The Metric Nature of Matter
Johannes Aastrup, Jesper M. Grimstrup

TL;DR
This paper develops a geometric framework using a metric on gauge connection space, leading to a non-perturbative quantum field theory that unifies Yang-Mills and Dirac fields on curved backgrounds.
Contribution
It introduces an infinite-dimensional Bott-Dirac operator and a non-commutative algebra to encode quantum field relations in a geometric, metric-based setting.
Findings
Constructs a metric structure on gauge connections.
Derives Yang-Mills and Dirac Hamiltonians from the Bott-Dirac operator.
Establishes a geometric, non-perturbative approach to quantum field theory.
Abstract
We construct a metric structure on a configuration space of gauge connections and show that it naturally produces a candidate for a non-perturbative, 3+1 dimensional Yang-Mills-Dirac quantum field theory on a curved background. The metric structure is an infinite-dimensional Bott-Dirac operator and the fermionic sector of the emerging quantum field theory is generated by the infinite-dimensional Clifford algebra required to construct this operator. The Bott-Dirac operator interacts with the algebra, which is a non-commutative algebra generated by holonomy-diffeomorphisms on the underlying manifold, i.e. parallel-transforms along flows of vector fields. This algebra combined with the Bott-Dirac operator encode the canonical commutation and anti-commutation relations of the quantised bosonic and fermionic fields. The square of the Bott-Dirac operator produces both the…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
