Yang-Mills theories, Quadratic forms and Nicolai maps

Abstract

In this thesis, we examine supersymmetric Yang-Mills theories from a non-standard perspective, namely from that of a Nicolai map, a non-linear transformation of the bosonic fields that maps the full interacting theory to a free bosonic one. We overview the procedure to systematically generate such maps for supersymmetric Yang-Mills theories,and the implications of this idea. We then analyze a related idea, namely quadratic form Hamiltonians, a structure unique to pure and maximally superymmetric (integer spin lambda) theories when formulated in the light-cone gauge, and their ties to scattering amplitudes in the corresponding theories.