  This is an up-to-date survey of the p-mechanical construction (see
funct-an/9405002, quant-ph/9610016, math-ph/0007030, quant-ph/0212101,
quant-ph/0303142), which is a consistent physical theory suitable for a
simultaneous description of classical and quantum mechanics. Observables in
p-mechanics are defined to be convolution operators on the Heisenberg group
H^n. Under irreducible representations of H^n the p-observables generate
corresponding observables in classical and quantum mechanics. p-States are
defined as positive linear functionals on p-observables. It is shown that both
states and observables can be realised as certain sets of
functions/distributions on the Heisenberg group. The dynamical equations for
both p-observables and p-states are provided. The construction is illustrated
by the forced and unforced harmonic oscillators. Connections with the
contextual interpretation of quantum mechanics are discussed. Keywords:
Classical mechanics, quantum mechanics, Moyal brackets, Poisson brackets,
commutator, Heisenberg group, orbit method, deformation quantisation,
symplectic group, representation theory, metaplectic representation, Berezin
quantisation, Weyl quantisation, Segal--Bargmann--Fock space, coherent states,
wavelet transform, Liouville equation, contextual interpretation, interaction
picture, forced harmonic oscillator.
