Parametrized scalar field on openR${\ge }^1$: Dynamical pictures, spacetime diffeomorphisms, and conformal isometries

As a preparation for a consistent Dirac constraint quantization and an anomaly-free operator representation of the spacetime diffeomorphism algebra, we develop a covariant canonical theory of a parametrized massless scalar field propagating on a cylindrical Minkowskian spacetime. We show how to pass from the Schrödinger picture to the Heisenberg picture on the extended phase space of this parametrized system, how to construct a pair of canonical representations of L DiffM by using these pictures, and how to relate canonical representations of conformal isometries to those of L DiffM. We reconstruct the spacetime structures needed for operator ordering from the geometric data on a single embedding. We keep the formalism covariant under all relevant transformations.