Jean Nuyts

Gauge theories and magnetic charge

Abstract If the magnetic field for an exact gauge group H (assumed compact and connected) exhibits an inverse square law behaviour at large distances then the generalized magnetic charge, appearing as the coefficient, completely determines the topological quantum number of the solution. When this magnetic charge operator is expressed as a linear combination of mutually commuting generators of H, the components are uniquely determined, up to the action of the Weyl group, and have to be weights of a new group Hν which is explicitly constructed out of H. The relation between the “electric” group H and the “magnetic” group Hν is symmetrical in the sense that (Hν)ν = H. The results suggest that H monopoles are Hν multiplets and vice versa and that the true symmetry group is H ⊗ Hν. In this duality topological and Noether quantum numbers exchange roles rather as in Sine-Gordon theory. A physical possibility is that H and Hν be the colour and weak electromagnetic gauge groups.

First-order equations for gauge fields in spaces of dimension greater than four

Abstract We consider the possibility of satisfying the gauge field equations in dimensions greater than four by imposing linear relations amongst the components of the field strength tensor, F μν , generalising the idea of self-duality in four dimensions.

Properties of the self dual equations for an SU(n) gauge theory

The Yang equations for all self dual solutions of SU(r,s) gauge theory are exhibited in simple form. Algebraic and Backlund transformations of the solutions of these equations are derived. The Backlund transformations change an SU(r,s) solution into an SU(r−1, s+1) solution.

Classification of Ten-dimensional Kinematical Groups With Space Isotropy

All the abstract ten‐dimensional real Lie algebras that contain as a subalgebra the algebra of the three‐dimensional rotation group (generators J) and decompose under the rotation group into three three‐vector representation spaces (J itself, K, and P) and a scalar (generator H) are classified. In all cases, the existence of a homogeneous space of dimension 4 is shown.

Magnetic monopoles in SU(4) gauge theories

All spherically symmetric magnetic poles are explictly constructed in SU(4). We show the relevance of the concept of the little group which transforms spherically symmetric solutions among themselves. Unlike the SU(2) and SU(3) situation this little group is not always Abelian in SU(4). On the other hand, it is shown that while the total strength of the pole is always quantized its projection along the Higgs field is sometimes arbitrary. This is also in contrast with the SU(2) and SU(3) cases.

Phenomenology of the term structure of interest rates with Padé Approximants

The classical approach in finance attempts to model the term structure of interest rates using specified stochastic processes and the no arbitrage argument. Up to now, no universally accepted theory has been obtained for the description of experimental data. We have chosen a more phenomenological approach. It is based on results obtained some 20 years ago by physicists, results which show that Pade Approximants are most suitable for approximating large classes of functions in a very precise and coherent way. In this paper, we have chosen to compare the Pade Approximants with very low indices with the experimental densities of interest rates variations. We have shown that the data published by the Federal Reserve System in the United States are very well reproduced with two parameters only. These parameters are rather simple functions of the lag and of the maturity and are directly related to the moments of the distributions.

Inference about the Tail of a Distribution: Improvementon the Hill Estimator

The Hill estimator is often used to infer the power behavior in tails of experimental distribution functions. This estimator is known to produce bad results in certain situations which have lead to the so-called Hill horror plots. In this brief note, we propose an improved estimator which is simple and coherent and often provides an efficient remedy in the bad situations, especially when the distribution is decreasing slowly, when the data is restricted by external cuts to lie within a finite domain, or even when the distribution is increasing.

Detailed empirical study of the term structure of interest rates. Emergence of power laws and scaling laws

The technique of Pade approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more “microscopic” level.

Supersymmetric Lorentz-covariant hyperspaces and self-duality equations in dimensions greater than (4 vertical bar 4)

We generalise the notions of supersymmetry and superspace by allowing generators and coordinates transforming according to more general Lorentz representations than the spinorial and vectorial ones of standard lore. This yields novel S0(3, 1 )-covariant superspaces, which we call hyperspaces, having dimensionality greater than (414) of traditional super-Minkowski space. As an application, we consider gauge fields on complexifications these superspaces; and extending the concept of self-duality, we obtain classes of completely solvable equations analogous to the four-dimensional self-duality equations. (~) 1997 Elsevier Science B.V.

Elementary Kaluza-Klein towers revisited

Considering that the momentum squared in the extra dimensions is the physically relevant quantity for the generation of the Kaluza-Klein mass states, we have reanalyzed mathematically the procedure for five dimensional scalar fields within the Arkhani-Ahmed, Dimopoulos and Dvali scenario. We find new sets of physically allowed boundary conditions. Beside the usual results, they lead to new towers with non regular mass spacing, to lonely mass states and to tachyons.