Operator Quantization of Second Class Systems

A. Farmany, M. Hatami, Hadi Noorizadeh +1 more

Masayoshi Nakamura

The quantization of the second-class constraint systems is discussed within the projection operator method(POM) of constraint systems. Through the nonlocal representation of the constraint hyper-operators, new star-products are defined. Then, the projected operator-algebra of the quantized constraint systems is constructed with these star-products, and it is shown that the commutators and symmetrized products among the projected operators contain the quantum corrections due to the noncommutativity among operators.

Прохоров Лев Васильевич, Sergei V. Shabanov

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.

Jeppe Olsen