In this review, we investigate the question of backreaction in different approaches to
cosmological perturbation theory, and with a special focus on quantum theoretical aspects …

The canonical approach to quantum gravity has been put on a firm mathematical foundation
in the recent decades. Even the quantum dynamics can be rigorously defined, however, due …

An introduction to loop quantum gravity is given, focussing on the fundamental aspects of
the theory, different approaches to the dynamics, as well as possible future directions. It is …

Using ideas from Jones, lattice gauge theory and loop quantum gravity, we construct 1+ 1 1+
1-dimensional gauge theories on a spacetime cylinder. Given a separable compact group G …

We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+ 1
dimensions (YM $ _ {1+ 1} $) by operator-algebraic methods. The latter are based on …

We analyze the tomographic representation for the Friedmann–Robertson–Walker (FRW)
model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi …

This article, as the first of three, aims at establishing the (time-dependent) Born-
Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for …

The way physics of loop quantum gravity is affected by the underlying quantization
ambiguities is an open question. We address this issue in the context of loop quantum …

The quantum-to-classical transition through decoherence is a major facet of the semi-
classical analysis of quantum models that are supposed to admit a classical regime, as …

This paper presents a novel path integral formalism for Einstein's theory of gravitation from
the viewpoint of optimal control theory. Despite its close connection to the well-known …