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Homework Statement
If D =7 and the metric g[tex]\mu[/tex][tex]\nu[/tex]=diag(+------), Using the outer product of matrices, A [tex]\otimes[/tex] B construct a suitable set of [tex]\gamma[/tex] matrices from the 2 x 2 [tex]\sigma[/tex]-matrices
Homework Equations
[tex]\sigma[/tex]1=(0, 1 ) [tex]\sigma[/tex]2=(0, -i)
(1, 0) (i, 0)
[tex]\o[/tex]3=(1, 0)
(0, -1)
we need only refer to the basic properties of the sigma matrices
[tex]\sigma[/tex]i[tex]\sigma[/tex]j = i [tex]\epsilon[/tex]ijk[tex]\sigma[/tex]k + [tex]\delta[/tex]ijI2
and
[tex]\sigma[/tex]1T=[tex]\sigma[/tex]1, [tex]\sigma[/tex]2T=[tex]\sigma[/tex]2, [tex]\sigma[/tex]3T=-[tex]\sigma[/tex]3, [tex]\sigma[/tex]1*=[tex]\sigma[/tex]1, [tex]\sigma[/tex]2*=[tex]\sigma[/tex]3*=-[tex]\sigma3[/tex]
The Attempt at a Solution
As of yet I have found no [tex]\gamma[/tex]-matrices that satisfy {[tex]\gamma[/tex][tex]\mu[/tex], [tex]\gamma[/tex][tex]\nu[/tex]} = 2g[tex]\mu[/tex][tex]\nu[/tex]. The closest I have come is a set which satisfy {[tex]\gamma[/tex][tex]\mu[/tex], [tex]\gamma[/tex][tex]\nu[/tex]} = 2[tex]\delta[/tex][tex]\mu[/tex][tex]\nu[/tex]I7