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Fibre bundle formulation of time-dependent mechanics (1303.1735v1)
Published 7 Mar 2013 in math-ph and 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.