- #1
arroy_0205
- 129
- 0
As far as I remember, I heard from someone that the matrix
[tex]
\gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3
[/tex]
also known as the chirality operator in 3+1 dimension is not defined in odd dimensions. I do not understand why that should be the case. Suppose I am in the 4+1 dimension and I choose one more gamma matrix suitably to close the Clifford algebra in five dimensions and then define analogously to the 4 dimensional case, the operator
[tex]
\Gamma^c=i\gamma^0\gamma^1\gamma^2\gamma^3\gamma^4
[/tex]
as my chirality operator. Will that be a mistake?
What about six dimensions? Can I define my chirality operator by multiplying the required no. of basic gamma matrices in that dimension?
[tex]
\gamma^5=i\gamma^0\gamma^1\gamma^2\gamma^3
[/tex]
also known as the chirality operator in 3+1 dimension is not defined in odd dimensions. I do not understand why that should be the case. Suppose I am in the 4+1 dimension and I choose one more gamma matrix suitably to close the Clifford algebra in five dimensions and then define analogously to the 4 dimensional case, the operator
[tex]
\Gamma^c=i\gamma^0\gamma^1\gamma^2\gamma^3\gamma^4
[/tex]
as my chirality operator. Will that be a mistake?
What about six dimensions? Can I define my chirality operator by multiplying the required no. of basic gamma matrices in that dimension?