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Henrique Gomes

Publications and source records attributed to Henrique Gomes.

At least 19 recordsLinked to original sources
arXiv2026

Ghosts that Connect

The Faddeev--Popov procedure poses two conceptual puzzles. \emph{Puzzle~(1)}: if gauge-equivalent configurations represent the same physics, the quotient $\F/\G$ should suffice to compute physical amplitudes --- yet the procedure requires anti-commuting auxiliary fields, the ghosts, with no analogue on the quotient. What structure of $\F$ do they encode? \emph{Puzzle~(2)}: gauge-fixing was supposed to eliminate local gauge symmetry, yet the gauge-fixed theory retains BRST --- a residual symmetry that acts on the gauge potential as an infinitesimal gauge transformation. Why does it survive? Both puzzles dissolve together. Following \textcite{Dougherty2021} and \textcite{DoughertyRead2026}, I take ghosts to encode classical content of $\F \to \F/\G$, but identify a different structure: a principal connection $\varpi$ on this bundle. The ghost is $\varpi$; the BRST operator is the vertical exterior derivative on field space; the Maurer--Cartan equation is its vertical Cartan structure equation. The Faddeev--Popov calculus draws only on $\varpi$'s vertical content, which the algebraic reading also captures; $\varpi$'s horizontal content, on which the Vilkovisky--DeWitt programme rests, supplies the cross-orbit pairing that gauge-fixing, dressing-based quantisation, and counterfactual comparison require and the quotient discards. BRST is the rigid, vertical symmetry that preserves this pairing; this is why it survives gauge-fixing.

physics.hist-ph↗
arXiv2026

The geometry-first formulation of gauge theory is not equivalent to the symmetry-first one

This paper argues that the geometry-first and symmetry-first formulations of gauge theory are not equivalent. They differ in three respects. First, the geometry-first formulation---in which gauge groups arise as automorphism groups of structured fundamental vector bundles---admits fewer theories when its generating structures are restricted to finite tensorial data. Charged theories with additive structure group $\mathbb{R}$ have no such presentation. Second, even when a symmetry-first theory has a geometry-first presentation, its principal bundle and matter bundles do not determine which structured vector bundles generated the gauge group. Third, the natural functor from geometry-first generating objects to principal bundles with matter is faithful but neither essentially surjective nor full. Essential surjectivity fails for the diagonal quotient of the Standard Model gauge group on what I call `the classical menu', and for the additive-$\mathbb{R}$ examples on every finite tensorial menu. Fullness fails for a real oriented fibre $\mathbb{R}^{2m}$: the principal-bundle category admits the outer automorphism of $SO(2m)$ induced by an improper orthogonal map, but no structure-preserving fibre map induces it.

physics.hist-ph↗
arXiv2026

Boomeranging through the Earth: when free fall doesn't maximize proper time

In teaching special relativity, John Bell emphasised the value of pre-relativistic intuitions. His famous spaceship puzzle showed that, in certain cases, the older heuristics of Lorentz and FitzGerald get the right answer to a genuinely relativistic problem more reliably than the principles of special relativity themselves. In teaching general relativity, John Wheeler emphasised the value of simplicity, illustrating curved-spacetime geometry with capsules boomeranging through a tunnel along the Earth's diameter. Here I put the two ideas together. I share a simple thought experiment, involving genuinely general-relativistic effects, in which the standard GR heuristic -- ``freely falling observers maximise proper time'' -- gives the wrong answer, while the older heuristic of velocity and gravitational time dilation, applied in a single frame, gets it right immediately. The resolution involves conjugate points and the distinction between local and global extremality of geodesics, but the moral is the same as Bell's: do not let a newer slogan overwrite a perfectly sound older intuition.

physics.gen-ph↗
arXiv2026

Making Symmetry Explicit: The Limits of Sophistication

Symmetry is often treated in philosophy of physics as an interpretive problem. A particularly lively dispute concerns local symmetries: do they indicate surplus structure that ought to be expunged, or are they merely a harmless redundancy? One influential response favours the second option for certain theories -- those dubbed internally sophisticated. And indeed, in much of physics practice, local symmetries are left implicit: one simply works "up to isomorphism'' without pausing over invariance. But not always. In some settings, local symmetry and invariance become pressing practical concerns for physicists. Yet philosophical discussions of sophistication have paid little sustained attention to when, and why, this happens. Surveying textbook general relativity (GR) and gauge theory, I identify the settings in which diffeomorphism invariance or gauge invariance must be handled explicitly. (Here a setting is a choice of representational framework or background assumptions within which one formulates and uses the theory -- for instance, linearisation, an initial-value formulation, or a Hamiltonian $3+1$ formalism.) I propose an operational criterion -- background-relative sophistication (BRS) -- and argue that it accounts well for the pattern: it marks just where symmetry can stay implicit and where it must be made explicit. Quantum and subsystem settings raise a further difficulty: there, certain tasks (superposition and gluing) force symmetry into view even for theories that are BRS.

