CONSTRAINTS, HERMITICITY, AND CORRESPONDENCE

In order to expose the essential features of the quantization of a theory with constraints, we consider the most elementary system, that of a free particle. We show that even for this simple system, when expressed in a constraint formalism, it requires the introduction of an indefinite metric in the Hilbert space, non-Hermitian constraints, and indeed most other features which we have come to associate with the Gupta-Bleuler formalism of electrodynamics. By introducing a conceptually new object, the quasiobservable, we show how an Ehrenfest correspondence principle may be obtained for the resulting quantum theory. © 1979 The American Physical Society.