Singular perturbation theory for interacting fermions in two dimensions

Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points - Fold and Canard Points in Two Dimensions

The geometric approach to singular perturbation problems is based on powerful methods from dynamical systems theory. These techniques have been very successful in the case of normally hyperbolic critical manifolds. However, at points where normal hyperbolicity fails, the well-developed geometric theory does not apply. We present a method based on blow-up techniques, which leads to a rigorous ge...

Bosonization of Interacting Fermions in Arbitrary Dimensions

Singular perturbation theory

When we apply the steady-state approximation (SSA) in chemical kinetics, we typically argue that some of the intermediates are highly reactive, so that they are removed as fast as they are made. We then set the corresponding rates of change to zero. What we are saying is not that these rates are identically zero, of course, but that they are much smaller than the other rates of reaction. The st...

Geometric Singular Perturbation Theory

Perturbation Theory for Slac Lattice Fermions

I study a class of lattice versions of QED with fermions with the aim of clarifying the relationship between the fermion spectrum (doubled or not), continuous chiral symmetry, the range of the lattice interactions, and the validity of perturbation theory. Theories of this class with an undoubled spectrum, such as the SLAC formulation, have infiniterange interactions and infrared-divergent pertu...