Related papers: Quantum Strata of Coadjoint Orbits
We consider quantum trajectories of composite systems as generated by the stochastic unraveling of the respective Lindblad-master-equation. Their classical limit is taken to correspond to local jumps between orthogonal states. Based on…
We introduce a linear algebraic object called a bidiagonal triple. A bidiagonal triple consists of three diagonalizable linear transformations on a finite-dimensional vector space, each of which acts in a bidiagonal fashion on the…
We study the geometrical structure of the coadjoint orbits of an arbitrary complex or real Lie algebra ${\mathfrak g}$ containing some ideal ${\mathfrak n}$. It is shown that any coadjoint orbit in ${\mathfrak g}^*$ is a bundle with the…
In this paper, we argue that quantum coherence in a bipartite system can be contained either locally or in the correlations between the subsystems. The portion of quantum coherence contained within correlations can be viewed as a kind…
We are focused on the idea that observables in quantum physics are a bit more than just hermitian operators and that this is, in general, a "tricky business". The origin of this idea comes from the fact that there is a subtle difference…
We introduce and study the notion of continuous orbit equivalence of actions of countable discrete groups on Cartan pairs in (twisted) groupoid context. We characterize orbit equivalence of actions in terms of the corresponding…
This talk is a survey of the question of joint measurability of coexistent observables and its is based on the monograph Operational Quantum Physics [1] and on the papers [2,3,4].
I give an answer to the question ``Which groups have compact coadjoint orbits?''. Whilst I thought that the answer, which is straightforward, must be in the literature, I was unable to find it. This note aims to rectify this. It is also a…
We survey indications from different branches of Physics that the fine scale structure of spacetime is not adequately described by a manifold. Based on the hints we accumulate, we propose a new structure, which we call a quantum topos. In…
Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an…
Interest in combinatorial interpretations of mathematical entities stems from the convenience of the concrete models they provide. Finding a bijective proof of a seemingly obscure identity can reveal unsuspected significance to it. Finding…
This paper is meant to be an informal introduction to Quantum Groups, starting from its origins and motivations until the recent developments. We call in particular the attention on the newly descovered relationship among quantum groups,…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
Using the concept of mixable shuffles, we formulate explicitly the quantum quasi-shuffle product. We also provide a desirable description of the subalgebra generated by the set of primitive elements of the quantum quasi-shuffle bialgebra. A…
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain…
We discuss a general quantum theoretical example of quantum cohomology and show that various mathematical aspects of quantum cohomology have quantum mechanical and also observable significance.
We show that coorbit spaces can be characterized in terms of arbitrary phase-space covers, which are families of phase-space multipliers associated with partitions of unity. This generalizes previously known results for time-frequency…
A class of non-selfadjoint, $\PT$-symmetric operators is identified similar to a self-adjoint one, thus entailing the reality of the spectrum. The similarity transformation is explicitly constructed through the method of the quantum normal…
We investigate the canonical pseudo-Riemannian metrics associated with Jordan-analogues of the coadjoint orbits for pseudo-Euclidean Jordan superalgebras.