Global critical points of the Standard Model on four-dimensional spacetimes of expanding type

TL;DR

This paper provides a rigorous geometric formulation of the Standard Model on expanding four-dimensional spacetimes and proves the existence of global solutions to its equations under certain conditions.

Contribution

It offers a mathematically rigorous, gauge-invariant framework for the Standard Model on globally hyperbolic manifolds and establishes global existence results for its equations.

Findings

Existence of global solutions for the Standard Model equations on expanding spacetimes.

Development of a gauge-invariant energy estimate.

Mathematically rigorous geometric formulation of the Standard Model.

Abstract

The Standard Model of elementary particle physics is one of the most successful models of contemporary theoretical physics being in full agreement with experiments. However, its mathematical structure deserves further investigations both from a geometric and an analytic point of view. The aim of this manuscript is to provide a mathematically well-defined and self-contained description of the Standard Model in terms of gauge theory and differential geometry on globally hyperbolic manifolds. Within this setup we then prove the existence of a global solution for the Euler-Lagrange equations of the Standard Model (with the conformal Higgs potential) under the assumptions that the globally hyperbolic manifold is a four-dimensional spacetime of expanding type and small initial data. This is achieved by establishing a gauge-invariant energy estimate which is of independent mathematical interest.