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This work demonstrates that a complete description of the interaction of matter and all forces, gravitational and non-gravitational, can in fact be realized within a quantum affine algebraic framework. Using the affine group formalism, we construct elements of a physical Hilbert space for full, Lorentzian quantum gravity coupled to the Standard Model in four spacetime dimensions. Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant.
We systematically derive an action for a nonrelativistic spinning partile in flat background and discuss its canonical formulation in both Lagrangian and Hamiltonian approaches. This action is taken as the starting point for deriving the correspondin
A detailed canonical treatment of a new action for a nonrelativistic particle coupled to background gravity, recently given by us, is performed both in the Lagrangian and Hamiltonian formulations. The equation of motion is shown to satisfy the geodes
Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $Lambda$, is reexpressed as an affine algebra with the commutator of the imaginary part of the Chern-Simo
We discuss reality conditions and the relation between spacetime diffeomorphisms and gauge transformations in Ashtekars complex formulation of general relativity. We produce a general theoretical framework for the stabilization algorithm for the real
A spin-foam model is derived from the canonical model of Loop Quantum Gravity coupled to a massless scalar field. We generalized to the full theory the scheme first proposed in the context of Loop Quantum Cosmology by Ashtekar, Campiglia and Henderso