physics.hist-ph↗
arXiv2025

Charge quantisation without compactness: the Higgs and Yukawa mechanisms from matter geometry

In the \emph{geometry-first} formulation of gauge theory \citep{Gomes_internal}, Hermitian vector bundles and their covariant derivatives are the primitive objects. Here gauge groups arise only as the automorphism groups of a small set of structured fundamental fibres, and every matter field is a section of a tensor product of the fundamental bundles. This is a constraint on gauge theories. In the abelian sector it enforces charge quantisation, even without compactness: charges count tensor powers of a fundamental line bundle, so they lie on an integral lattice even when the automorphism group is the non-compact $\mathbb{C}^\times$, whereas a symmetry-first theory built on $\mathbb{R}$ admits irrationally related charges. The Standard Model satisfies the constraint, and its two mass-generating mechanisms follow from the fibre geometry. The Higgs mechanism arises from the second fundamental form of the sub-bundle singled out by the Higgs vacuum. This works with no appeal to symmetry breaking or Goldstone's theorem, and the full electroweak spectrum, $m_W=m_Z\cos\theta_W$ included, is computed from the same operator. Each Yukawa coupling is the canonical fibrewise contraction fixed by the inner products and volume forms of the fundamental bundles. Exceptional gauge groups remain formally presentable, but on progressively less elementary fibre structure; at $E_8$ the fundamental fibre is the Lie algebra $\mathfrak{e}_8$ itself, and the claim of conceptual priority collapses. A companion paper shows the two formulations are not equivalent, in a categorical sense \citep{Gomes_nonequiv}.

physics.hist-ph↗
arXiv2025

The Aharonov-Bohm effect: reality and folklore

The Aharonov-Bohm (A-B) effect has been a major focus of the foundations of physics. And yet, much confusion persists. In particular, the effect purportedly leads to a dilemma: on one horn, we have a non-local action of a gauge-invariant quantity on charged particles; on the other, we get a local action on these particles, but of a non-gauge invariant quantity. This is the folklore, but the folklore is filled with misconceptions. Here, by deploying a recently defended formulation of gauge theory that dispenses with principal bundles, gauge potentials, and explicit gauge symmetries, I argue, with previous authors, that the A-B effect can be understood gauge-independently. But here my argument will go further: I will show that the A-B effect, when expressed in terms of the covariant derivative of a vector bundle, is \emph{entirely} analogous to the holonomy of spacetime vectors, and can be understood completely locally. The only surprising idea illustrated by the A-B effect is that, in some circumstances, there is more to the covariant derivative than can be accounted for by the curvature and underlying topology of a vector bundle.

physics.hist-ph↗
arXiv2025

Identification is Pointless: Quantum Coordinates, Localisation of Events, and the Quantum Hole Argument

The study of quantum reference frames (QRFs) is motivated by the idea of taking into account the quantum properties of the reference frames used, explicitly or implicitly, in our description of physical systems. Like classical reference frames, QRFs can be used to define physical quantities relationally. Unlike their classical analogue, they relativise the notions of superposition and entanglement. Here, we explain this feature by examining how configurations or locations are identified across different branches in superposition. We show that, in the presence of symmetries, whether a system is in "the same" or "different" configurations across the branches depends on the choice of QRF. Hence, sameness and difference -- and thus superposition and entanglement -- lose their absolute meaning. We apply these ideas to the context of semi-classical spacetimes in superposition and use coincidences of four scalar fields to construct a comparison map between spacetime points in the different branches. This reveals that the localisation of an event is frame-dependent. We discuss the implications for indefinite causal order and the locality of interaction and conclude with a generalisation of Einstein's hole argument to the quantum context.

