We provide a brief overview of the basic tools and concepts of quantum field theoretical scattering theory. This article is commissioned by the Encyclopedia of Mathematical Physics, edited by J.-P. Françoise, G. Naber and T.S. Tsun, to be published by the Elsevier publishing house. 1 Physical Motivation and Mathematical Setting The primary connection of relativistic quantum field theory to expe...

We use thermodynamic Bethe ansatz to study nonrelativistic scattering theory of low energy excitations of 1D Hubbard model, using the S-matrices proposed by Eßler and Korepin. This model can be described by two types of excitation states, holons and spinons, as asymptotic states. In the attractive regime, the spinon is massive while the holon is massless. The situation is reversed with a repuls...

In models of (non-relativistic and pseudo-relativistic) electrons interacting with static nuclei and with the (ultraviolet-cutoff) quantized radiation field, the existence of asymptotic electromagnetic fields is established. Our results yield some mathematically rigorous understanding of Rayleigh scattering and of the phenomenon of relaxation of isolated atoms to their ground states. Our proofs...

Observations of both gamma-ray burst sources and certain classes of active galaxy indicate the presence of relativistic shock waves and require the production of high energy particles to explain their emission. In this paper we first review the basic theory of shock waves in relativistic hydrodynamics and magneto-hydrodynamics, emphasising the astrophysically interesting cases. This is followed...

High energy scattering experiments involving nuclei are typically analyzed in terms of light front variables. The desire to provide realistic, relativistic wave functions expressed in terms of these variables led me to try to use light front dynamics to compute nuclear wave functions. Here calculations of infinite nuclear matter in the mean field approximation and also in a light front version ...

We analyze the unitarity of a non-relativistic non-commutative scalar field theory. We show that electric backgrounds spoil unitarity while magnetic ones do not. Furthermore, unlike its relativistic counterparts, unitarity can not be restored (at least at the level of one-to-one scattering amplitude) by adding new states to the theory. This is a signal that the model cannot be embedded in a nat...