As described previously, the Dirac–Kähler equation in flat spacetime is equivalent to four copies of the Dirac equation, despite being a set of equations for antisymmetric tensor fields. The ability of integer spin tensor fields to describe half integer spinor fields is explained by the fact that Lorentz transformations do not commute with the internal Dirac–Kähler SO ( 2 , 4 ) symmetry, with the parameters of this symmetry being tensors rather than scalars. This means that the Lorentz transformations mix different spins together and the Dirac fermions are not strictly speaking half-integer spin representations of the Clifford algebra. They instead correspond to a coherent superposition of differential forms. In higher dimensions, particularly on 2 2 n dimensional surfaces, the Dirac–Kähler equation is equivalent to 2 2 n − − 1 Dirac equations.