Searcharxiv⌕ Search

arXiv subjects

Jan Govaerts

Publications and source records attributed to Jan Govaerts.

At least 55 records · Page 3Linked to original sources
arXiv2006

Topological Quantum Field Theory and Pure Yang-Mills Dynamics

By considering specific limits in the gauge coupling constant of pure Yang--Mills dynamics, it is shown how there exist topological quantum field theory sectors in such systems defining nonperturbative topological configurations of the gauge fields which could well play a vital role in the confinement and chiral symmetry breaking phenomena of phenomenologically realistic theories such as quantum chromodynamics, the theory for the strong interactions of quarks and gluons. A general research programme along such lines is outlined. A series of other topics of possible relevance, ranging from particle phenomenology to the quest for the ultimate unification of all interactions and matter including quantum gravity, are raised in passing. The general discussion is illustrated through some simple examples in 0+1 and 1+1 dimensions, clearly showing the importance of properly accounting for quantum topological properties of the physical and configuration spaces in gauge theories based on compact gauge groups.

hep-th↗
arXiv2006

Topological Background Fields as Quantum Degrees of Freedom of Compactified Strings

It is shown that background fields of a topological character usually introduced as such in compactified string theories correspond to quantum degrees of freedom which parametrise the freedom in choosing a representation of the zero mode quantum algebra in the presence of non-trivial topology. One consequence would appear to be that the values of such quantum degrees of freedom, in other words of the associated topological background fields, cannot be determined by the nonperturbative string dynamics.

hep-th↗
arXiv2004

Self-Adjoint Extensions of the Dirac Hamiltonian with a delta-Sphere Interaction

The purpose of this paper is to make an explicit construction of specific self-adjoint extensions of the Dirac Hamiltonian in the presence of a $δ$-sphere interaction of finite radius. The exact resolvent kernel of the free Dirac operator is given. This specifies related results that have recently appeared in the literature.

hep-th↗
arXiv2004

The Cosmological Constant of One-Dimensional Matter Coupled Quantum Gravity is Quantised

Coupling any interacting quantum mechanical system to gravity in one (time) dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantised, even though the gravity sector is free of any quantum dynamics. Furthermore, physical states are also confined to the subspace of the matter quantum states for which the energy coincides with the value of the cosmological constant. These general facts are illustrated through some simple examples. The physical projector quantisation approach readily leads to the correct representation of such systems, whereas other approaches relying on gauge fixing methods are often plagued by Gribov problems in which case the quantisation rule is not properly recovered. Whether such a quantisation of the cosmological constant as well as the other ensuing consequences in terms of physical states extend to higher dimensional matter-gravity coupled quantum systems is clearly a fascinating open issue.

hep-th↗
arXiv2002

A General Four-Fermion Effective Lagrangian for Dirac and Majorana Neutrino-Charged Matter Interactions

Given the most general Lorentz invariant four-fermion effective interaction possible for two neutrinos and two charged fermions, whether quarks or leptons, all possible 2-to-2 processes involving two neutrinos, whether Dirac or Majorana ones, and two charged fermions are considered. Explicit and convenient expressions are given for the associated differential cross-sections. Such a parametrization should help assess the sensitivity to physics beyond the Standard Model of neutrino beam experiments which are in the design stage at neutrino factories.

hep-ph↗
arXiv2002

The Quantum Geometer's Universe: Particles, Interactions and Topology

With the two most profound conceptual revolutions of XXth century physics, quantum mechanics and relativity, which have culminated into relativistic spacetime geometry and quantum gauge field theory as the principles for gravity and the three other known fundamental interactions, the physicist of the XXIst century has inherited an unfinished symphony: the unification of the quantum and the continuum. As an invitation to tomorrow's quantum geometers who must design the new rulers by which to size up the Universe at those scales where the smallest meets the largest, these lectures review the basic principles of today's conceptual framework, and highlight by way of simple examples the interplay that presently exists between the quantum world of particle interactions and the classical world of geometry and topology.

hep-th↗
arXiv2002

The Schwinger Model and the Physical Projector: a Nonperturbative Quantization without Gauge Fixing

