On page 158 of Fields, the supersymmetry algebra is represented in terms of the action on supercoordinates as

$$\delta \theta^\alpha = \epsilon^\alpha$$ $$\delta\bar{\theta}^{\dot{\alpha}} = \bar{\epsilon}^{\dot{\alpha}}$$ $$\delta x^{\alpha\dot{\beta}} = \frac{1}{2}i(\epsilon^\alpha \bar{\theta}^{\dot{\beta}} + \bar{\epsilon}^{\dot{\beta}}\theta^\alpha)$$

Further down on the page, the following statement is made:

In the supersymmetric case the infinitesimal invariants under the q's (and therefore p) are

$$d\theta^\alpha, \qquad d\bar{\theta}^{\dot{\alpha}}, \qquad dx^{\alpha\dot{\beta}} + \frac{1}{2}i(d\theta^\alpha)\bar{\theta}^{\dot{\beta}} + \frac{1}{2}i(d\bar{\theta}^{\dot{\beta}})\theta^\alpha$$

I get a sense that these should follow from the definition of the supersymmetry transformations, but what exactly does the quoted statement mean?

Thinking of the SUSY variation $\delta_\epsilon$ as something similar to a BRST variation, is this statement about nilpotency of the algebra in form notation or something?

This post imported from StackExchange Physics at 2015-05-22 21:05 (UTC), posted by SE-user leastaction