Geometric formulation of non-autonomous mechanics

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 fiber bundles over a time axis ℝ. Connections on these bundles describe reference frames. Quantum non-autonomous mechanics is phrased in geometric terms of Banach and Hilbert bundles and connections on these bundles. A quantization scheme speaking this language is geometric quantization. © World Scientific Publishing Company.