quant-ph↗
arXiv2025

Boundaries, frames and the issue of physical covariance

We focus on three distinct lines of recent developments: edge modes and boundary charges in gravitational physics, relational dynamics in classical and quantum gravity, and quantum reference frames. We argue that these research directions are in fact linked in multiple ways, and can be seen as different aspects of the same research programme. This research programme has two main physical goals and one general focus, as well as broader conceptual implications. The physical goals are to move beyond the two idealizations/approximations of asymptotic or closed boundary conditions in gravitational physics and of ideal reference frames (coded in coordinate frames or gauge fixings), thus achieving a more realistic modelling of (quantum) gravitational physical phenomena. These two goals combine to identify a key open issue: a proper characterization of physical covariance, i.e. covariance across fully physical (as opposed to idealized) reference frames. The broader conceptual implications concern the influence of observers in physics and possible physical limits to objectivity.

physics.hist-ph↗
arXiv2024

The Hole Argument for Reference Frames

We exploit the results of Bamonti and Gomes (2024) concerning the dynamical (un)coupling of reference frames to gravity to analyse the role of reference frames in the Hole Argument. We introduce a new possible threat to determinism, which we call Arbitrariness Problem (ARB), resulting from the inherent freedom in selecting a reference frame.

physics.hist-ph↗
arXiv2024

What Reference Frames Teach Us. Part I: About Symmetry Principles and Observability

This paper is an exploration of the nuanced realm of reference frames within the framework of General Relativity. Our analysis exposes a violation of Earman's SP1 principle in scenarios involving fields that are dynamically uncoupled, a common assumption for reference frames. Unlike other violations, we cannot foreclose it by eliminating background spacetime structure. Our analysis also leads us to challenge the conventional notion of partial observables as quantities that are associated with a measuring instrument and expressed within a coordinate system. Instead, we argue that a partial observable is inherently relational, even if gauge-variant, and needs dynamical coupling with other partial observables to form a bona-fide, gauge-invariant complete observables. This perspective allows us to distinguish between being relational and being gauge-invariant, two properties that are often conflated.

physics.hist-ph↗
arXiv2024

Representational conventions and invariant structure

In the philosophical literature, symmetries of physical theories are most often interpreted within the general doctrine called 'Sophistication'. Roughly speaking, it says that models related by symmetries can peacefully co-exist while representing the same physical possibility. But this interpretation still leaves open two main worries about Sophistication: (a) it allows the individuation of what I call 'structure-tokens' to remain intractable and thus of limited use, which is why practising physicists frequently invoke 'relational, symmetry-invariant observables'; and (b) it leaves us with no formal framework for expressing counterfactual statements about the world. Here, I will show that a new Desideratum to be satisfied by theories with symmetries answers these worries. The new Desideratum is that the theory admits what I will call representational conventions for its structure-tokens.

physics.hist-ph↗
arXiv2024

Gauge theory is about the geometry of internal spaces

In general relativity, the strong equivalence principle is underpinned by a geometrical interpretation of fields on spacetime: all fields and bodies probe the same geometry. This geometric interpretation implies that the parallel transport of all spacetime tensors and spinors is dictated by a single affine connection. Can something similar be said about gauge theory? Agreed, in gauge theory different symmetry groups rule the interactions of different types of charges, so we cannot expect to find the same kind of universality found in the gravitational case. Nonetheless, the parallel transport of all the fields that are charged under the same symmetry group is dictated by a single 'gauge connection', and they all transform jointly under a gauge transformation. Is this kind of 'restricted universality' as geometrically underpinned as in general relativity? Here I argue that it is. The key difference is that the gauge geometry concerns 'internal', as opposed to 'external', spaces. The gauge symmetry of the standard model is thus understood as merely the automorphism group of an internal geometric structure -- $C^3\otimes C^2\otimes C^1$ endowed with an orientation and canonical inner product -- in the same way as spacetime symmetries (such as Poincare transformations), are understood as the automorphism group of an external geometric structure (respectively, a Minkowski metric). And the Ehresmann connection can then be understood as determining parallelism for this internal geometry.

hep-th↗
arXiv2024

The hole argument meets Noether's theorem

The hole argument of general relativity threatens a radical and pernicious form of indeterminism. One natural response to the argument is that points belonging to different but isometric models should always be identified, or 'dragged-along', by the diffeomorphism that relates them. In this paper, I first criticise this response and its construal of isometry: it stumbles on certain cases, like Noether's second theorem. Then I go on to describe how the essential features of Einstein\rq{}s `point-coincidence' response to the hole argument avoid the criticisms of the `drag-along response' and are compatible with Noether's second theorem.

