A Field-Theory Action for the Constructive Standard Model

TL;DR

This paper presents a novel field-theory framework based on little group transformations that reproduces the Constructive Standard Model vertices, reduces degrees of freedom, and offers new insights into constructive amplitudes and potential non-perturbative applications.

Contribution

It introduces a new field-theory action based on little group transformations, simplifying the structure and providing a foundation for developing constructive field theories.

Findings

Reproduces CSM vertices using little group-based fields

Reduces unphysical components and degrees of freedom

Provides a basis for non-perturbative and renormalization studies

Abstract

We introduce a field-theory framework in which fields transform under the little group, rather than the Lorentz group, specific to each particle type. By utilizing these fields, along with spinor products and the x factor, we construct a field-theory action that naturally reproduces the vertices of the Constructive Standard Model (CSM). This approach eliminates unphysical components, significantly reduces the degrees of freedom compared to traditional field theory, and offers deeper insights into the power of constructive amplitudes. Our action is momentum-conserving, Lorentz-invariant, Hermitian, and non-local. We also discuss this as a framework for developing new constructive field theories, discussing their essential properties and potential applicability in renormalization theory and non-perturbative calculations.