arXiv subjects

J. François

Publications and source records attributed to J. François.

13 recordsLinked to original sources

arXiv2026

Mechanics as a general-relativistic gauge field theory, and Relational Quantization

We treat the Mechanics of point particles as a 1-dimensional general-relativistic gauge field theory, which may be referred to as Mechanical Field Theory (MFT), exploiting the bundle geometry of Mechanical Field Space (MFS). The diffeomorphism covariance of MFT encodes its relational character, arising - as in all general-relativistic physics - via the conjunction of a hole and a point-coincidence argument. Any putative "boundary problem", meaning the claim that 'spacetime' boundaries break diffeomorphism and gauge symmetries, thereby dissolves. It is highlighted that the standard path integral (PI) on the MFS, the exact analogue of the PI used in gauge field theory, is conceptually and technically distinct from the standard PI of Quantum Mechanics. We then use the Dressing Field Method to give a manifestly invariant and relational reformulation of MFT, which reproduces the standard textbook formulation when a clock field is chosen as a (natural) dressing field. The dressed, or basic, PI on the MFS, defining Relational Quantization - i.e. the quantization of invariant relational d.o.f. - is shown to reproduce the standard PI of Quantum Mechanics. This establishes the soundness of Relational Quantization as a general guiding principle: We outline it for general-relativistic gauge field theories.

physics.gen-ph↗

arXiv2026

Toward Manifest Relationality in Transformers via Symmetry Reduction

Transformer models contain substantial internal redundancy arising from coordinate-dependent representations and continuous symmetries, in model space and in head space, respectively. While recent approaches address this by explicitly breaking symmetry, we propose a complementary framework based on symmetry reduction. We reformulate representations, attention mechanisms, and optimization dynamics in terms of invariant relational quantities, eliminating redundant degrees of freedom by construction. This perspective yields architectures that operate directly on relational structures, providing a principled geometric framework for reducing parameter redundancy and analyzing optimization.

cs.LG↗

arXiv2026

Reassessing the foundations of Metric-Affine Gravity

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 translations". We first recall that Cartan geometry is the proper mathematical foundation for gauge theories of gravity, and that this problem never arises in that framework, which still allows to clarify the geometric status of gauge translations. Then, we show how the MAG kinematics is obtained via dressing in a technically streamlined way, which highlights that it reduces to a Cartan-geometric kinematics.

gr-qc↗

arXiv2026

Invariant Path-Integral Quantization and Anomaly Cancellation

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 encompasses Bardeen-Wess-Zumino counterterms. The resulting framework unifies invariant schemes across contexts ranging from electroweak theory to cosmology, and is amenable to lattice implementations, key to high-precision tests in both domains.

hep-th↗

arXiv2026

Relational bundle geometric formulation of non-relativistic quantum mechanics

We present a bundle geometric formulation of non-relativistic many-particles Quantum Mechanics. A wave function is seen to be a $\mathbb{C}$-valued cocyclic tensorial 0-form on configuration space-time seen as a principal bundle, while the Schrödinger equation flows from its covariant derivative, with the action functional supplying a (flat) cocyclic connection 1-form on the configuration bundle. In line with the historical motivations of Dirac and Feynman, ours is thus a Lagrangian geometric formulation of QM, in which the Dirac-Feynman path integral arises in a geometrically natural way. Applying the dressing field method, we obtain a relational reformulation of this geometric non-relativistic QM: a relational wave function is realised as a basic cocyclic 0-form on the configuration bundle. In this relational QM, any particle position can be used as a dressing field, i.e. as a "physical reference frame". The dressing field method naturally accounts for the freedom in choosing the dressing field, which is readily understood as a covariance of the relational formulation under changes of physical reference frame.

quant-ph↗

arXiv2025

Spacetime boundaries do not break diffeomorphism and gauge symmetries

In General Relativity and gauge field theory, one often encounters a claim, which may be called the boundary problem, according to which "boundaries break diffeomorphism and gauge symmetries". We argue that this statement has the same conceptual structure as the hole argument, and is thus likewise defused by the point-coincidence argument: We show that the boundary problem dissolves once it is understood that a physical region, thus its boundary, is relationally and invariantly defined. This insight can be technically implemented via the Dressing Field Method, a systematic tool to exhibit the gauge-invariant content of general-relativistic gauge field theories, whereby physical field-theoretical degrees of freedom co-define each other and define, coordinatize, the physical spacetime. We illustrate our claim with a simple application to the case of General Relativity.

