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Non-Perturbative Path Integrals for Quantum Gravity

Non-Perturbative Path Integrals for Quantum Gravity

Objective

One of the biggest gaps in our understanding of the physical world is the missing fundamental theory of gravity. Einstein and apos general relativity is a classical theory, but we know our world is quantum. So what is quantum gravity? Since, as Einstein taught us, any theory for gravity is also a theory of the geometry of space and time, this is an extremely challenging question - answering it will completely change our understanding of what space and time really are. This makes it also into a great intellectual adventure: it needs radically new ideas, new mathematics, and it will profoundly change physics. And what is more, in the not too distant future, effects of quantum gravity may be experimentally detectable!

Path integrals are a powerful and time honoured approach to quantum field theory. One can start working from an action, i.e. essentially just from symmetry properties of the theory in question, and in principle a reasonable classical limit is assured. All of that makes them very attractive for quantum gravity, too.

Of particular importance for us are three such approaches to quantum gravity: Loop Quantum Gravity, Spin Foam Models, and Causal Dynamical Triangulations. They all are promising approaches, but they also all have issues that are not yet well understood. Very important for us is that they are complementary in many ways. Relating the approaches to each other will shed new light on many old problems. Lessons learned in one can be applied to the other. And techniques developed for one can be transferred between the approaches.

In particular we propose to study the following issues:
- Divergence of spin foam amplitudes, and the relation between Euclidean and Lorentzian theory
- Mathematical foundations and diffeomorphism invariance of Causal Dynamical Triangulations
- Connection between Loop Quantum Gravity and Spin Foam Models

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Coordinator

UTRECHT UNIVERSITY

Address

Heidelberglaan 8
80125 Utrecht

Netherlands

Administrative Contact

Renate LOLL (Professor)

Project information

Grant agreement ID: 41316

  • Start date

    18 October 2006

  • End date

    17 September 2008

Funded under:

FP6-MOBILITY

Coordinated by:

UTRECHT UNIVERSITY

Netherlands