arXiv subjects

Jan Govaerts

Publications and source records attributed to Jan Govaerts.

At least 19 recordsLinked to original sources

arXiv2026

Light deflection in the gravimagnetic dipole spacetime

The gravimagnetic dipole is an asymptotically flat, stationary, axisymmetric vacuum solution to Einstein's General Relativity describing two non-extreme black holes with equal masses and opposite NUT charges connected by a Misner string. The string tension's can be set to zero by choosing the black hole separation accordingly, yielding a stable system of oppositely rotating black holes at a fixed distance. Numerical simulations of massless particle geodesics reveal gravitational lensing effects for extended sources at infinity on the equatorial plane or on the vertical axis.

gr-qc↗

arXiv2025

Velocity rotation curves in the gravimagnetic dipole spacetime

The gravimagnetic dipole spacetime consists of two counter-rotating black holes of equal mass connected by a Misner string. For a particular distance in between them, the string is tensionless with the black holes at equilibrium with each other. The geodesics of relativistic massive, or massless particles are considered, leading to the identification of circular rotation trajectories. The velocities of these trajectories are computed.

gr-qc↗

arXiv2024

Newtonian Gravity and Galaxy Rotation Curves: An Axisymmetric Green's Function Perspective

The standard proposal within the context of General relativity and its weak field Newtonian limit for the nature of dark matter is that it consists of dark matter particles of unknown type. In the present work and specifically for spiral galaxy rotation curves, an alternative possibility is explored, in the form of an axially symmetric vortex mass distribution of finite extent threading the centre of the galaxy and perpendicular to its disk. Some general considerations are developed and characteristic properties are identified, pointing to the potential interest of such an alternative to be studied in earnest.

gr-qc↗

arXiv2024

Noncommutativity in Configuration Space Induced by A Conjugate Magnetic Field in Phase Space

As is well known, an external magnetic field in configuration space coupled to a quantum dynamics induces noncommutativity in its velocity momentum space. By phase space duality, an external vector potential in the conjugate momentum sector of the system induces noncommutativity in its configuration space. Such a rationale for noncommutativity is explored herein for an arbitrary configuration space of Euclidean geometry. Ordinary quantum mechanics with a commutative configuration space is revisited first. Through the introduction of an arbitrary positive definite $*$-product, a one-to-one correspondence between the Hilbert space of abstract quantum states and that of the enveloping algebra of the position quantum operators is identified. A parallel discussion is then presented when configuration space is noncommutative, and thoroughly analysed when the conjugate magnetic field is momentum independent and nondegenerate. Once again the space of quantum states may be identified with the enveloping algebra of the noncommutative position quantum operators. Furthermore when the positive definite $*$-product is chosen in accordance with the value of the conjugate magnetic field which determines the commutator algebra of the coordinate operators, these operators span a Fock algebra of which the canonical coherent states are the localised noncommutative quantum analogues of the sharp and structureless local points of the associated commutative configuration space geometry. These results generalise and justify a posteriori within the context of ordinary canonical quantisation the heuristic approach to quantum mechanics in the noncommutative Euclidean plane as constructed and developed by F. G. Scholtz and his collaborators.

quant-ph↗

arXiv2023

External gauge field coupled quantum dynamics: gauge choices, Heisenberg algebra representations and gauge invariance in general, and the Landau problem in particular

Even though its classical equations of motion are then left invariant, when an action is redefined by an additive total derivative or divergence term (in time, in the case of a mechanical system) such a transformation induces nontrivial consequences for the system's canonical phase space formulation. This is even more true and then in more subtle ways for the canonically quantised dynamics, with in particular an induced transformation in the unitary configuration space representation of the Heisenberg algebra being used for the quantum system. When coupled to a background gauge field, such considerations become crucial for a proper understanding of the consequences for the system's quantum dynamics of gauge transformations of that classical external background gauge field, while under such transformations the system's degrees of freedom, abstract quantum states and quantum dynamics are certainly strictly invariant. After a detailed analysis of these different points in a general context, these are then illustrated specifically in the case of the quantum Landau problem with its classical external background magnetic vector potential for which the most general possible parametrised gauge choice is implemented herein. The latter discussion aims as well to clarify some perplexing statements in the literature regarding the status of gauge choices to be made for the magnetic vector potential for that quantum system. The role of the global space-time symmetries of the Landau problem and their gauge invariant Noether charges is then also emphasized.

