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Résumé |
Quantum field theories (QFTs) provide a very effective
framework for describing relativistic quantum systems with an infinite
number of degrees of freedom. In particular, their setting allows one to
provide expressions for the so-called correlation functions that are
directly measured in experiments. However, even though a lot of progress
has been made regarding the rigorous constructions of QFTs using various
techniques, there are still numerous open questions remaining. In the
60s, Wightman proposed a scheme allowing one to construct a QFT from the
knowledge of its correlation functions, satisfying specific properties
called Wightman axioms. Since then, multiple approaches have been
developed, leading to the constructions of several QFTs in various
dimensions. In this talk, I will focus on one approach, based on the
integrable bootstrap. This approach, applicable to general integrable
quantum field theories in 1+1 dimensions, will be illustrated by the
example of the Sinh-Gordon model, which is the simplest of such
theories. Using this approach, we managed to derive fully explicit and
well-defined expressions for appropriately regularized multi-point
correlation fonctions, from which the regular correlation functions can
be obtained and satisfy Wightman axioms, assuming some convergence
properties. This is a joint work with K. Kozlowski. |
