y35dp
Nov24-10, 04:18 AM
1. The problem statement, all variables and given/known data
If D =7 and the metric g\mu\nu=diag(+------), Using the outer product of matrices, A \otimes B construct a suitable set of \gamma matrices from the 2 x 2 \sigma-matrices
2. Relevant equations
\sigma1=(0, 1 ) \sigma2=(0, -i)
(1, 0) (i, 0)
\o3=(1, 0)
(0, -1)
we need only refer to the basic properties of the sigma matrices
\sigmai\sigmaj = i \epsilonijk\sigmak + \deltaijI2
and
\sigma1T=\sigma1, \sigma2T=\sigma2, \sigma3T=-\sigma3, \sigma1*=\sigma1, \sigma2*=\sigma3*=-\sigma3
3. The attempt at a solution
As of yet I have found no \gamma-matrices that satisfy {\gamma\mu, \gamma\nu} = 2g\mu\nu. The closest I have come is a set which satisfy {\gamma\mu, \gamma\nu} = 2\delta\mu\nuI7
If D =7 and the metric g\mu\nu=diag(+------), Using the outer product of matrices, A \otimes B construct a suitable set of \gamma matrices from the 2 x 2 \sigma-matrices
2. Relevant equations
\sigma1=(0, 1 ) \sigma2=(0, -i)
(1, 0) (i, 0)
\o3=(1, 0)
(0, -1)
we need only refer to the basic properties of the sigma matrices
\sigmai\sigmaj = i \epsilonijk\sigmak + \deltaijI2
and
\sigma1T=\sigma1, \sigma2T=\sigma2, \sigma3T=-\sigma3, \sigma1*=\sigma1, \sigma2*=\sigma3*=-\sigma3
3. The attempt at a solution
As of yet I have found no \gamma-matrices that satisfy {\gamma\mu, \gamma\nu} = 2g\mu\nu. The closest I have come is a set which satisfy {\gamma\mu, \gamma\nu} = 2\delta\mu\nuI7