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Quantum Field Theory with Gaussian Multiplicative Chaos

Project description

Probabilistic methods help unify quantum mechanics and general relativity

The Standard Model of particle physics has several acknowledged gaps, one of which is that it does not account for the force of gravity. Quantum gravity attempts to reconcile quantum mechanics and general relativity via a quantum description of gravity as packets of magnetism. Quantum field theory (QFT) is the mathematical framework for modern particle physics. Whereas quantum mechanics deals with the behaviour of one or a few microscopic particles, QFT can be used to describe quantum systems with many particles, so-called many-body problems. Through an in-depth exploration of probabilistic approaches in QFT, the EU-funded QuantGMC project is developing probabilistic methods that will help us better understand the theory of quantum gravity.

Objective

The proposed goal for our research program is to attack some mathematical problems arising in constructive two dimensional Quantum Field Theory (QFT) and two dimensional Quantum Gravity (QG) using probabilistic methods.

The physical theory of Quantum Gravity has the aim of providing a unified framework which encompasses the two descriptions of nature provided by quantum mechanics and general relativity.
The two dimensional version of the theory is more tractable than the one corresponding to the four dimensional space-time and thus is used as a testing workbench to understand higher dimensional physics.

In order to reinforce the rigourous mathematical understanding of this theory, we wish to explore two particular aspects of QFT which are based on a probabilistic construction called Gaussian Multiplicative chaos. The objectives of QuantGMC are:

A- To obtain an explicit construction of canonical random surfaces equipped with a structure of Kähler manifold. In technical terms this corresponds to the construction of a path integral corresponding to the coupling of Liouville functional and the Mabuchi K-energy on 2D manifold of arbitrary genus.

B- To enhance the current understanding of the Quantum Sine-Gordon model, which can be interpreted as a random version of the Sine-Gordon equation. This model is conjectured to undergo an infinite sequence of collapse transitions when the inverse temperature increases. However up to now, rigorous renormalization theory of the model can only allow to witness the three first of these transitions. We plan to use Gaussian Multiplicative Chaos to provide a more efficient renormalization scheme which would allow to account for all the transitions.

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Coordinator

UNIVERSITE D'AIX MARSEILLE
Net EU contribution
€ 114 746,24
Address
Boulevard charles livon 58 le pharo
13284 Marseille
France

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Region
Provence-Alpes-Côte d’Azur Provence-Alpes-Côte d’Azur Bouches-du-Rhône
Activity type
Higher or Secondary Education Establishments
Links
Other funding
€ 0,00