Functional Quantization of Second Class Systems

Bing-Sheng Lin, Tai-Hua Heng

In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in [Formula: see text] is proportional to the Dirac bracket. In this way an oscillator system in a deformed fermionic phase space is analyzed and the corresponding energy level and Wigner functions are evaluated according to scheme of deformation quantization. We also study the entanglement entropy induced by the deformation of the fermionic phase space.

Franco Gallone, Antonio Sparzani

Segal quantization, usually thought of and used as a tool for quantizing kinematical frameworks, is extended to (finite-dimensional) dynamical systems, i.e., to kinematical frameworks plus dynamical motions applied to them. Such a procedure allows us to classify quantum dynamical systems, and to understand how physical inequivalence appears in spite of von Neumann unitary equivalence, for the former is also grounded on the evolution operators of the systems being different functions of the labeled observables of the systems. Second quantization is also examined and is shown to be just one possible procedure of quantization, which can only be used in a particular class of cases.

Joakim Hallin

Masayoshi Nakamura, Hiroaki Minowa

It is shown that the operator formulation of the quantization of dynamical systems subject to second class constraints by Batalin and Fradkin (BF method) is equivalent to the projection-operator method (POM), which is the alternative method of the quantization of such systems, at the commutator level. It is also shown that the commutators in the BF method as well as those in the POM contain a quantum effect, which is completely missed in the usual quantization scheme with the Dirac brackets.

Sergio A Albeverio, Jürgen Jost, Sylvie Paycha +1 more