Yang-Mills theories and quadratic forms

Abstract

We show that the Hamiltonian of ( N=1 , d = 10) super Yang-Mills can be expressed as a quadratic form in a very similar manner to that of the ( N=4 , d = 4) theory. We find a similar quadratic form structure for pure Yang-Mills theory but this feature, in the non-supersymmetric case, seems to be unique to four dimensions. We discuss some consequences of this feature