Multiparticle Systems and Field Quantization

Bipin R. Desai

I. Laba

Yue Yu, Zhu Zhongyuan

Geometric quantization of multiparticle systems in 2 dimensions is studied. The interpretation of the global geometry to the phase factors describing the quantum statistics of the systems is presented.

И.П. Базаров, Pavel Nikolaev

V. P. Belavkin, Виктор Павлович Маслов

Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization of classical systems to arbitrary Hamiltonian (Lie-Jordan, or Poissonian) algebras, in particular to the algebras of operators in indefinite spaces. A functional calculus is developed for the uniformized observables, which unifies the calculi of generating functionals for classical, Bosonian and Fermionian multiparticle variables. The nonlinear kinetic equation of Vlasov and Hartree type are derived for both classical and quantum multiparticle Hamiltonian systems in the mean field approximation. The possibilities for finding approximate solutions of these equations from the solutions of uniformized linear equations are investigated.

W. H. Klink, S. Wickramasekara