1,552,858 research outputs found
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
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