory with an infinite-dimensional gauge group and a…
We construct a 2-parameter family of unitarily equivalent irreducible representations of the triply extended group $\g$ of translations of $\mathbb{R}^{4}$ associated with a family of its 4-dimensional coadjoint orbits and show how a…
Novel quantization properties related to the state vectors and the energy spectrum of a two-dimensional system of free particles are obtained in the framework of noncommutative (NC) quantum mechanics (QM) supported by the Weyl-Wigner…
Covariant integral quantizations are based on the resolution of the identity by continuous or discrete families of normalised positive operator valued measures (POVM), which have appealing probabilistic content and which transform in a…
We present in the article the formulation of a version of Lorentz covariant quantum mechanics based on a group theoretical construction from a Heisenberg-Weyl symmetry with position and momentum operators transforming as Minkowski…
We study the commutation relations, uncertainty relations and spectra of position and momentum operators within the framework of quantum group % symmetric Heisenberg algebras and their (Bargmann-) Fock representations. As an effect of the…
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
Quantum groups and quantum homogeneous spaces - developed by several authors since the 80's - provide a large class of examples of algebras which for many reasons we interpret as `coordinate algebras' over noncommutative spaces. This…
In high-energy physics, coordinate noncommutativity represents the core idea that space itself can be quantized, as expressed through the frameworks of string theory and noncommutative field theory. Influence of such a noncommutativity on…
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…
In~this paper, we construct noncommutative coherent states using various families of unitary irreducible representations (UIRs) of $\g$, a connected, simply connected nilpotent Lie group, that was identified as the kinematical symmetry…
We consider the problem of existence of the diagonal representation for operators in the space of a family of generalized coherent states associated with an unitary irreducible representation of a (compact) Lie group. We show that necessary…
We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and…
We combine the coordinate method and Erlangen program in the framework of noncommutative geometry through an investigation of symmetries of noncommutative coordinate algebras. As the model we use the coherent states construction and the…
The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid…
Conformal Galilei algebra contains so(1,2) subalgebra which is the conformal algebra in one dimension. In this note we generalize methods previously developed for one-dimensional many-body systems and construct a unitary map relating a…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
Despite the impressive amount of literature on the foundations of quantum mechanics, the relevance of symmetry in interpretation is not properly acknowledged. In fact, although it is usually said that quantum mechanics is invariant under…
We introduce new representations to formulate quantum mechanics on noncommutative coordinate space, which explicitly display entanglement properties between degrees of freedom of different coordinate components and hence could be called…