- 94-121 Vladimir V. Kisil.
- No More Than Mechanics. I.
Plain Mechanics: Classical and Quantum Mechanics as Well
(36K, LaTeX2e)
May 2, 94
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Abstract. One can introduce so-called {\em Plain Mechanics\/} having
an {\bf operator realization}. Then the set of
one-dimension representations of this operator realization
may be identified with the Classical Mechanics. Different
irreducible infinite-dimension representations may be
recognized as Quantum Mechanics for different $\hbar$ (the
Planck constant). It can be done in the such manner that
the following diagram will be commutative.
Plain Mechanics
/ \
/ \
/ \
\/ \/
Quantum Mechanics -------> Classical Mechanics
h->0
Here the horizontal arrow is well known correspondence between
Quantum and Classical Mechanics if Planck constant tensing to zero.
A {\em realization\/} of this scheme for a particle in
$n$-dimensional space by two-sided convolutions on the
Heisenberg group is constructed. We also introduce the
{\em motion equations\/} for observables in this
realization. The left arrow of the given diagram carries
this equation to the Heisenberg one and the right arrow
maps it to the Hamilton equation.
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