Related papers: Gauge Fixing in QFT and the Dressing Field Method
There is solid consensus among physicists and philosophers that, in gauge field theory, for a quantity to be physically meaningful or real, it must be gauge-invariant. Yet, every "elementary" field in the Standard Model of particle physics…
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…
Relationality is the paradigmatic conceptual core of general-relativistic gauge field theory. It can be made manifest via the Dressing Field Method (DFM) of symmetry reduction, a systematic tool to achieve gauge-invariance by extracting the…
We describe a method to implement finite group global and gauged $q$-form symmetries into the axiomatic structure of $d$-dimensional Topological Quantum Field Theory (TQFT) in terms of bordisms decorated by cohomology classes. Namely, on a…
We reinterpret the Faddeev-Popov gauge-fixing procedure of Yang-Mills theories as the definition of a topological quantum field theory for gauge group elements depending on a background connection. This has the advantage of relating…
We treat Mechanics as a 1-dimensional general-relativistic gauge field theory, Mechanical Field Theory (MFT), introducing what we call the Mechanical Field Space (MFS) and exploiting its bundle geometry. The diffeomorphism covariance of MFT…
We analyze how gauge fixing, which is required by any practical continuum approach to gauge systems, can interfere with the physical symmetries of such systems. In principle, the gauge fixing procedure, which deals with the (unphysical)…
We discuss the problem of gauge fixing for the partition function in generalized quantum (or trace) dynamics, deriving analogs of the De Witt-Faddeev-Popov procedure and of the BRST invariance familiar in the functional integral context.
The unitary gauge fixing technique is applied to the QCD hamiltonian formulated in terms of angular variables. It is demonstrated that in this formulation projections on the physical Hilbert space are unnecessary to separate physical and…
We reassess foundational aspects of Metric-Affine Gravity (MAG) in light of the Dressing Field Method, a tool allowing to systematically build gauge-invariant field variables. To get MAG started, one has to deal with the problem of "gauge…
Gauge symmetries are a cornerstone of modern physics but they come with technical difficulties when it comes to quantization, to accurately describe particles phenomenology or to extract observables in general. These shortcomings must be…
We gauge fix the Standard Model Effective Field Theory in a manner invariant under background field gauge transformations using a geometric description of the field connections.
We review a recently proposed SuperGeometric (SG) approach to Quantum Field Theories (QFTs) that allow for scalar-fermion field transformations in a manifestly reparameterisation covariant manner. By adopting natural choices for the…
The dressing field method is a tool to reduce gauge symmetries. Here we extend it to cover the case of diffeomorphisms. The resulting framework is a systematic scheme to produce Diff(M)-invariant objects, which has a natural relational…
We examine the incorporation of gauge symmetries in the modern effective field theory (EFT) matching paradigm with a particular focus on spontaneously broken symmetries. The presence of gauge symmetries entails the introduction of…
We consider the covariant gauge field theory of fractons, which describe a new type of quasiparticles exhibiting novel and nontrivial properties. In particular, we focus on the field theoretical peculiarities which characterize this theory,…
We present an invariant relational path-integral quantization framework for general-relativistic gauge field theories based on the Dressing Field Method. The construction implements an automatic anomaly-cancellation mechanism that…
Quantum simulation of synthetic dynamic gauge field has attracted much attentions in recent years. There are two traditional ways to simulate gauge theories. One is to directly simulate the full Hamiltonian of gauge theories with local…
In the absence of Gribov complications, the modified gauge fixing in gauge theory $ \int{\cal D}A_{\mu}\{\exp[-S_{YM}(A_{\mu})-\int f(A_{\mu})dx] /\int{\cal D}g\exp[-\int f(A_{\mu}^{g})dx]\}$ for example, $f(A_{\mu})=(1/2)(A_{\mu})^{2}$, is…
We study a slight variation of the unimodular gauge condition which we call "the derivative gauge condition". We show that at the classical level these conditions are completely equivalent up to a surface term. At the quantum level the…