Volume 11, Issue Supplement 1, October 2004, Pages 157 - 166
Classical and Quantized Affine Physics: A Step towards it
Jan J. Slawianowski, Vasyl Kovalchuk
Jan J. Slawianowski
Available Online 1 October 2004.
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- 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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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 -