Related papers: Remarks on quantization of classical r-matrices
Some natural inequalities related to rearrangement in matrix products can also be regarded as extensions of classical inequalities for sequences or integrals. In particular, we show matrix versions of Chebyshev and Kantorovich type…
In the classical world one can construct two identical systems which have identical behavior and give identical measurement results. We show this to be impossible in the quantum domain. We prove that after the same quantum measurement two…
The expressions for the $\hat{R}$--matrices for the quantum groups SO$_{q^2}$(5) and SO$_q$(6) in terms of the $\hat{R}$--matrices for Sp$_q$(2) and SL$_q$(4) are found, and the local isomorphisms of the corresponding quantum groups are…
We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.
We discuss to what extent classical singularities persist upon quantization in two simple cosmological models.
The different facets of the $R$-matrix method are presented pedagogically in a general framework. Two variants have been developed over the years: $(i)$ The "calculable" $R$-matrix method is a calculational tool to derive scattering…
Particular class of skew orthogonal polynomials are introduced and investigated, which possess Laurent symmetry. They are also shown to appear as eigenfunctions of symplectic generalized eigenvalue problems. The modification of these…
Skew orthogonal polynomials arise in the calculation of the $n$-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely…
In [3], the authors showed the existence and the uniqueness of a sl(m+1,\R)-equivariant quantization in the non-critical situations. The curved generalization of the sl(m+1,\R)-equivariant quantization is the natural and projectively…
We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.
The definitions of classical and quantum singularities in general relativity are reviewed. The occurence of quantum mechanical singularities in certain spherically symmetric and cylindrically symmetric (including infinite line…
The singularity theorems of classical general relativity are briefly reviewed. The extent to which their conclusions might still apply when quantum theory is taken into account is discussed. There are two distinct quantum loopholes: quantum…
Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…
In this paper we quantize symplectic dynamical r-matrices over a possibly nonabelian base. The proof is based on the fact that the existence of a star-product with a nice property (called strong invariance) is sufficient for the existence…
A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical…
Schlesinger transformations are discrete monodromy preserving symmetry transformations of a meromorphic connection which shift by integers the eigenvalues of its residues. We study Schlesinger transformations for twisted sl_N-valued…
In quantum mechanics, wave functions and density matrices represent our knowledge about a quantum system and give probabilities for the outcomes of measurements. If the combined dynamics and measurements on a system lead to a density matrix…
This paper presents a derivation of the possible residual symmetries of rational K-matrices which are invertible in the ''classical limit'' (the spectral parameter goes to infinity). This derivation uses only the boundary Yang-Baxter…
Simple classical mechanical systems and solution spaces of classical field theories involve singularities. In certain situations these singularities can be understood in terms of stratified Kaehler spaces. We give an overview of a research…
An integrable deformation of the known integrable model of two interacting p-dimensional and q-dimensional spherical tops is considered. After reduction this system gives rise to the generalized Lagrange and the Kowalevski tops. The…