Flavour mixing and mass matrices via anticommuting properties

Five anticommuting property coordinates can accommodate all the known fundamental particles in their three generations plus more. We describe the points of difference between this scheme and the standard model and show how flavour mixing arises through a set of expectation values carried by a single Higgs superfield.Comment: 12 pages, LaTe

A Possible Way of Connecting the Grassmann Variables and the Number of Generation

We construct a Left-Right symmetric model in which the number of generation is related to Grassmann variables. We introduce two sets of complex Grassmann variables ($\theta^1_q$,$\theta^2_q$), ($\theta^1_l$, $\theta ^2_l$) and associate each variable with left- and right-handed quark and lepton fields, respectively. Expanding quark and lepton fields in powers of the Grassmann variables, we find that there are exactly three generations of quarks and leptons. Integrating out the Grassmann variables, we obtain phenomenologically acceptable fermion mass matrices.Comment: 7 pages, Revtex, UM-P-93/40, OZ-93/1

The determination of derivative parameters for a monotonic rational quadratic interpolant

Explicit formulae are developed for determining the derivative parameters of a monotonic interpolation method of Gregory and Delbourgo (1982)

The low energy effective Lagrangian for photon interactions in any dimension

The subject of low energy photon-photon scattering is considered in arbitrary dimensional space-time and the interaction is widened to include scattering events involving an arbitrary number of photons. The effective interaction Lagrangian for these processes in QED has been determined in a manifestly invariant form. This generalisation resolves the structure of the weak-field Euler-Heisenberg Lagrangian and indicates that the component invariant functions have coefficients related, not only to the space-time dimension, but also to the coefficients of the Bernoulli polynomial.Comment: In the revised version, the results have been expressed in terms of Bernoulli polynomials instead of generalized zeta functions; they agree for spinor QED with those of Schubert and Schmidt (obtained differently by path integral methods)

Piecewise rational quadratic interpolation to monotonic data

An explicit representation of a piecewise rational quadratic function is developed which produces a monotonic interpolant to given monotonic data. The explicit representation means that the piecewise monotonic interpolant is easily constructed and numerical experiments indicate that the method produces visually pleasing curves. Furthermore, the use of the method is justified by an 0(h4) convergence result