Affine group formulation of the Standard Model coupled to gravity

摘要

In this work we apply the affine group formalism for four dimensional gravity of Lorentzian signature, which is based on Klauder's affine algebraic program, to the formulation of the Hamiltonian constraint of the interaction of matter and all forces, including gravity with non-vanishing cosmological constant Λ, as an affine Lie algebra. We use the hermitian action of fermions coupled to gravitation and Yang-Mills theory to find the density weight one fermionic super-Hamiltonian constraint. This term, combined with the Yang-Mills and Higgs energy densities, are composed with York's integrated time functional. The result, when combined with the imaginary part of the Chern-Simons functional Q, forms the affine commutation relation with the volume element V(x). Affine algebraic quantization of gravitation and matter on equal footing implies a fundamental uncertainty relation which is predicated upon a non-vanishing cosmological constant.