2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/138318Canonical quantization of gravity requires knowledge about the representation theory of its constraint algebra, which is physically equivalent to the algebra of arbitrary 4-diffeomorphisms. All interesting lowest-energy representations are projective, making the relevant algebra into a four-dimensional generalization of the Virasoro algebra. Such diffeomorphism anomalies are invisible in field theory, because the relevant cocycles are functionals of the observer's trajectory in spacetime. The multi-dimensional Virasoro algebra acts naturally in the phase space of arbitrary histories, with dynamics playing the role of first-class constraints. General relativity is regularized by expanding all fields in Taylor series around the observer's trajectory, and truncating at some fixed order. This regularized but manifestly general-covariant theory is quantized in the history phase space, and dynamics is imposed afterwards, in analogy with BRST quantization. Infinities arise when the regularization is removed; it is presently unclear how these should be dealt with.In: Focus on quantum gravity research, ed: David C. Moore, pp 261-310, 2006 Nova Science Publishers Inc. ISBN 1-59454-660-6High Energy Physics - TheoryGeneral Relativity and Quantum Cosmologytext