Lecture Notes on Symmetry Reduction via the Dressing Field Method

TL;DR

This paper introduces the Dressing Field Method as a systematic approach for symmetry reduction in general-relativistic gauge theories, enabling extraction of gauge-invariant physical observables with diverse illustrative examples.

Contribution

It presents the Dressing Field Method as a novel systematic framework for symmetry reduction in gRGFT, with applications across various gauge and gravitational theories.

Findings

Provides a systematic approach for extracting gauge-invariant observables.

Demonstrates the method with examples from gauge theories and general relativity.

Shows the versatility of the Dressing Field Method across different models.

Abstract

These notes - prepared for the conference school "Foundations of General-Relativistic Gauge Field Theory", held on March 17-19, 2026 at the Politecnico di Torino - present introductory material on symmetry reduction in general-relativistic Gauge Field Theory (gRGFT) via the Dressing Field Method (DFM). The DFM provides a systematic framework for extracting gauge- and diffeomorphism-invariant, manifestly relational, physical observables and degrees of freedom in gRGFT. A range of illustrative examples are discussed, spanning both Gauge Field Theory and general-relativistic settings. These include applications to non-Abelian Chern-Simons theory, Maxwell electromagnetism, the non-Abelian Higgs model, supersymmetric field theory, General Relativity, and scalar coordinatization.