Journal of Nonlinear Mathematical Physics

Volume 11, Issue Supplement 1, October 2004, Pages 157 - 166

Classical and Quantized Affine Physics: A Step towards it

Authors
Jan J. Slawianowski, Vasyl Kovalchuk
Corresponding Author
Jan J. Slawianowski
Available Online 1 October 2004.
DOI
https://doi.org/10.2991/jnmp.2004.11.s1.21How to use a DOI?
Abstract
The classical and quantum mechanics of systems on Lie groups and their homogeneous spaces are described. The special stress is laid on the dynamics of deformable bodies and the mutual coupling between rotations and deformations. Deformative modes are discretized, i.e., it is assumed that the relevant degrees of freedom are controlled by a finite number of parameters. We concentrate on the situation when the effective configuration space is identical with affine group (affinely-rigid bodies). The special attention is paid to left- and right-invariant geodetic systems, when there is no potetial term and the metric tensor underlying the kinetic energy form is invariant under left or/and right regular translations on the group. The dynamics of elastic vibrations may be encoded in this way in the very form of kinetic energy. Although special attention is paid to invariant geodetic systems, the potential case is also taken into account.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
11 - Supplement 1
Pages
157 - 166
Publication Date
2004/10
ISBN
91-974824-2-0
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2004.11.s1.21How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Jan J. Slawianowski
AU  - Vasyl Kovalchuk
PY  - 2004
DA  - 2004/10
TI  - Classical and Quantized Affine Physics: A Step towards it
JO  - Journal of Nonlinear Mathematical Physics
SP  - 157
EP  - 166
VL  - 11
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2004.11.s1.21
DO  - https://doi.org/10.2991/jnmp.2004.11.s1.21
ID  - Slawianowski2004
ER  -