Studies in Quantization: Methods for constrained systems and semi-classical spectra of Many-Body Systems

S. Naka, Tetsuo Gotô

Oscar L. Acevedo, Arghavan Safavi-Naini, Johannes Schachenmayer +2 more

Alexandre M. Zagoskin

Ghanashyam Date, Parampreet Singh

Algebraic quantization scheme has been proposed as an extension of the Dirac quantization scheme for constrained systems. Semi-classical states for constrained systems is also an independent and important issue, particularly in the context of quantum geometry. In this work we explore this issue within the framework of algebraic quantization scheme by means of simple explicit examples. We obtain semi-classical states as suitable coherent states a la Perelomov. Remarks on possible generalizations are also included.

Jean‐Pierre Gazeau, T Koide, D Noguera

Abstract We implement the so-called Weyl–Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is illustrated with the basic example of the one-dimensional motion of a free particle in an interval, and yields a fuzzy boundary, a position-dependent mass, and an extra potential on the quantum level. The consistency of our quantization is discussed by analyzing the semi-classical phase space portrait of the derived quantum dynamics, which is obtained as a regularization of its original classical counterpart.