Related papers: Group Theory Structures Underlying Integrable Syst…
Schwinger's algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids.…
We classify all group topologies coarser than the topology of stabilizers of finite sets in the case of automorphism groups of countable free-homogeneous structures, Urysohn space and Urysohn sphere, among other related results.
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in…
For systems of evolutionary partial differential equations the tau-structure is an important notion which originated from the deep relation between integrable systems and quantum field theories. We show that, under a certain non-degeneracy…
Let $X$ be a smooth projective variety of dimension $n\geq 2$. It is shown that a finite configuration of points on $X$ subject to certain geometric conditions possesses rich inner structure. On the mathematical level this inner structure…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler…
The elements of the wide class of quantum universal enveloping algebras are prooved to be Hopf algebras $H$ with spectrum $Q(H)$ in the category of groups. Such quantum algebras are quantum groups for simply connected solvable Lie groups…
Quantum fields are shown to provide an example of infinite-dimensional quantum groups. A dictionary is established between quantum field and quantum group concepts: the expectation value over the vacuum is the counit, Wick's theorem is the…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
The transverse group associated to some continuous quantum measuring processes is analyzed in the presence of nonvanishing gravitational fields. This is done considering, as an exmaple, the case of a particle whose coordinates are being…
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden…
Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…
The class of abelian $p$-groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory $T_p$ whose models are each bi-interpretable with the disjoint union of an…
We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…
Axiomatizing mathematical structures and theories is an objective of Mathematical Logic. Some axiomatic systems are nowadays mere definitions, such as the axioms of Group Theory; but some systems are much deeper, such as the axioms of…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…