nLab superparticle




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics

Quantum field theory




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.


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.


Analysis in classical field theory in terms of supergeometry is in

  • Daniel Freed, lecture 4 of Classical field theory and Supersymmetry, IAS/Park City Mathematics Series Volume 11 (2001) (pdf)

The pure spinor superparticle:

In a super-background field:

Last revised on September 26, 2022 at 04:17:07. See the history of this page for a list of all contributions to it.