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Dirac equation in curvilinear coordinates

  1. May 10, 2010 #1
    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. jcsd
  3. May 11, 2010 #2
    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.


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