2003/05/28 by A. J. Bracken · 24 citations
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #Mathematical formulation of quantum mechanics #Method of quantum characteristics #Quantum statistical mechanics #Quantum mechanics #Classical mechanics #Supersymmetric quantum mechanics #Physics #Quantum dynamics #Mathematics #Quantum process #Quantum
paper · pdf · doi:10.1088/0305-4470/36/23/101
published in Journal of Physics A Mathematical and General 36(23), L329-L335 (Institute of Physics)
openalex publication_date 2003/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.