Field diffeomorphisms and the algebraic structure of perturbative expansions

We consider field diffeomorphisms in the context of real scalar field theories. Starting from free field theories we apply non-linear field diffeomorphisms to the fields and study the perturbative expansion for the transformed theories. We find that tree level amplitudes for the transformed fields must satisfy BCFW type recursion relations for the S-matrix to remain trivial. For the massless field theory these relations continue to hold in loop computations. In the massive field theory the situation is more subtle. A necessary condition for the Feynman rules to respect the maximal ideal and co-ideal defined by the core Hopf algebra of the transformed theory is that upon renormalization all massive tadpole integrals (defined as all integrals independent of the kinematics of external momenta) are mapped to zero.Comment: 8 pages, 2 figure

Renormalization group and isochronous oscillations

We show how the condition of isochronicity can be studied for two dimensional systems in the renormalization group (RG) context. We find a necessary condition for the isochronicity of the Cherkas and another class of cubic systems. Our conditions are satisfied by all the cases studied recently by Bardet et al \cite{bard} and Ghose Choudhury and Guh

Dressing the nucleon in a dispersion approach

We present a model for dressing the nucleon propagator and vertices. In the model the use of a K-matrix approach (unitarity) and dispersion relations (analyticity) are combined. The principal application of the model lies in pion-nucleon scattering where we discuss effects of the dressing on the phase shifts.Comment: 17 pages, using REVTeX, 6 figure

Properties of Clifford algebras for fundamental particles

As William Kingdon Clifford commented in the abstract of his paper “On the Classification of Geometric Algebras” communicated to the London Mathematical Society on 10 March 1876, “… the system is the natural language of metrical geometry and of physics”1. The system which he was describing is his geometric algebra, which we now know as Clifford algebra. The paper was never finished, but was discovered following his death and published in his collected Mathematical Papers. Nevertheless the use of his algebras, not just in four dimensions, is evident today in models of physics

Gauge transformations of spinors within a Clifford algebraic structure

Algebraic spinors can be defined as minimal left ideals of Clifford algebras. We consider gauge transformations which an two-sided equivalence transformations of a complete algebra, including the spinors. These transformations of the spinors introduce new interaction terms which appear hard to interpret. We establish algebraic theorems which allow these new interaction terms to be evaluated and use these ideas to provide a new formulation of Glashow's electroweak interactions of leptons. The theorems also lead us to propose a new Clifford algebraic definition of spinors based on nilpotents, rather than idempotents

Unified Spin Gauge-Model and the top-Quark Mass

Spin gauge models use a real Clifford algebraic structure R(p,q) associated with a real manifold of dimension p+q to describe the fundamental interactions of elementary particles. This review provides a comparison between those models and the standard model, indicating their similarities and differences. By contrast with the standard model, the spin gauge model based on R(3,8) generates intermediate boson mass terms without the need to use the Higgs-Kibble mechanism and produces a precise prediction for the mass of the top quark. The potential of this model to account for exactly three families of fermions is considered

Spin gauge-theories - principles and predictions

The paper provides an overview of spin gauge theories by first describing the principles on which they are based. These principles are grouped together in four basic categories and are illustrated by referring to a particular spin gauge theory model. The principles have evolved over a number of years and are considerably more sophisticated now compared with those used in our first models (see for example, [1-5])