Abstract
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 Schr\"odinger 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.
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