Canonical and Covariant Dynamics of Quantum Gravity

Group Leader: Dr. Bianca Dittrich

This Max Planck Research Group is funded by the Max Planck Society. Its research focuses on the construction and examination of quantum gravity models. Its aim is to obtain a satisfactory description of the dynamics of quantum gravity theories.

In recent years a number of different approaches to quantum gravity, such as Loop Quantum Gravity, Spin Foams, Quantum Regge Calculus and Causal Dynamical Triangulations emerged as serious candidates for successful models of a quantized theory of gravity. These approaches have in common that they do not assume a given space time manifold as a `background', but such a background space time needs to emerge dynamically out of the basic ingredients of the models. This also implies that a notion of space and in particular time itself is not predefined but has to be identified after having established the dynamics. These ideas are connected to diffeomorphism invariance, which is the concept that there are no preferred coordinate systems.

Diffeomorphism invariance is indeed the symmetry at the heart of general relativity as it is deeply intertwined with its dynamics. It can be regarded as replacement for the much smaller Poincare invariance of special relativity. The requirement of Poincare invariance imposes very stringent restrictions on the allowed dynamics in quantum field theories, the same should hold for diffeomorphism invariance and the dynamics of quantum gravity theories.

In the last years much progress has been made that allows for a good understanding of the kinematics of quantum gravity theories. These developments also provide the necessary tools to construct the dynamics of the models, which is the main research focus of the group. Of particular importance are (quantum) representations of the diffeomorphism symmetry, since such a representation is actually equivalent to the definition of the dynamics of the theory. As diffeomorphism symmetry is a concept from continuum physics, whereas many quantum gravity models involve discrete features, one important question is whether and how these two aspects can be reconciled. This question requires the consideration of a continuum/large scale limit and involves methods from statistical physics and renormalization theory.

Apart from being a very important conceptual question, the fate of diffeomorphism invariance in a theory of quantum gravity will have a strong impact on its phenomenological predictions, for instance regarding a possible Lorentz invariance breaking.

The problem of dynamics is common to most of the quantum gravity approaches. We are therefore not so much focussed on one particular approach, but try to combine the best features of different models. For instance, in covariant models an understanding of the full diffeomorphism group is typically easier to obtain, whereas canonical models provide a clean path towards quantization.

We work in close collaboration with the independent research group "Microscopic Quantum Structure and Dynamics of Spacetime", led by Dr. Daniele Oriti, and interact as well with the Quantum Gravity and Unified Theories division of the Albert Einstein Institute, directed by Prof. Nicolai.

Microscopic Quantum Structure & Dynamics of Spacetime
 Group Leader: Dr. Daniele Oriti

Quantum Gravity & Unified Theories division