Based on the physical projector approach, a nonpertubative quantization of the massless Schwinger model is considered which does not require any gauge fixing. The spectrum of physical states, readily identified following a diagonalization of the operator algebra, is that of a massive pseudoscalar field, namely the electric field having acquired a mass proportional to the gauge coupling constant. The physical spectrum need not be identified with confined bound fermion-antifermion pairs, an interpretation which one is otherwise led to given whatever gauge fixing procedure but which is not void of gauge fixing artefacts.

hep-th↗
arXiv2002

The Cosmological Constant of One-Dimensional Matter Coupled Quantum Gravity is Quantized

Coupling any interacting quantum mechanical system to gravity in one dimension requires the cosmological constant to belong to the matter energy spectrum and thus to be quantized, even though the gravity sector is free of any quantum dynamics, while physical states are also confined to the subspace of matter quantum states whose energy coincides with the cosmological constant value. These general facts are illustrated through some simple examples. The physical projector quantization approach readily leads to the correct representation of such systems, whereas other approaches relying on gauge fixing methods are often plagued by Gribov problems in which case the quantization rule is not properly recovered. Whether such a quantization of the cosmological constant as well as the other ensuing consequences in terms of physical states extend to higher dimensional matter-gravity coupled quantum systems is clearly a fascinating open issue.

hep-th↗
arXiv2002

Neutrino-Charged Matter Interactions: a General Four-Fermion Effective Parametrization

Given the eventuality of neutrino and muon factories in the foreseeable future, all possible 2-to-2 processes involving two neutrinos, whether Dirac or Majorana ones, and two charged fermions are considered on the basis of the most general Lorentz invariant four-fermion effective interaction possible, in the limit of massless particles. Such a parametrization should enable the assessment of the sensitivity to physics beyond the Standard Model, including the eventual discrimination between the Dirac or Majorana character of neutrinos, of specific experimental beam and detector designs.

hep-ph↗
arXiv2000

Half-Integer Winding Number Solutions to the Landau-Ginzburg-Higgs Equations and Instability of the Abrikosov-Nielsen-Olesen Vortex

New solutions to the abelian U(1) Higgs model, corresponding to vortices of integer and half-integer winding number bound onto the edges of domain walls and possibly surrounded by annular current flows, are described, based on a fine-grained analysis of the topology of such configurations in spacetime. The existence of these states, which saturate BPS bounds in specific limits and are quite reminiscent of D-branes and membranes in general, could have interesting and some important consequences in a wide range of physical contexts. For instance, they raise the possibility that for some regimes of couplings the usual vortex of unit winding number would split into two vortices each of one-half winding number bound by a domain wall. A similar approach may also be relevant to other known topological states of field theory.

hep-th↗
arXiv2000

On Electric Fields in Low Temperature Superconductors

The manifestly Lorentz covariant Landau-Ginzburg equations coupled to Maxwell's equations are considered as a possible framework for the effective description of the interactions between low temperature superconductors and magnetic as well as electric fields. A specific experimental set-up, involving a nanoscopic superconductor and only static applied fields whose geometry is crucial however, is described, which should allow to confirm or invalidate the covariant model through the determination of the temperature dependency of the critical magnetic-electric field phase diagram and the identification of some distinctive features it should display.

cond-mat.supr-con↗
arXiv2000

Nuclear Muon Capture on the Proton and 3He within the Standard Model and Beyond

Nuclear muon capture on the proton and $^3$He is considered both within and beyond the Standard Model in terms as general as is possible. Explicit and precise analytic expressions for all possible observables are given, assuming only a Dirac neutrino in the limit of vanishing mass. These results allow both for precision tests of the Standard Model and new physics, as well as for the assessment of the potential physics reach of experiments designed to measure specific observables. Using these expressions, stringent constraints can already be inferred from a recent precision measurement of the statistical capture rate on $^3$He. Likewise, similar constraints should follow the completion of a precision measurement in progress of the singlet capture rate on the proton.

nucl-th↗
arXiv1999

The Physical Projector and Topological Quantum Field Theories: U(1) Chern-Simons Theory in 2+1 Dimensions

The recently proposed physical projector approach to the quantisation of gauge invariant systems is applied to the U(1) Chern-Simons theory in 2+1 dimensions as one of the simplest examples of a topological quantum field theory. The physical projector is explicitely demonstrated to be capable of effecting the required projection from the initially infinite number of degrees of freedom to the finite set of gauge invariant physical states whose properties are determined by the topology of the underlying manifold.

hep-th↗