Skip to Main content Skip to Navigation
Journal articles

Wigner Quantization of Hamilton–Dirac Systems

Abstract : This paper describes the states of quantum versions of finite dimensional Hamilton–Dirac systems in terms of (analogues of) the Wigner function (various definitions of Wigner functions for classical Hamiltonian systems can be found in [8]). We give a system of equations, which we call the Moyal–Dirac system, describing the evolution of this Wigner function. The passage from the Moyal equation describing the evolution of the quantum version of a classical Hamiltonian system to the Moyal–Dirac system describing the evolution of the quantum version of the corresponding Hamilton–Dirac system is similar to the passage from the Liouville equation describing the evolution of a classical Hamiltonian system to the Liouville–Dirac system of equations describing the evolution of the corresponding Hamilton–Dirac system. Thus, our Moyal–Dirac system is a generalization of both the Liouville–Dirac system and the Moyal equation
Document type :
Journal articles
Complete list of metadata

Cited literature [5 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01398473
Contributor : Christian Cardillo <>
Submitted on : Thursday, November 17, 2016 - 12:00:46 PM
Last modification on : Friday, November 18, 2016 - 1:02:47 AM
Long-term archiving on: : Thursday, March 16, 2017 - 3:58:30 PM

File

wigner_quantization.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

T. S. Ratiu, O. G. Smolyanov. Wigner Quantization of Hamilton–Dirac Systems. Доклады Академии Наук / Doklady Mathematics, MAIK Nauka/Interperiodica, 2015, 91 (1), pp.114-116. ⟨10.1134/S1064562415010287⟩. ⟨hal-01398473⟩

Share

Metrics

Record views

129

Files downloads

230