Related papers: A note on quantum groups and integrable systems
A simple quantum generalisation of the Liouville-Arnold criterion of classical integrability is proposed: A system is quantum-integrable if it has an abelian Lie group of Wigner symmetries of dimension equal to the number of degrees of…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
The quantum field algebra of real scalar fields is shown to be an example of infinite dimensional quantum group. The underlying Hopf algebra is the symmetric algebra S(V) and the product is Wick's normal product. Two coquasitriangular…
A simple exposition of the rarely discussed fact that a set of free boson fields describing different, i.e. kinematically different particle types can be quantized with mutual anticommutation relations is given by the explicit construction…
When path integrals are discussed in quantum field theory, it is almost always assumed that the fields take values in a vector bundle. When the fields are instead valued in a possibly-curved fiber bundle, the independence of the formal path…
The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators. The quantum theory of an ordinary fluid is…
A class of free quantum fields defined on the Poincare' group, is described by means of their two-point vacuum expectation values. They are not equivalent to fields defined on the Minkowski spacetime and they are "elementary" in the sense…
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question…
We show that the quantum coordinate ring of the unipotent subgroup N(w) of a symmetric Kac-Moody group G associated with a Weyl group element w has the structure of a quantum cluster algebra. This quantum cluster structure arises naturally…
We outline, test, and apply a new scheme for nonpertubative analyses of quantized field systems in contact with dynamical gravity. While gravity is treated classically in the present paper, the approach lends itself for a generalization to…
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
The relations between quantum coherence and quantum interference are discussed. A general method for generation of quantum coherence through interference-induced state selection is introduced and then applied to `simple' atomic systems…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
Quantum codes are subspaces of the state space of a quantum system that are used to protect quantum information. Some common classes of quantum codes are stabilizer (or additive) codes, non-stabilizer (or non-additive) codes obtained from…
Using unitary irreducible representations of the de Sitter group, we construct the Fock space of a massive free scalar field. In this approach, the vacuum is the unique dS invariant state. The quantum field is a posteriori defined by an…
A definition is given and the physical meaning of quantum transformations of a non-commutative configuration space (quantum group coactions) is discussed. It is shown that non-commutative coordinates which are transformed by quantum groups…
This is a self-contained introduction to quantum Riemannian geometry based on quantum groups as frame groups, and its proposed role in quantum gravity. Much of the article is about the generalisation of classical Riemannian geometry that…
This is mainly a brief review of some key achievements in a `hot'' area of theoretical and mathematical physics. The principal aim is to outline the basic structures underlying {\em integrable} quantum field theory models with {\em…
In unified field theories with more than four dimensions, the form of the equations of physics in spacetime depends in general on the choice of coordinates in higher dimensions. The reason is that the group of coordinate transformations in…