Eur. Phys. J. C 19, 383-390
DOI: 10.1007/s100520100590

Boundary conditions as Dirac constraints

M.M. Sheikh-Jabbari¹ and A. Shirzad<sup>1, 2

1</sup>  Institute for Studies in Theoretical Physics and Mathematics, IPM, P.O. Box 19395-5531, Tehran, Iran
²  Department of Physics, Isfahan University of Technology, Isfahan, Iran

(Received: 16 October 2000 / Revised version: 8 January 2001 / Published online: 23 February 2001 -© Springer-Verlag 2001)

Abstract
In this article we show that boundary conditions can be treated as Lagrangian and Hamiltonian constraints. Using the Dirac method, we find that boundary conditions are equivalent to an infinite chain of second class constraints, which is a new feature in the context of constrained systems. Constructing the Dirac brackets and the reduced phase space structure for different boundary conditions, we show why mode expanding and then quantizing a field theory with boundary conditions is the proper way. We also show that in a quantized field theory subjected to the mixed boundary conditions, the field components are non-commutative.

© Società Italiana di Fisica, Springer-Verlag 2001