In this work we investigate the question, under what conditions Hilbert spaces that are induced by measures on the space of generalized connections carry a representation of certain non-Abelianâ€¦ (More)

Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariantâ€¦ (More)

In this article and the companion paper [1] we address the question of how one might obtain the semiclassical limit of ordinary matter quantum fields (QFT) propagating on curved spacetimes (CST) fromâ€¦ (More)

In loop quantum gravity, matter fields can have support only on the â€˜polymer-likeâ€™ excitations of quantum geometry, and their algebras of observables and Hilbert spaces of states can not refer to aâ€¦ (More)

Loop quantum gravity is an approach to quantum gravity that starts from the Hamiltonian formulation in terms of a connection and its canonical conjugate. Quantization proceeds in the spirit of Dirac:â€¦ (More)

We summarize a recently proposed concrete programme for investigating the (semi)classical limit of canonical, Lorentzian, continuum quantum general relativity in four spacetime dimensions. Theâ€¦ (More)

The present paper is the companion of [1] in which we proposed a scheme that tries to derive the Quantum Field Theory (QFT) on Curved Spacetimes (CST) limit from background independent Quantumâ€¦ (More)

We provide a precise definition and analysis of quantum causal histories (QCHâ€™s). A QCH consists of a discrete, locally finite, causal pre-spacetime with matrix algebras encoding the quantumâ€¦ (More)

The characterization of Hadamard states in terms of a specific form of the wavefront set of their two-point functions has been developed some years ago by Radzikowski for scalar fields on aâ€¦ (More)

In the setting of vector-valued quantum fields obeying a linear wave-equation in a globally hyperbolic, stationary spacetime, it is shown that the two-point functions of passive quantum statesâ€¦ (More)