A homotopy-theoretic context for CKM/Birkhoff renormalization

TL;DR

This paper introduces a novel geometric framework using two-sphere fibrations with a specific structure group to parametrize regularizations in renormalization theory, blending homotopy theory with quantum field concepts.

Contribution

It proposes a new homotopy-theoretic geometric object for understanding renormalization, extending traditional bundle models with a more subtle fibration structure.

Findings

Defines a two-sphere fibration with structure group Ω²_e S² as a new geometric object.

Links the geometric model to the metaphysics of renormalization.

Provides a foundation for future exploration of homotopy-theoretic renormalization methods.

Abstract

We propose a geometric object slightly subtler than a complex line bundle with connection, a two-sphere fibration with structure group $\Omega^2_e S^2$, to parametrize a space of dimensional regularizations in the metaphysics of renormalization theory. Comments, corrections, advice and suggestions are very welcome. To be continued.