Related papers: A note on quantum groups and integrable systems
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or wave-particle duality on curved spaces…
We introduce the key ideas behind the group field theory approach to quantum gravity, and the basic elements of its formalism. We also briefly report on some recent results obtained in this approach, concerning both the mathematical…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
This article focuses on the connection between the possibility of quantum computers, the predictability of complex quantum systems in nature, and the issue of free will.
We define covariantly a deformation of a given algebra, then we will see how it can be related to a deformation quantization of a class of observables in Quantum Field Theory. Then we will investigate the operator order related to this…
We consider the quantum Hall effect in terms of an effective field theory formulation of the edge states, providing a natural common framework for the fractional and integral effects.
The quantum entanglements are studied in terms of the invariants under local unitary transformations. A generalized formula of concurrence for $N$-dimensional quantum systems is presented. This generalized concurrence has potential…
The basic principles of the quantum mechanics in the K-field formalism are stated in the paper. The basic distinction of this theory arises from that the quantum theory equations (including well-known Schrodinger, Klein-Gordon and quadratic…
A geometric interpretation of quantum self-interacting string field theory is given. Relations between various approaches to the second quantization of an interacting string are described in terms of the geometric quantization. An algorithm…
The coherent states are reviewed with particular application to the free particle system. The didactic advantages of the formalism is emphasized. Several interesting features, like the relation of the coherent states with the Galilei group…
We introduce a framework for $\mathbb{Z}$-gradings on cluster algebras (and their quantum analogues) that are compatible with mutation. To do this, one chooses the degrees of the (quantum) cluster variables in an initial seed subject to a…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
In this contribution I summarize the achievements of separation of variables in integrable quantum systems from the point of view of path integrals. This includes the free motion on homogeneous spaces, and motion subject to a potential…
Dynamical quantum field theories (QFTs), such as those in which spacetimes are equipped with a metric and/or a field in the form of a smooth map to a target manifold, can be formulated axiomatically using the language of…
Candidate microstates of a spherically symmetric geometry are constructed in the group field theory formalism for quantum gravity, for models including both quantum geometric and scalar matter degrees of freedom. The latter are used as a…
A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational…
We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions…
We study the free complexification operation for compact quantum groups, $G\to G^c$. We prove that, with suitable definitions, this induces a one-to-one correspondence between free orthogonal quantum groups of infinite level, and free…
A noncommutative geometric generalisation of the quantum field theoretical framework is developed by generalising the Heisenberg commutation relations. There appear nonzero minimal uncertainties in positions and in momenta. As the main…
The issue of field redefinition invariance of path integrals in quantum field theory is reexamined. A ``paradox'' is presented involving the reduction to an effective quantum-mechanical theory of a $(d+1)$-dimensional free scalar field in a…