Yang-Mills theories and quadratic forms

TL;DR

This paper demonstrates that the Hamiltonian of certain super Yang-Mills theories can be expressed as quadratic forms, revealing a unique structural feature in four-dimensional pure Yang-Mills theory with implications for understanding its properties.

Contribution

It shows the Hamiltonian of (N=1;d=10) super Yang-Mills can be written as a quadratic form, similar to (N=4;d=4), and discusses the uniqueness of this feature in four dimensions.

Findings

Hamiltonian expressed as quadratic form in super Yang-Mills theories

Quadratic form structure found in pure Yang-Mills theory in four dimensions

This quadratic form feature appears unique to four-dimensional non-supersymmetric Yang-Mills

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.