quant-ph↗

arXiv2023

The Gravito-Electromagnetic Approximation to the Gravimagnetic Dipole and its Velocity Rotation Curve

In view of the observed flat rotation curves of spiral galaxies and motivated by the simple fact that within newtonian gravity a stationary axisymmetric mass distribution or dark matter vortex of finite extent readily displays a somewhat flattened out velocity rotation curve up to distances comparable to the extent of such a vortex transverse to the galaxy's disk, the possibility that such a flattening out of rotation curves may rather be a manifestation of some stationary axisymmetric space-time curvature of purely gravitational character, without the need of some dark matter particles, is considered in the case of the gravimagnetic dipole carrying opposite NUT charges and in the tensionless limit of its Misner string, as an exact vacuum solution to Einstein's equations. Aiming for a first assessment of the potential of such a suggestion easier than a full fledged study of its geodesics, the situation is analysed within the limits of weak field gravito-electromagnetism and nonrelativistic dynamics. Thereby leading indeed to interesting and encouraging results.

gr-qc↗

arXiv2023

Magnetic Monopoles with No Strings Attached: A Portal to the Dark Side of Dual Electrodynamics

It has long been known that in the absence of electric charges and currents, Maxwell's electromagnetism in 4 dimensional vacuum Minkowski space-time is invariant under SO(2) dual transformations that mix its electric and magnetic fields. Extending this symmetry to include the coupling to electrically charged matter, requires a dual coupling to magnetically charged matter as well, leading to Maxwell equations for SO(2) dual electrodynamics. Based on a doubled ensemble of SO(2) dual 4-vector gauge potentials which does away with the need of Dirac string singularities for magnetic monopoles, a local Lagrangian action principle for SO(2) dual electromagnetism is known, which manifestly displays all the required space-time and internal symmetries, and reduces to the experimentally well established Maxwell electrodynamics in the absence of magnetic charges and currents. Applying the same considerations for the matter action of electrically and magnetically charged point particles, a unique SO(2) dual generalised Lorentz force is identified for SO(2) dual electrodynamics, truly different from the usual SO(2) dual invariant choice motivated by simplicity, but yet made arbitrarily and which does not derive from some action principle. This generalised Lorentz force involves a single real and new coupling constant of unknown value, without the requirement of a Dirac-Schwinger-Zwanziger quantisation condition for electric and magnetic charges of dyons. A physical consequence for SO(2) dual electrodynamics of this coupling constant if nonvanishing, is to open a channel, or portal between the otherwise mutually totally ``dark'' sectors of electric and magnetic charges for electromagnetic interactions.

hep-th↗

arXiv2021

Noether Symmetries, Dynamical Constants of Motion, and Spectrum Generating Algebras

When discussing consequences of symmetries of dynamical systems based on Noether's first theorem, most standard textbooks on classical or quantum mechanics present a conclusion stating that a global continuous Lie symmetry implies the existence of a time independent conserved Noether charge which is the generator of the action on phase space of that symmetry, and which necessarily must as well commute with the Hamiltonian. However this need not be so, nor does that statement do justice to the complete scope and reach of Noether's first theorem. Rather a much less restrictive statement applies, namely that the corresponding Noether charge as an observable over phase space may in fact possess an explicit time dependency, and yet define a constant of the motion by having a commutator with the Hamiltonian which is nonvanishing, thus indeed defining a dynamical conserved quantity. Furthermore, and this certainly within the Hamiltonian formulation, the converse statement is valid as well, namely that any dynamical constant of motion is necessarily the Noether charge of some symmetry leaving the system's action invariant up to some total time derivative contribution. The present contribution revisits these different points and their consequences, straightaway within the Hamiltonian formulation which is the most appropriate for such issues. Explicit illustrations are also provided through three general but simple enough classes of systems.

