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11.P: Exercises
 Last updated
 08:45, 16 Nov 2014

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 Noting that , prove that the and matrices all have zero trace. Hence, deduce that each of these matrices has eigenvalues , and eigenvalues , where is the dimension of the matrices.
 Verify that the matrices (1125) and (1126) satisfy Equations (1117)(1119).
 Verify that the matrices (1123) and (1124) satisfy the anticommutation relations (1122).
 Verify that if
where is a 4vector field, then
is Lorentz invariant, where the integral is over all space, and it is assumed that as .  Verify that (1168) is a solution of (1167).
 Verify that the matrices , defined in (1189), satisfy the standard anticommutation relations for Pauli matrices: i.e.,