Canonical correlations measure cosines of principal angles between random vectors. These cosines multiplicatively decompose concentration ellipses for second-order filtering and additively decompose information rate for the Gaussian channel. Moreover, they establish a geometrical connection between error covariance, error rate, information rate, and principal angles. There is a limit to how sma...

We discuss the q deformation of Weyl-Heisenberg algebra in connection with the von Neumann theorem in Quantum Mechanics. We show that the q-deformation parameter labels the Weyl systems in Quantum Mechanics and the unitarily inequivalent representations of the canonical commutation relations in Quantum Field Theory. PACS 02.20.+b; 03.65.Fd; 11.30.Qc;

The gauge fixed polygon model of 2 + 1 gravity with zero cosmological constant and arbitrary number of spinless point particles is reconstructed from the firstorder formalism of the theory in terms of the triad and the spin connection. The induced symplectic structure is calculated and shown to agree with the canonical one in terms of the variables. PACS number: 04.20.Fy

The current paper is devoted to the study of integral curves of constant type in parabolic homogeneous spaces. We construct a canonical moving frame bundle for such curves and give the criterium when it turns out to be a Cartan connection. Generalizations to parametrized curves, to higher-dimensional submanifolds and to general parabolic geometries are discussed.

It is shown that the non-commutative three-sphere introduced by Matsumoto is a total space of the quantum Hopf bundle over the classical two-sphere. A canonical connection is constructed, and is shown to coincide with the standard Dirac magnetic monopole.

The Hamiltonian form of the Hilbert action in the rst order tetrad formalism is examined. We perform a non-linear eld redeenition of the canonical variables isolating the part of the spin connection which is canonically conjugate to the tetrad. The geometrical meaning of the constraints written in these new variables is examined.

Introduction Lecture 1. Algebraic properties of correlators in 2D topological field theory. Moduli of a 2D TFT and WDVV equations of associativity. Lecture 2. Equations of associativity and Frobenius manifolds. Deformed flat connection and its monodromy at the origin. Lecture 3. Semisimplicity and canonical coordinates. Lecture 4. Classification of semisimple Frobenius manifolds. Lecture 5. Mon...

We construct a novel observable for finite temperature QCD that relates confinement and chi-ral symmetry. It uses phases as boundary conditions for the fermions. We discuss numerical and analytical aspects of this observable, like its spectral behavior below and above the critical temperature, as well as the connection to chiral condensate, center symmetry and the canonical ensemble.

The Hamiltonian form of the Hilbert action in the first order tetrad formalism is examined. We perform a non-linear field redefinition of the canonical variables isolating the part of the spin connection which is canonically conjugate to the tetrad. The geometrical meaning of the constraints written in these new variables is examined.

Introduction Lecture 1. Algebraic properties of correlators in 2D topological field theory. Moduli of a 2D TFT and WDVV equations of associativity. Lecture 2. Equations of associativity and Frobenius manifolds. Deformed flat connection and its monodromy at the origin. Lecture 3. Semisimplicity and canonical coordinates. Lecture 4. Classification of semisimple Frobenius manifolds. Lecture 5. Mon...