University of Cambridge

## Talks by Paul Townsend

## Jordan algebras: from QM to 5D supergravity to … Standard Model?

Paul Townsend
University of Cambridge

This talk will be about two applications of Jordan algebras. The first, to quantum mechanics, follows on from the talk of John Baez. I will explain how time dependence makes use of the associator, and how this is related to the commutator in the standard density matrix formulation.
The associator of a Jordan algebra also determines the curvature of a Riemannian metric on its positive cone, invariant under the symmetry group of the norm (mentioned in the talk of John Baez); the cone is foliated by hypersurfaces of constant norm.

## Supersymmetry and RCHO revisited

Paul Townsend
University of Cambridge

Various links between supersymmetry and the normed division algebras
R,C,H,O were found in the
1980s. This talk will focus on the link between K=R,C,H,0 and
supersymmetric field theories in a Minkowski spacetime of dimension
D=3,4,6,10. The first half will survey the history starting with a
1944/5 paper of Dirac and heading towards the links found in 1986/7
between R,C,H,O and super-Yang-Mills theories.