Well-defined equations of motion without constraint of external sources

TL;DR

This paper introduces a new formalism for constrained classical fields that automatically incorporates symmetry restrictions into external sources, improving the accuracy of models like cosmological dynamics with relativistic sources.

Contribution

It develops a novel approach to include symmetry restrictions in external sources within the action formalism, avoiding ad hoc assumptions common in traditional methods.

Findings

Symmetry restrictions in Fourier space are automatically applied to external sources.

The new method reduces leading-order errors in modeling systems with external sources.

Application to cosmology shows relativistic pressure sources significantly influence dynamics.

Abstract

We present a new approach to constrained classical fields that enables the action formalism to dictate how external sources must enter the resulting equations of motion. If symmetries asserted upon the varied fields can be modeled as restrictions in Fourier space, we prove that these restrictions are automatically applied to external sources in an unambiguous way. In contrast, the typical procedure inserts symmetric ansatze into the Euler-Lagrange differential equations, even for external sources not being solved. This requires ad hoc constraint of external sources, which can introduce leading-order errors to model systems despite superficial consistency between model field and source terms. To demonstrate, we consider Robertson-Walker cosmologies within General Relativity and prove that the influence of point-like relativistic pressure sources on cosmological dynamics cannot be excluded by theoretical arguments.