Related papers: Quantum groups and functional relations for lower …
This article presents an "in-a-nutshell" yet self-contained introductory review on loop quantum gravity (LQG) -- a background-independent, nonperturbative approach to a consistent quantum theory of gravity. Instead of rigorous and…
The majority of current understanding of the quantum correlations is in the field of non-relativistic quantum mechanics. To develop quantum information and computation tasks fully, one must inevitably take into account the relativistic…
In quantum field theory the creation and annihilation operators that are located at the points in 3-momentum space have commutation relations that are conserved under the action of a $U({\infty})$ group. Here it is shown how to define an…
We study the classical and quantum oscillator in the context of a non-additive (deformed) displacement operator, associated with a position-dependent effective mass, by means of the supersymmetric formalism. From the supersymmetric partner…
Quantum groups have been widely explored as a tool to encode possible nontrivial generalisations of reference frame transformations, relevant in quantum gravity. In quantum information, it was found that the reference frames can be…
We present a pedagogical introduction to the notions underlying the connection formulation of General Relativity - Loop Quantum Gravity (LQG) - with an emphasis on the physical aspects of the framework. We begin by reviewing General…
When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
A spin network is a generalization of a knot or link: a graph embedded in space, with edges labelled by representations of a Lie group, and vertices labelled by intertwining operators. Such objects play an important role in 3-dimensional…
In this text, we study derived versions of the fusion category associated to Lusztig's quantum group $\textbf{U}_q$. The categories that so arise are non-semisimple but recovers the usual fusion ring when passing to complexified…
Can a large system be fully characterized using its subsystems via inductive reasoning? Is it possible to completely reduce the behavior of a complex system to the behavior of its simplest "atoms"? In the following paper we answer these…
Quantum computing has been a fascinating research field in quantum physics. Recent progresses motivate us to study in depth the universal quantum computing models (UQCM), which lie at the foundation of quantum computing and have tight…
The quantum completion of the space of connections in a manifold can be seen as the set of all morphisms from the groupoid of the edges of the manifold to the (compact) gauge group. This algebraic construction generalizes an analogous…
3d quantum mechanical systems with position dependent masses (PDM) admitting at least one second order integral of motion and symmetries with respect to dilatation or shift transformations are classified. Twenty-seven such systems are…
It is shown that the principle of locality and noncommutative geometry can be connnected by a sheaf theoretical method. In this framework quantum spaces are introduced and examples in mathematical physics are given. With the language of…
The relation between quantum systems associated to root systems and radial parts of Laplace operators on symmetric spaces is established. From this it follows the complete integrability of some quantum systems.
A quantum set is defined to be simply a set of nonzero finite-dimensional Hilbert spaces. Together with binary relations, essentially the quantum relations of Weaver, quantum sets form a dagger compact category. Functions between quantum…
The problem of introducing a dependence of elements of quantum group on classical parameters is considered. It is suggested to interpret a homomorphism from the algebra of functions on quantum group to the algebra of sections of a sheaf of…
A generalization of the quantum inverse scattering method is proposed replacing the quantum group $RLL$ commutation relations of Lax operators by reflection equation type $RLRL$ commutation relations. Under some natural assumptions the most…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…