Quantization of Non-Hamiltonian Systems

In this paper a generalization of quantization
which maps a dynamical
operator in a function space to a dynamical superoperator in an
operator space is suggested. Quantization of dynamical
operator, which cannot be represented as Poisson bracket
with some function, is considered.Quantization of classical systems which evolution is defined by
Hamilton function is equivalent to canonical quantization.
Generalized quantization of non-hamiltonian dynamical operators is not
defined by canonical quantization. Moreover the
canonical quantization is a specific case of suggested quantization if
dynamical operator is a operator of multiplication on a function.
This approach allows to define consistent quantization
procedure for non-hamiltonian and dissipative systems.
Examples of the harmonic oscillator with friction and a system which
evolves by Fokker-Planck-type equation are considered.

Document number: 2000-33/637

Authors: Vasily E. Tarasov

Email: tarasov@theory.npi.msu.su