Related papers: Quantum Group and Quantum Symmetry
General Theory of Relativity and Quantum theory gives two different description of the same mother nature in the big and small scale respectively. Mathematical languages of these two theories are entirely different, one is geometric while…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
In the classification of solutions of the Yang--Baxter equation, there are solutions that are not deformations of the trivial solution (essentially the identity). We consider the algebras defined by these solutions, and the corresponding…
Quantum gravity (or quantum spacetime) is to unify general relativity and quantum mechanics into a single theoretical framework and presented as the most important open puzzle in fundamental physics. The development of a microscopic theory…
The scope of this review is to give a pedagogical introduction to some new calculations and methods developed by the author in the context of quantum groups and their applications. The review is self- contained and serves as a "first aid…
The goal of this article is to present an introduction to loop quantum gravity -a background independent, non-perturbative approach to the problem of unification of general relativity and quantum physics, based on a quantum theory of…
Motivated by the work of Goswami on quantum isometry groups of noncommutative manifolds we define the quantum symmetry group of a unital C*-algebra A equipped with an orthogonal filtration as the universal object in the category of compact…
Symmetry is fundamental in the description and simulation of quantum systems. Leveraging symmetries in classical simulations of many-body quantum systems can results in significant overhead due to the exponentially growing size of some…
We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods.…
de Sitter symmetry on quantum level implies that operators describing a given system satisfy commutation relations of the de Sitter algebra. This approach gives a new perspective on fundamental notions of quantum theory. We discuss…
Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…
New solutions of the quantum Yang-Baxter equation, depending in general on three arbitrary parameters, are written down. They are based on the root of unity representations of the quantum orthosymplectic superalgebra \\U, which were found…
The quantum gauge general relativity is proposed in the framework of quantum gauge theory of gravity. It is formulated based on gauge principle which states that the correct symmetry for gravitational interactions should be gravitational…
We summarize basic features of quantum field theories with discrete symmetry $\mathbb{Q}/\mathbb{Z}$ (possibly higher form, global or gauged). The classification of representations and anomalies is quite rich and involves the ring of…
In QCD one can change the representation of the gauge group for quarks and/or the gauge group itself. Examples of such generalizations are: (a) supersymmetric Yang-Mills theory with gauge group SU(2) or SU(3); (b) QCD with SU(2) colour and…
We propose a new framework for simulating $\text{U}(k)$ Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to…
Dimensional reduction of various gravity and supergravity models leads to effectively two-dimensional field theories described by gravity coupled G/H coset space sigma-models. The transition matrices of the associated linear system provide…
The appearance of quantum groups in conformal field theories is traced back to the Poisson-Lie symmetries of the classical chiral theory. A geometric quantization of the classical theory deforms the Poisson-Lie symmetries to the quantum…
We develop the quantum cluster algebra approach recently introduced by Sun and Yagi to investigate the tetrahedron equation, a three-dimensional generalization of the Yang-Baxter equation. In the case of square quiver, we devise a new…
We introduce the group field theory (GFT) formalism for non-perturbative quantum gravity, and present it as a potential unifying framework for several other quantum gravity approaches, i.e. loop quantum gravity and simplicial quantum…