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arXiv · 1910.01841

Non-perturbative Quantum Field Theory and the Geometry of Functional Spaces

Johannes Aastrup·Jesper M. Grimstrup
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Abstract

In this paper we construct a non-commutative geometry over a configuration space of gauge connections and show that it gives rise to a candidate for an interacting, non-perturbative quantum gauge theory coupled to a fermionic field on a curved background. The non-commutative geometry is given by an infinite-dimensional Bott-Dirac type operator, whose square gives the Hamilton operator, and which interacts with an algebra generated by holonomy-diffeomorphisms. The Bott-Dirac operator and the associated Hilbert space relies on a metric on the configuration space of connections, which effectively works as a covariant ultra-violet regulator. We show that the construction coincides with perturbative quantum field theory in a local limit. Questions concerning Lorentz invariance and the fermionic sector as well as the issue of existence are left open.

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Johannes Aastrup, Jesper M. Grimstrup. 2019-10-04. Non-perturbative Quantum Field Theory and the Geometry of Functional Spaces. https://arxiv.org/abs/1910.01841

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