A systematic approach to model building

TL;DR

This paper presents a systematic method for constructing and analyzing field theories by deriving all continuous symmetries using Lie point symmetries, aiding the development of more predictive models including the Standard Model.

Contribution

It introduces a comprehensive approach to identify symmetries and parameter relationships in field theories, applicable to various models including gravity and beyond Standard Model.

Findings

Method derives all continuous symmetries systematically.

Identifies parameter relationships leading to enhanced symmetries.

Applicable to standard model, gravity, and beyond.

Abstract

We outline a new, systematic way of constructing and analysing field theories, where all possible continuous symmetries of a given model are derived using the method of Lie point symmetries. If the model has free parameters, and relationships amongst any of these parameters yields an enhanced symmetry, then all such relationships are found, along with the resulting symmetry group. We discuss how the method can be applied to the standard model and beyond, to direct the search for a more predictive field theory. The method handles compact and non-compact continuous groups, spontaneously broken symmetries, and is also applicable to general relativity.