  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.