physics.hist-ph↗
arXiv2023

The Hole Argument and Beyond, Part I: The Story so Far

In this two-part paper, we review, and then develop, the assessment of the hole argument for general relativity. This first Part reviews the literature hitherto, focussing on the philosophical aspects. It also introduces two main ideas we will need in Part II: which will propose a framework for making comparisons of non-isomorphic spacetimes. In Section 1 of this paper, we recall Einstein's original argument. Section 2 recalls the argument's revival by philosophers in the 1980s and 1990s. This includes the first main idea we will need in Part II: namely, that two spacetime points in different possible situations are never strictly identical -- they are merely counterparts. In Section 3, we report -- and rebut -- more recent claims to "dissolve" the argument. Our rebuttal is based on the fact that in differential geometry, and its applications in physics such as general relativity, points are in some cases identified, or correspond with each other, between one context and another, by means other than isometry (or isomorphism). We call such a correspondence a threading of points. This is the second main idea we shall use in Part II.

physics.hist-ph↗
arXiv2023

The Hole Argument and Beyond, Part II: Treating Non-isomorphic Spacetimes

In this two-part paper we review, and then develop, the assessment of the hole argument for general relativity. The review (in Part I) discussed how to compare points in isomorphic spacetimes, i.e. models of the theory. This second Part proposes a framework for making comparisons of {\em non}-isomorphic spacetimes. It combines two ideas we discussed in Part I -- the philosophical idea of counterparts, and the idea of threading points between spacetimes other than by isomorphism -- with the mathematics of fibre bundles. We first recall the ideas from Part I (Section 1). Then in Section 2 and an Appendix, we define a fibre bundle whose fibres are isomorphic copies of a given spacetime or model, and discuss connections on this fibre bundle. This material proceeds on analogy with field-space formulations of gauge theories. Finally, in Section 3, we show how this fibre bundle gives natural expressions of the philosophical ideas of counterparts, and of threading.

physics.hist-ph↗
arXiv2023

On the analogies between gravitational and electromagnetic radiative energy

We give a conceptual exposition of aspects of gravitational radiation, especially in relation to energy. Our motive for doing so is that the strong analogies with electromagnetic radiation seem not to be widely enough appreciated. In particular, we reply to some recent papers in the philosophy of physics literature that seem to deny that gravitational waves carry energy. Our argument is based on two points: (i) that for both electromagnetism and gravity, in the presence of material sources, radiation is an effective concept, unambiguously emerging only in certain regimes or solutions of the theory; and (ii) similarly, energy conservation is only unambiguous in certain regimes or solutions of general relativity. Crucially, the domain of (i), in which radiation is meaningful, has a significant overlap with the domain of (ii), in which energy conservation is meaningful. Conceptually, the overlap of regimes is no coincidence: the long-standing question about the existence of gravitational waves was settled precisely by finding a consistent way to articulate their energy and momentum.

physics.hist-ph↗
arXiv2022

Same-diff? Conceptual similarities between gauge transformations and diffeomorphisms. Part I: Symmetries and isomorphisms

The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: how are gauge transformations and spacetime diffeomorphisms understood as symmetries, in which ways are they similar, and in which are they different? To what extent are we justified in endorsing different attitudes -- nowadays called sophistication, haecceitism, and eliminativism -- towards each? This is the first of four papers taking up this question. This first paper will discuss notions of symmetries and isomorphisms that will be used in the remaining papers in the series. There are several such notions in the literature and the question of how they mesh with empirical discernibility is a delicate one; even the orthodox view that symmetries are empirically unobservable (even in principle) has recently been challenged by Belot. Focusing on local field theories, I will provide a precise definition of dynamical symmetries in terms of the space of states of the theory at hand. I will then apply the definition to Yang-Mills theories and general relativity and show that these symmetries correspond to automorphisms of `natural' geometric structures: the small diffeomorphisms of the spacetime manifold and the small fiber-preserving diffeomorphisms of a fibered space. Finally, I will show that these automorphisms can be given a passive gloss, since they correspond 1-1 to the coordinate transformations of the underlying manifolds.

physics.hist-ph↗