gr-qc↗

arXiv2025

Raising galaxy rotation curves via dressing

We present a manifestly diffeomorphism-invariant simple model of galaxy dynamics obtained by applying the Dressing Field Method (DFM) to a general-relativistic system comprising the metric and four scalar fields, phenomenologically representing the four-velocity of a cosmological fluid or dust field. The DFM, a systematic tool for extracting the gauge-invariant content in general-relativistic theories, provides a physical coordinatization that yields corrective terms to the rotational velocity profile. These corrections produce galaxy rotation curves that combine a Keplerian and a constant velocity terms, effectively emulating a Dark Matter contribution. We compare DFM-derived rotation curves to observed data for spiral galaxies, from the Spitzer Photometry and Accurate Rotation Curves (SPARC) database, showing that the DFM allows to fit them well.

gr-qc↗

arXiv2025

Off-shell supersymmetry via manifest invariance

A fundamental challenge in supersymmetric field theory is that supersymmetry transformations on field variables generally form an algebra only on-shell, i.e. upon imposing the field equations. We show that this issue is defused in a manifestly relational - and thus automatically invariant - formulation of supersymmetric field theory, achieved through the application of the Dressing Field Method of symmetry reduction, a systematic tool to exhibit the gauge-invariant content of general-relativistic gauge field theories.

hep-th↗

arXiv2025

Unconventional Supersymmetry via the Dressing Field Method

We re-construe unconventional supersymmetry, a notion introduced by Alvarez-Valenzuela-Zanelli (AVZ), as an attempt to use the framework of supersymmetric field theory to describe fermionic matter fields and bosonic gauge fields in a unified way, as parts of a single superconnection. It hinges upon the so-called matter ansatz. Unfortunately, the formal and conceptual status of the ansatz has remained unclear, preventing unconventional supersymmetry to be used in a principled way as a general approach beyond the model in which it was first considered. In this letter, we lift this restriction by showing that the ansatz is a special case of the Dressing Field Method, a new systematic tool to exhibit the gauge-invariant content of general-relativistic gauge field theories.

hep-th↗

arXiv2025

Relational Supersymmetry via the Dressing Field Method and Matter-Interaction Supergeometric Framework

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 physical degrees of freedom representing relations among field variables. We review and further expand on some applications of the DFM to the very foundations of the supersymmetric framework, where it allows to build relational supersymmetric field theory and (dis)solves crucial issues. Furthermore, we elaborate on a novel approach within the relational supersymmetric field theory framework giving a unified description of fermionic matter fields and bosonic gauge fields, and thus close to Berezin's original motivation for the introduction of supergeometry in fundamental physics: a Matter-Interaction Supergeometric Unification (MISU). This new approach stands irrespective from the ultimate empirical status of standard supersymmetric field theory, about which it is agnostic.

hep-th↗

arXiv2024

Dressing fields for supersymmetry: The cases of the Rarita-Schwinger and gravitino fields

In this paper we argue that the gauge-fixing conditions typically used to extract the (off-shell) degrees of freedom of the Rarita-Schwinger spinor-vector and gravitino, respectively in rigid supersymmetric field theory and supergravity, are actually instances of the dressing field method of symmetry reduction. Since the latter has a natural relation interpretation, solving the ``gauge-fixing condition" -- or, better, ``dressing functional constraints" -- actually realises the Rarita-Schwinger spinor-vector and the gravitino fields as (non-local) relational variables. To the best of our knowledge, this is the first application of the dressing field method to supersymmetric theories.

hep-th↗

arXiv2024

Cartan geometry, supergravity, and group manifold approach

We make a case for the unique relevance of Cartan geometry for gauge theories of gravity and supergravity. We introduce our discussion by recapitulating historical threads, providing motivations. In a first part we review the geometry of classical gauge theory, as a background for understanding gauge theories of gravity in terms of Cartan geometry. The second part introduces the basics of the group manifold approach to supergravity, hinting at the deep rooted connections to Cartan supergeometry. The contribution is intended, not as an extensive review, but as a conceptual overview, and hopefully a bridge between communities in physics and mathematics.

math-ph↗

arXiv2017

The dressing field method of gauge symmetry reduction, a review with examples

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 met by essentially finding a way to effectively reduce gauge symmetries. We propose a review of a way to do so which we call the dressing field method. We show how the BRST algebra satisfied by gauge fields, encoding their gauge transformations, is modified. We outline noticeable applications of the method, such as the electroweak sector of the Standard Model and the local twistors of Penrose.

math-ph↗