Mapping an Instanton to Spacetime

B. E. Eichinger

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arXiv · 2209.06329

Mapping an Instanton to Spacetime

B. E. Eichinger

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Abstract

A mapping from the Lie algebra of the complexified Lorentz group to the $\mathfrak{su}(2)\times\mathfrak{su}(2) \sim\mathfrak{sp}(1)\times\mathfrak{sp}(1)$ part of the algebra the coset space $Sp(2)/[Sp(1)\times Sp(1)]$ is presented. The coset space is shown to be home to the instanton, the curvature form that optimizes the Yang-Mills functional. Arguments are presented to support the generalization to $Sp(n)/Sp(1)^n$ to yield a self-consistent many-body theory for $n$ particles interacting with one another via fields that reside in the coset space.

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B. E. Eichinger. 2022-09-13. Mapping an Instanton to Spacetime. https://arxiv.org/abs/2209.06329

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