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An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor ordering singularities and can be defined in symmetric and non-symmetric form. We work in the real connection representation and obtain a(More)
We continue here the analysis of the previous paper of the Wheeler-DeWitt constraint operator for four-dimensional, Lorentzian, non-perturbative, canon-ical vacuum quantum gravity in the continuum. In this paper we derive the complete kernel, as well as a physical inner product on it, for a non-symmetric version of the Wheeler-DeWitt operator. We then deene(More)
This paper deals with several technical issues of non-perturbative four-dimensional Lorentzian canonical quantum gravity in the continuum that arose in connection with the recently constructed Wheeler-DeWitt quantum constraint operator. 1) The Wheeler-DeWitt constraint mixes the previously discussed diffeomorphism superselection sectors which thus become(More)
We combine I. background independent Loop Quantum Gravity (LQG) quantization techniques, II. the mathematically rigorous framework of Algebraic Quantum Field Theory (AQFT) and III. the theory of integrable systems resulting in the invariant Pohlmeyer Charges in order to set up the general representation theory (superselection theory) for the closed bosonic(More)
We introduce a new top down approach to canonical quantum gravity, called Algebraic Quantum Gravity (AQG): The quantum kinematics of AQG is determined by an abstract * −algebra generated by a countable set of elementary operators labelled by an algebraic graph. The quantum dynamics of AQG is governed by a single Master Constraint operator. While AQG is(More)
A Wheeler-Dewitt quantum constraint operator for four-dimensional, non-perturbative Lorentzian vacuum quantum gravity is defined in the continuum. The regulated Wheeler-DeWitt constraint operator is densely defined, does not require any renor-malization and the final operator is anomaly-free and at least symmmetric. The technique introduced here can also be(More)