The Relationship between Bare and Renormalized Couplings in Scalar Electrodynamics

When using dimensional regularization, the bare couplings are expressed as a power series in (2 - n/2)^{-1} where n is the number of dimensions. It is shown how the renormalization group can be used to sum the leading pole, next to leading pole etc. contributions to these sums in scalar electrodynamics (or any theory with multiple couplings.)Comment: 6 page

Travelling waves in a tissue interaction model for skin pattern formation

Tissue interaction plays a major role in many morphogenetic processes, particularly those associated with skin organ primordia. We examine travelling wave solutions in a tissue interaction model for skin pattern formation which is firmly based on the known biology. From a phase space analysis we conjecture the existence of travelling waves with specific wave speeds. Subsequently, analytical approximations to the wave profiles are derived using perturbation methods. We then show numerically that such travelling wave solutions do exist and that they are in good agreement with our analytical results. Finally, the biological implications of our analysis are discussed

A Gauge Theory that mixes Bosonic and Fermionic Gauge Fields

Using a gauge symmetry derived by applying the Dirac constraint formalism to supergravity with cosmological term in 2+1 dimensions, we construct a gauge theory with many characteristics of Yang-Mills theory. The gauge transformation mixes two Bosonic fields and one Fermionic field

The Renormalization Group and the Effective Potential in the Wess-Zumino model

We consider the effective potential V in the massless Wess-Zumino model. By using the renormalization group equation, we show that the explicit dependence of V on the renormalization mass scale mu cancels. If V has an extremum at some non-vanishing value of the background field, then it follows that V is "flat", independent of the background field. This is consistent with the general requirement that V be complex. The consequences for supersymmetric gauge theories are briefly considered