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

Self-consistent nonperturbative anomalous dimensions

A self-consistent treatment of two and three point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted nonperturbatively by solving and suitably truncating the topologies of the full set of Dyson-Schwinger equations. The first step requires a sensible ansatz for the full vertex part which conforms to first order perturbation theory at least. We model this vertex to obtain typical transcendental equations between anomalous dimension and coupling constant $g$ which coincide with know results to order $g^4$.Comment: 15 pages LaTeX, no figures. Requires iopart.cl

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

Minimal Uncertainty States For Quantum Groups

The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any finite dimensional irreducible representation, the highest weight vector and those unitarily related to it are the quasi-classical states.Comment: 4 pages, late

Rational quadratic spline interpolation to monotonic data.

In an earlier paper by Gregory & Delbourgo (1982), a piecewise rational quadratic function is developed which produces a monotonic interpolant to monotonic data. This interpolant gives visually pleasing curves and is of continuity class C1 . In the present paper, the data is restricted to be strictly monotonic and it is shown that it is possible to obtain a monotonic rational quadratic spline interpolant which is of continuity class .C2 An ○(h4) convergence analysis is included

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)