math-ph↗

arXiv2021

Deformed Hopfion-Rañada Knots in ModMax Electrodynamics

Source-free so-called ModMax theories of nonlinear electrodynamics in the four dimensional Minkowski spacetime vacuum are the only possible continuous deformations -- and as a function of a single real and positive parameter -- of source-free Maxwell linear electrodynamics in the same vacuum, which preserve all the same Poincaré and conformal spacetime symmetries as well as the continuous duality invariance of Maxwell's theory. Null field configurations of the latter however, including null electromagnetic knots, are singular for the Lagrangian formulation of any spacetime Poincaré and conformal invariant theory of nonlinear electrodynamics. In particular null hopfion-Rañada knots are a distinguished and fascinating class on their own of topologically nontrivial solutions to Maxwell's equations. This work addresses the fate of these configurations within ModMax theories. A doubled class of ModMax deformed hopfion-Rañada knots is thereby identified, each of which coalescing back in a continuous fashion to the original hopfion-Rañada knot when the nonlinear deformation parameter is turned off.

physics.gen-ph↗

arXiv2019

Time Dependent Conserved Charges and their Gauging -- A Modest Case Study in Shared Memory of Victor --

There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The generators of such symmetries certainly do not commute with the Hamiltonian, and yet these charges are conserved observables for the classical and quantised dynamics. Furthermore within the Hamiltonian formalism and in the case of global symmetries such charges may be gauged to allow for arbitrary time dependent symmetry transformations, simply by extending the Hamiltonian to include the Noether charges as first-class constraints. An explicit illustration of these issues is presented in a simple and most familiar model that applies also to the constant gravitational force. This note draws its primary motivation from the quest towards a theory for quantum gravity, in wanting to understand better the tension existing between the local Equivalence Principle of the gravitational interaction and the fundamental principles of Quantum Mechanics by considering the formulation of quantum systems relative to reference frames that are inertial or noninertial, and thus accelerated relative to one another through arbitrary time dependent spatial translations.

hep-th↗

arXiv2019

Non Local Global Symmetries of a Free Scalar Field in a Bounded Domain

BMS symmetries have been attracting a great deal of interest in recent years. Originally discovered as being the symmetries of asymptotically flat spacetime geometries at null infinity in General Relativity, BMS symmetries have also been shown to exist for free field theories over Minkowski spacetime. In wanting to better understand their status and the underlying reasons for their existence, this work proposes a general rationale towards identifying all possible global symmetries of a free field theory over Minkowski spacetime, by allowing the corresponding conserved generators not to be necessarily spatially local in phase space since fields and their conjugate momenta are intrinsically spatially non local physical entities. As a preliminary towards a separate study of the role of asymptotic states for BMS symmetries in an unbounded Minkowski spacetime, the present discussion focuses first onto a 2+1 dimensional free scalar field theory in a bounded spatial domain with the topology of a disk and an arbitrary radial Robin boundary condition. The complete set of global symmetries of that system, most of which are dynamical symmetries but include as well those generated by the local total energy and angular-momentum of the field, is thereby identified.

math-ph↗

arXiv2018

Mass Generation in Abelian U(1) Gauge Theories: A Rich Network of Dualities

Following a novel approach, all known basic mass generation mechanisms consistent with an exact abelian U(1) gauge symmetry are shown to be related through an intricate network of dualities whatever the spacetime dimension. This equivalence which applies in the absence of any supersymmetry, is however restricted by the presence of topological terms generating possible topological effects. In particular in 3+1 dimensions the duality relations between the Maxwell-Higgs model, the Stueckelberg and the topological mass generation mechanisms are then established following a careful treatment of the gauge symmetry content. This result offers a new framework for an effective description of superconductivity or topological defects built from fields beyond the SM.

hep-th↗

arXiv2018

Towards the Quantum Geometry of Saturated Quantum Uncertainty Relations: The Case of the (Q,P) Heisenberg Observables

This contribution to the present Workshop Proceedings outlines a general programme for identifying geometric structures--out of which to possibly recover quantum dynamics as well--associated to the manifold in Hilbert space of the quantum states that saturate the Schrödinger-Robertson uncertainty relation associated to a specific set of quantum observables which characterise a given quantum system and its dynamics. The first step in such an exploration is addressed herein in the case of the observables Q and P of the Heisenberg algebra for a single degree of freedom system. The corresponding saturating states are the well known general squeezed states, whose properties are reviewed and discussed in detail together with some original results, in preparation of a study deferred to a separated analysis of their quantum geometry and of the corresponding path integral representation over such states.

