相关论文: On the geometry of quantum indistinguishability
In the framework of quantum group theory we obtain a noncommutative analog for the algebra of functions in a bounded symmetric domain, endowed with a whole symmetry. Also we provide a construction for its faithfull irreducible…
In third paper of the series we construct a large family of representations of the quantum toroidal $\gl_1$ algebra whose bases are parameterized by plane partitions with various boundary conditions and restrictions. We study the…
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes is to give an introduction to the mathematical methods used in describing…
The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related…
The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham's Canonical Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of…
Studying the geometry of sets appearing in various problems of quantum information helps in understanding different parts of the theory. It is thus worthwhile to approach quantum mechanics from the angle of geometry -- this has already…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
It is well known that certain features of a quantum theory cannot be described in the standard picture on a Hilbert space. In particular, this happens when we try to formally frame a quantum field theory, or a thermodynamic system with…
We propose a skein model for the quantum cluster algebras of surface type with coefficients. We introduce a skein algebra $\mathscr{S}_{\Sigma,\mathbb{W}}^{A}$ of a walled surface $(\Sigma,\mathbb{W})$, and prove that it has a quantum…
Symmetries are widely used in modeling quantum systems but they do not contribute in postulates of quantum mechanics. Here we argue that logical, mathematical, and observational evidence require that symmetry should be considered as a…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
Quantum field theory in curved spacetime is perhaps the most reliable framework in which one can investigate quantum effects in the presence of strong gravitational fields. Nevertheless, it is often studied by means of perturbative…
We revisit the topic of two-state quantum systems using Geometric Algebra (GA) in three dimensions $\mathcal G_3$. In this description, both the quantum states and Hermitian operators are written as elements of $\mathcal G_3$. By writing…
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…
A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS) construction, is introduced. It considers states as well as algebras of observables on an equal footing. The conventional approach to the emergence of mixed from…
Using extended Schwinger's quantization approach quantum mechanics on a Riemannian manifold $M$ with a given action of an intransitive group of isometries is developed. It was shown that quantum mechanics can be determined unequivocally…
A new method for nonperturbative investigations of quantum gravity is presented in which the simplicial path integral is approximated by the partition function of a spin system. This facilitates analytical and numerical computations…
The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced…
Both, spin and statistics of a quantum system can be seen to arise from underlying (quantum) group symmetries. We show that the spin-statistics theorem is equivalent to a unification of these symmetries. Besides covering the Bose-Fermi case…