How to deal with gama5 in dimensional regularization?

[weifengchiu]

Note that the anti_symmetric tensor ε_μνρλis only defined in four-dimension space.

 

[Bill_K]

Quoting http://www.phys.vt.edu/~ersharpe/6455/janhand1.pdf:

Furthermore, we need to generalize γ⁵ to d dimensions. Doing so requires a certain amount of care. In particular, we previously defined γ⁵ = iγ⁰γ¹γ²γ³, but in d dimensions this is no longer the product of all the gamma matrices. One way to try to proceed would be to define γ⁵ to be a matrix with the property that {γ⁵, γ^μ} = 0 for all μ in all dimensions d, but this leads to a contradiction. Instead, we will proceed as follows. We define γ⁵ = iγ⁰γ¹γ²γ³ which formally looks the same as our previous definition in four dimensions, but which now has the consequence that although γ⁵ anticommutes with γ^μ for μ = 0, 1, 2, 3, it commutes with γ^μ for other values of μ.