相关论文: Quantum Thetas on Noncommutative T^d with General …

Quantum groups lead to an algebraic structure that can be realized on quantum spaces. These are noncommutative spaces that inherit a well defined mathematical structure from the quantum group symmetry. In turn such quantum spaces can be…

A TQFT is a functor from a cobordism category to the category of vector spaces, satisfying certain properties. An important property is that the vector spaces should be finite dimensional. For the WRT TQFT, the relevant 2+1-cobordism…

Various aspects of the theory of quantum integrable systems are reviewed. Basic ideas behind the construction of integrable ultralocal and nonultralocal quantum models are explored by exploiting the underlying algebraic structures related…

Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body…

Generalizations of classical theta functions are proposed that include any even number of analytic parameters for which conditions of quasi-periodicity are fulfilled and that are representations of extended Heisenberg group. Differential…

We introduce a novel approach that exploits the intersection of quantum computing, machine learning and reduced density matrix functional theory to leverage the potential of quantum computing to improve simulations of interacting quantum…

Using the Cartan formulation of General Relativity, we construct a well defined lattice-regularized theory capable to describe large non-perturbative quantum fluctuations of the frame field (or the metric) and of the spin connection. To…

We define analogue of theta-functions on the Kodaira--Thurston manifold which is a compact 4-dimensional symplectic manifold and use them to construct canonical symplectic embedding of the Kodaira--Thurston manifold into the complex…

We propose a general formulation of perturbative quantum field theory on (finitely generated) projective modules over noncommutative algebras. This is the analogue of scalar field theories with non-trivial topology in the noncommutative…

We consider a twisted version of quantum groups corepresentations. This generalization amounts to include in the theory the case where quantum space coordinates and its endomorphism matrix entries belong to a non-commutative quadratic…

The basic framework for a systematic construction of a quantum theory of Riemannian geometry was introduced recently. The quantum versions of Riemannian structures --such as triad and area operators-- exhibit a non-commutativity. At first…

Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…

We study the class of noncommutative theories in $d$ dimensions whose spatial coordinates $(x_i)_{i=1}^d$ can be obtained by performing a smooth change of variables on $(y_i)_{i=1}^d$, the coordinates of a standard noncommutative theory,…

We establish an explicit embedding of a quantum affine $\mathfrak{sl}_n$ into a quantum affine $\mathfrak{sl}_{n+1}$. This embedding serves as a common generalization of two natural, but seemingly unrelated, embeddings, one on the quantum…

General relativity under the assumption of noncommuting components of the tetrad field is considered in this paper. Since the algebraic properties of the tetrad field representing the gravitational field are assumed to correspond to the…

Given an integral lattice $\Lambda$ of rank $n$ and a finite sequence $m_1 \leq m_2 \leq ... \leq m_k$ of natural numbers we construct a modular form $\Theta_{m_1,m_2,...,m_k,\Lambda}$ of level $N=N(\Lambda)$. The weight of this modular…

We apply the embedding method of Batalin-Tyutin for revealing noncommutative structures in the generalized Landau problem. Different types of noncommutativity follow from different gauge choices. This establishes a duality among the…

We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…

A recent method of constructing quantum mechanics in noncommutative coordinates, alternative to implying noncommutativity by means of star product is discussed. Within this approach we study Hall effect as well as quantum phases in…