Hi,

I have a superspace spanned by 4 commuting coordinates + 2 anti-commuting ones $\{x^\mu,\theta^\alpha\}$, I have to do the change of coordinates $dx^\mu\to dy^\mu= dx^\mu+d\theta^\alpha \eta_\alpha^{\;\:\mu}$ where $\eta$ have to be a local function i.e: $\eta\equiv\eta(x)$, and leave the $d\theta$'s unchanged, so how can I translate this change on coordinates themselves? In particular I need to express $\partial_\mu$ in the new coordinate system.

If the $\eta$ fcts where global it would be simply $x^\mu\to y^\mu= x^\mu+\theta^\alpha \eta_\alpha^{\;\:\mu}$, so what if $\eta$'s where not global?

constantand by a "local function" you simply mean afunction. This sort of nonstandard language might be confusing to some people. – José Figueroa-O'Farrill Feb 20 '10 at 14:46