We study the concentration of measure in metric-measurable (mm)-spaces. define notion locus a flag sequence Some examples infinite group action on an dimensional compact and non-compact manifold show role played by trajectory locus. also provide some applications physics, which emphasize gravitational effects.

carrier space formalism for the irreducible tensor operators of compact quantum group algebras Abstract Defining conditions for irreducible tensor operators associated with the uni-tary irreducible corepresentations of compact quantum group algebras are deduced within the framework of the abstract carrier space formalism. It is shown that there are two types of irreducible tensor operator, whic...

We sketch a group-theoretical framework, based on the Heisenberg–Weyl group, encompassing both quantum and classical statistical descriptions of unconstrained, non-relativistic mechanical systems. We redefine in group-theoretical terms a kinematical arena and a space of statistical states of a system, achieving a unified quantum-classical language and an elegant version of the quantum-toclassic...

A set of coordinates in the non parametric loop-space is introduced. We show that these coordinates transform under infinite dimensional linear representations of the diffeomorphism group. An extension of the group of loops in terms of these objects is proposed. The enlarged group behaves locally as an infinite dimensional Lie group. Ordinary loops form a subgroup of this group. The algebraic p...

As is well-known, there is a variational principle for the Euler–Poincaré equations on a Lie algebra g of a Lie group G obtained by reducing Hamilton’s principle on G by the action of G by, say, left multiplication. The purpose of this paper is to give a variational principle for the Lie–Poisson equations on g∗, the dual of g, and also to generalize this construction. The more general situation...