Tunneling into a quantum Hall system and the infrared catastrophe

We calculate the tunneling density of states for a two-dimensional interacting electron gas in a quantizing magnetic field. We show that the observed pseudogap in the density of states of the lowest Landau level can be regarded to be a consequence of an infrared catastrophe, resulting from the response of the electron system to the potential produced by the abruptly added charge during a tunneling event. Our formalism can be applied at any filling factor without the use of Chern-Simons or composite fermion theory.