This work highlights the use of the projection operator formalism of constraint quantization to generate gauge invariant Green's functions. While the projection operator formalism was originally designed to be able to quantize even the anomalous constraints of general relativity, here the formalism is used to quantize a finite dimensional toy model resembling a gauge theory. Using the projection operator to construct observable operators, the propagators for this model are explicitly calculated. The gauge structure of N-point correlators involving these observables is then exploited to derive path integral expressions. Lastly, it is shown how these N-point functions can be obtained by a gauge invariant generating functional.
SU(2) Principal bundles acted upon by a 2d-compact group are studied. Some applications are shown in the context of the Ashtekar-Barbero formulation of gravity, with special attention to the case of a compact base, which comprises the most simple non-homogeneous exact cosmological models, the so called Gowdy universes in metric variables.
The effect of the gauge transformation in the action principle for Hamiltonian gauge systems is formulated in terms of non-canonical symplectic structures is studied and, in particular, the compatibility between gauge conditions and boundary conditions is analized. The theory is applied to two non-trivial models having SL(2,R) and SU(2) gauge symmetries, respectively; whose extended phase spaces are endowed with non-canonical symplectic structures involving noncommuting coordinates.
The term added by Holst to the Palatini Lagrangian 4-form to generate the canonical variables used as the starting point for canonical quantization of gravity in the so-called loop quantum gravity, defines by itself a 4-dimensional field theory. The aim of this work is to study, in the framework of Dirac canonical analysis and without destroying Lorentz covariance explicitly, the type of constraints of this theory.