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It is an old speculation in physics that, once the gravitational field issuccessfully quantized, it should serve as the natural regulator of infraredand ultraviolet singularities that plague quantum field theories in abackground metric. We demonstrate that this idea is implemented in a precisesense within the framework of four-dimensional canonical Lorentzian quantumgravity in the continuum. Specifically, we show that the Hamiltonian of thestandard model supports a representation in which finite linear combinations ofWilson loop functionals around closed loops, as well as along open lines withfermionic and Higgs field insertions at the end points are densely definedoperators. This Hamiltonian, surprisingly, does not suffer from anysingularities, it is completely finite without renormalization. This propertyis shared by string theory. In contrast to string theory, however, we aredealing with a particular phase of the standard model coupled to gravity whichis entirely non-perturbatively defined and second quantized.Comment: 34p, LATE

Quantum spin dynamics (QSD): V. Quantum gravity as the natural regulator of the Hamiltonian constraint of matter quantum field theories