Unit Invariance as a Unifying Principle of Physics

TL;DR

This paper explores the principle of unit invariance as a fundamental symmetry in physics, unifying various theories through Weyl invariance, a gauge field called the scale, and tractor calculus from conformal geometry.

Contribution

It introduces a unifying framework based on unit invariance and Weyl invariance, deriving new conformally invariant theories and unifying massless and massive excitations.

Findings

Unified massless, massive, and partially massless fields.

Derived stability bounds in anti de Sitter spaces.

Constructed new Weyl invariant theories using tractor calculus.

Abstract

A basic principle of physics is the freedom to locally choose any unit system when describing physical quantities. Its implementation amounts to treating Weyl invariance as a fundamental symmetry of all physical theories. In this thesis, we study the consequences of this "unit invariance" principle and find that it is a unifying one. Unit invariance is achieved by introducing a gauge field called the scale, designed to measure how unit systems vary from point to point. In fact, by a uniform and simple Weyl invariant coupling of scale and matter fields, we unify massless, massive, and partially massless excitations. As a consequence, masses now dictate the response of physical quantities to changes of scale. This response is calibrated by certain "tractor Weyl weights". Reality of these weights yield Breitenlohner-Freedman stability bounds in anti de Sitter spaces. Another valuable outcome of our approach is a general mechanism for constructing conformally invariant theories. In particular, we provide direct derivations of the novel Weyl invariant Deser--Nepomechie vector and spin three-half theories as well as new higher spin generalizations thereof. To construct these theories, a "tractor calculus" coming from conformal geometry is employed, which keeps manifest Weyl invariance at all stages. In fact, our approach replaces the usual Riemannian geometry description of physics with a conformal geometry one. Within the same framework, we also give a description of fermionic and interacting supersymmetric theories which again unifies massless and massive excitations.