Infra-red problems and a response

• The standard approach to the infra-red problem is to sum over degenerate final states to remove soft divergences (Bloch-Nordsiech), and over both initial and final states for collinear divergences (Lee-Nauenberg). We show that this division is inconsistent, and further that the Lee-Nauenberg recipe leads to ill-defined results in a variety of theories. We then argue that infra-red divergences are due to using unphysical variables to describe in and out states and introduce gauge invariant, physical ‘dressed’ states. Perturbative and non-perturbative properties of physical electron and quark states are then discussed. It is shown in SU(2) lattice simulations that the overlap between the ground state and our dressed state increases as we approach finer lattices.

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