Gravitation and quadratic forms

Abstract

Abstract The light-cone Hamiltonians describing both pure ( N $$ \mathcal{N} $$ = 0) Yang-Mills and N $$ \mathcal{N} $$ = 4 super Yang-Mills may be expressed as quadratic forms. Here, we show that this feature extends to theories of gravity. We demonstrate how the Hamiltonians of both pure gravity and N $$ \mathcal{N} $$ = 8 supergravity, in four dimensions, may be written as quadratic forms. We examine the effect of residual reparametrizations on the Hamiltonian and the resulting quadratic form.

Keywords

• Classical Theories of Gravity
• Gauge Symmetry
• Supergravity Models
• Superspaces