quant-ph↗

arXiv2014

Non-Perturbative Dynamics, Pair Condensation, Confinement and Dynamical Masses in Massless QED2+1

Quantum electrodynamics in three spacetime dimensions, with one massless fermion species, is studied using a non-perturbative variational approach. Quantization of the theory follows Dirac's Hamiltonian procedure, with a gauge invariant factorization of the physical degrees of freedom. Due to pair condensation in the vacuum state, the symmetry of parity is spontaneously broken. As a consequence, fermionic quasi-particles propagating in the condensate can be identified and are seen to possess a confining dynamical mass, while the propagating physical electromagnetic mode also acquires a non-vanishing dynamical mass. The issues of gauge invariance and confinement of the constituent fermions are carefully discussed.

hep-th↗

arXiv2014

The N = 1 Supersymmetric Wong Equations and the Non-Abelian Landau Problem

A Lagrangian formulation is given extending to N = 1 supersymmetry the motion of a charged point particle with spin in a non-abelian external field. The classical formulation is constructed for any external static non-abelian SU(N) gauge potential. As an illustration, a specific gauge is fixed enabling canonical quantization and the study of the supersymmetric non-abelian Landau problem. The spectrum of the quantum Hamiltonian operator follows in accordance with the supersymmetric structure.

hep-th↗

arXiv2013

Quantum gravity and the cosmological constant: lessons from two-dimensional dilaton gravity

In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can provide a way of addressing the issue: we consider the case of two-dimensional quantum dilaton gravity non-minimally coupled to a U(1) gauge field, in the presence of an arbitrary number of massless scalar matter fields, intended also as an effective description of highly symmetrical higher-dimensional models. We are able to quantize the system non-perturbatively and obtain an expression for the cosmological constant Λin terms of the quantum physical states, in a generalization of the usual QFT approach. We discuss the role of the classical and quantum gravitational contributions to Λand present a partial spectrum of values for it.

hep-th↗

arXiv2012

Supersymmetric Quantum Mechanics, Engineered Hierarchies of Integrable Potentials, and the Generalised Laguerre Polynomials

Within the context of Supersymmetric Quantum Mechanics and its related hierarchies of integrable quantum Hamiltonians and potentials, a general programme is outlined and applied to its first two simplest illustrations. Going beyond the usual restriction of shape invariance for intertwined potentials, it is suggested to require a similar relation for Hamiltonians in the hierarchy separated by an arbitrary number of levels, N. By requiring further that these two Hamiltonians be in fact identical up to an overall shift in energy, a periodic structure is installed in the hierarchy of quantum systems which should allow for its solution. Specific classes of orthogonal polynomials characteristic of such periodic hierarchies are thereby generated, while the methods of Supersymmetric Quantum Mechanics then lead to generalised Rodrigues formulae and recursion relations for such polynomials. The approach also offers the practical prospect of quantum modelling through the engineering of quantum potentials from experimental energy spectra. In this paper these ideas are presented and solved explicitly for the cases N=1 and N=2. The latter case is related to the generalised Laguerre polynomials, for which indeed new results are thereby obtained. At the same time new classes of integrable quantum potentials which generalise that of the harmonic oscillator and which are characterised by two arbitrary energy gaps are identified, for which a complete solution is achieved algebraically.

math-ph↗

arXiv2011

Duality between 1+1 dimensional Maxwell-Dilaton gravity and Liouville field theory

We present an interesting reformulation of a collection of dilaton gravity models in two space-time dimensions into a field theory of two decoupled Liouville fields in flat space, in the presence of a Maxwell gauge field. An effective action is also obtained, encoding the dynamics of the dilaton field and the single gravitational degree of freedom in a decoupled regime. This effective action represents an interesting starting point for future work, including the canonical quantization of these classes of non trivial models of gravity coupled matter systems.

hep-th↗