superalgebra

and

supergeometry

# Contents

## Idea

The superparticle is a sigma-model quantum field theory analogous to the ordinary relativistic particle but where either the worldline or the target space are taken to be supermanifolds. Described by supersymmetric quantum mechanics.

## Definitions

One way to define what this means classically is to give an action functional on spaces of maps from the worldline into super target space. One such is the

The quantization of this action functional to a 1-dimensional worldvolume QFT is still largely an open problem.

An axiomatic description of the worldvolume QFT of the superparticle can be given in terms of FQFT as a representation of a category of super-cobordisms. One such approach is described at

The algebraic data encoded by such a representation is essentially that of a

See there for more details.

Revised on June 10, 2013 14:51:07 by Urs Schreiber (89.204.137.122)