37 research outputs found
Quantization of systems with internal degrees of freedom in two-dimensional manifolds
Presented is a primary step towards quantization of infinitesimal rigid body
moving in a two-dimensional manifold. The special stress is laid on spaces of
constant curvature like the two-dimensional sphere and pseudosphere
(Lobatschevski space). Also two-dimensional torus is briefly discussed as an
interesting algebraic manifold.Comment: 19 page
Mechanics of Systems of Affine Bodies. Geometric Foundations and Applications in Dynamics of Structured Media
In the present paper we investigate the mechanics of systems of
affinely-rigid bodies, i.e., bodies rigid in the sense of affine geometry.
Certain physical applications are possible in modelling of molecular crystals,
granular media, and other physical objects. Particularly interesting are
dynamical models invariant under the group underlying geometry of degrees of
freedom. In contrary to the single body case there exist nontrivial potentials
invariant under this group (left and right acting). The concept of relative
(mutual) deformation tensors of pairs of affine bodies is discussed. Scalar
invariants built of such tensors are constructed. There is an essential novelty
in comparison to deformation scalars of single affine bodies, i.e., there exist
affinely-invariant scalars of mutual deformations. Hence, the hierarchy of
interaction models according to their invariance group, from Euclidean to
affine ones, can be considered.Comment: 50 pages, 4 figure
Quasiclassical and Quantum Systems of Angular Momentum. Part II. Quantum Mechanics on Lie Groups and Methods of Group Algebras
In Part I of this series we presented the general ideas of applying
group-algebraic methods for describing quantum systems. The treatment was there
very "ascetic" in that only the structure of a locally compact topological
group was used. Below we explicitly make use of the Lie group structure. Basing
on differential geometry enables one to introduce explicitly representation of
important physical quantities and formulate the general ideas of quasiclassical
representation and classical analogy