2004/06/12 by L. V. Prokhorov, Prokhorov, L. V.
Physics and Astronomy · #FOS: Physical sciences #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0406079
minor changes, 9 pages
arxiv created 2005/03/25 · arxiv updated 2009/12/01
Relations between Hamiltonian mechanics and quantum mechanics are studied. It is stressed that classical mechanics possesses all the specific features of quantum theory: operators, complex variables, probabilities (in case of ergodic systems). The Planck constant and the Fock space appear after putting a dynamical system in a thermal bath. For harmonic oscillator in a thermal bath, the probability amplitudes can be identified with the complex valued phase functions f(q+ip) describing small deviations from the equilibrium state, when the time of relaxation is large. A chain of such oscillators models both the one-dimensional space (or string), and one-dimensional quantum field theory.