相关论文: Dynamical Quantum Groups - The Super Story
The new approach to quantum mechanical problems is proposed. Quantum states are represented in an algebraic program, by lists of variable length, while operators are well defined functions on these lists. Complete numerical solution of a…
We show, in a simple quantum mechanical model, how a theory can become supersymmetric in the presence of interactions even when the free theory is not. This dynamical generation of supersymmetry relaxes the condition on the equality of…
We suggest a cohomological framework to describe groups of $I$-type and involutive Yang-Baxter groups. These groups are key in the study of involutive non-degenerate set-theoretic solutions of the quantum Yang-Baxter equation. Our main tool…
Topological interpretation of the link invariants associated with the Weinstein--Xu classical solutions of the quantum Yang-Baxter equation are provided.
Generalization of the quantum Yang-Baxter equation solutions to an arbitrary grading is studied. The noncommutative differential calculi corresponding to such solutions is considered. The connection with the ordinary and supersymmetric…
This theoretical review is intended to give non-theorists a flavor of the ideas driving the current efforts to experimentally find supersymmetry. We discuss the main reasons behind the expectation that supersymmetry may be "just around the…
In this paper, by making use of category theory, we construct dynamical reflection maps, solutions to a version of the reflection equation associated with suitable dynamical Yang-Baxter maps, set-theoretic solutions to the braid relation…
This is a short, self-contained expository survey, focused on algebraic and analytic aspects of quantum groups. Topics covered include the definition of ``quantum group,'' the Yang-Baxter equation, quantized universal enveloping algebras,…
The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable…
Over the past two decades quantum engineering has made significant advances in our ability to create genuine quantum many-body systems using ultracold atoms. In particular, some prototypical exactly solvable Yang-Baxter systems have been…
Following a preceding paper of Tarasov and the second author, we define and study a new structure, which may be regarded as the dynamical analogue of the Weyl group for Lie algebras and of the quantum Weyl group for quantized enveloping…
We treat continuous histories within the histories approach to generalised quantum mechanics. The essential tool is the `history group': the analogue, within the generalised history scheme, of the canonical group of single-time quantum…
To the Yang-Baxter equation an additional relation can be added. This is the reflection equation which appears in various places, with or without spectral parameter. For example, in factorizable scattering on a half-line, integrable lattice…
Some very elementary ideas about quantum groups and quantum algebras are introduced and a few examples of their physical applications are mentioned.
Quantum theory is extremely successful in explaining most physical phenomena, and is not contradicted by any experiment. Yet, the theory has many puzzling features : the occurrence of probabilities, the unclear distinction between the…
A formulation of quantum mechanics based on replacing the general unitary group by finite groups is considered. To solve problems arising in the context of this formulation, we use computer algebra and computational group theory methods.
We construct integrable modifications of 2d lattice gauge theories with finite gauge groups.
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
The quantum super Yangian $Y_q(gl(M|N))$ associated with the Perk - Schultz solution of the Yang - Baxter equation is introduced. Its structural properties are investigated, in particular, an extensive study of its central algebra is…
In this note, we survey some elementary theorems and proofs concerning dynamical matrices theory. Some mathematical concepts and results involved in quantum information theory are reviewed. A little new result on the matrix representation…