On the boundary conditions as Dirac constraints

In this paper, the canonical quantization of singular Lagrangian defined in a finite volume is discussed by studying a 1 + 1 dimensional free Schrödinger field. We take the boundary conditions (BCs) as Dirac constraints, and show that those BCs as well as the intrinsic constraints (which are introduced by the singularities of Lagrangian) form the second class constraints. The quantization is performed canonically.Received: 30 August 2004, Revised: 2 October 2004, Published online: 17 December 2004PACS: 11.25-W, 04.60.D, 11.10.E