# Lagrangian for a supersymmetric point particle

1. Jul 20, 2010

### jdstokes

Does anyone know where I can find the lagrangian for this?

From memory I believe it looks something like

$S = \frac{1}{2} \int \frac{d\tau}{e}[\dot{X}^2 +i \dot{\psi}{\psi}-2ie\nu \dot{X} \psi]$

where e is the graviton and nu is the gravitino. Does anyone know of a reference that supports this?

2. Jul 21, 2010

### Haelfix

That looks correct to me up to constants in front of each term. If you solve the eom you could verify that the constants are correct or not.

3. Jul 22, 2010

### jdstokes

Hi Haelfix,

Thanks for your response. I do not have the equations of motion handy so I was hoping someone might know of a reference which discusses this.

I believe this Lagrangian can be used to motivate the worldsheet Lagrangian in superstring theory.

4. Jul 23, 2010

### jdstokes

For future reference, the answer can be found in problem 4.1 of Becker, Becker and Shwarz.