Related papers: An account of transforms on \bar {{\cal A}/{\cal G…

A summary of the known results on integration theory on the space of connections modulo gauge transformations is presented and its significance to quantum theories of gauge fields and gravity is discussed. The emphasis is on the underlying…

Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue…

Loop quantum gravity in its Hamiltonian form relies on a connection formulation of the gravitational phase space with three key properties: 1.) a compact gauge group, 2.) real variables, and 3.) canonical Poisson brackets. In conjunction,…

General relativity can be recast as a theory of connections by performing a canonical transformation on its phase space. In this form, its (kinematical) structure is closely related to that of Yang-Mills theory and topological field…

Group field theories represent a 2nd quantized reformulation of the loop quantum gravity state space and a completion of the spin foam formalism. States of the canonical theory, in the traditional continuum setting, have support on graphs…

The quantum-reduced loop-gravity technique has been introduced for dealing with cosmological models. We show that it can be applied rather generically: anytime the spatial metric can be gauge-fixed to a diagonal form. The technique selects…

In loop quantum gravity (LQG), states of the gravitational field are represented by labeled graphs called spin networks. Their dynamics can be described by a Hamiltonian constraint, { which acts on the spin network states modifying both…

Let P be a principal bundle with semisimple compact simply connected structure group G over a compact simply connected four-manifold M. In this note we give explicit formulas for the rational homotopy groups and cohomology algebra of the…

The intention of this thesis is to provide general tools and concepts that allow to perform a mathematically substantiated symmetry reduction in (quantum) gauge field theories. Here, the main focus is on the framework of loop quantum…

We argue that a conformally invariant extension of general relativity coupled to the Standard Model is the fundamental theory that needs to be quantized. We show that it can be treated by loop quantum gravity techniques. Through a gauge…

A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's…

We present a group of transformations in the quantum configuration space of loop quantum gravity that contains the set of all transformations generated by the flux variables.

We show that loop gravity can equally well be formulated in in terms of spinorial variables (instead of the group variables which are commonly used), which have recently been shown to provide a direct link between spin network states and…

Within the framework of Quantum Reduced Loop Gravity we quantize the Hamiltonian for a gauge vector field. The regularization can be performed using tools analogous to the ones adopted in full Loop Quantum Gravity, while the matrix elements…

Is "Gravity" a deformation of "Electromagnetism"? Deformation theory suggests quantizing Special Relativity: formulate Quantum Information Dynamics $SL(2,C)_h$-gauge theory of dynamical lattices, with unifying gauge ``group'' the quantum…

For various theories, in particular gauge field theories, the algebraic form of the Hamiltonian simplifies considerably if one writes it in terms of certain complex variables. Also general relativity when written in the new canonical…

We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.

The Fourier transform, known in classical analysis, and generalized in abstract harmonic analysis, can also be considered in the theory of locally compact quantum groups. In this note, I discuss some aspects of this more general Fourier…

In this paper we put forward a systematic and unifying approach to construct gauge invariant composite fields out of connections. It relies on the existence in the theory of a group valued field with a prescribed gauge transformation. As an…

We consider the construction of gauge theories of gravity that are invariant under local conformal transformations. We first clarify the geometric nature of global conformal transformations, in both their infinitesimal and finite forms, and…