- #1

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[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?