# Dirac equation in curvilinear coordinates

1. May 10, 2010

### paweld

I wonder how Dirac equation transform under change of coordinates (in flat spacetime).
Should I simply express partial derivaties of one coordinates in another or it is
necessary to transform Dirac matrices as well?

2. May 11, 2010

### schieghoven

There's a good review paper

Brill & Wheeler, Rev Mod Phys 29 (1957) 465

and many others subsequently, one off the top of my head is

Chamseddine, hep-th/0511074 (2005)

I'm a bit rusty on the details but I recall the Dirac matrices have to change so that the anticommutator relation
$$\gamma^\mu \gamma^\nu + \gamma^\nu \gamma^\mu = 2 g^{\mu\nu}$$
remains true. There is some sort of spinor connection which is a spinor analog of the covariant derivative.

Best,

Dave