Fibre bundle formulation of time-dependent mechanics
Mathematical Physics
2013-03-08 v1 math.MP
Abstract
We address classical and quantum mechanics in a general setting of arbitrary time-dependent transformations. Classical non-relativistic mechanics is formulated as a particular field theory on smooth fibre bundles over a time axis. Connections on these bundles describe reference frames. Quantum time-dependent mechanics is phrased in geometric terms of Banach and Hilbert bundles and connections on these bundles. A quantization scheme speaking this language is leafwise geometric quantization.
Cite
@article{arxiv.1303.1735,
title = {Fibre bundle formulation of time-dependent mechanics},
author = {G. Sardanashvily},
journal= {arXiv preprint arXiv:1303.1735},
year = {2013}
}
Comments
13 pages