# How to deal with gama5 in dimensional regularization?

1. Nov 28, 2011

### weifengchiu

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

2. Nov 28, 2011

### Bill_K

Quoting Eric Sharpe:

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, γμ} = 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 γμ for μ = 0, 1, 2, 3, it commutes with γμ for other values of μ.