  Two methods can be used to calculate explicitly the Killing form on the Lie
algebras. The first one is a direct calculation of the traces of the generators
in a matrix representation of the algebra, and the second one is the usage of
the group invariance of the scalar product. We use both methods in our
calculation of the scalar product on the extended Poincare algebra in order to
have a cross check of our results. The algebra is infinite-dimensional and
requires careful treatment of the infinities. The scalar product on the
extended algebra found by both methods coincides and the important conclusion
which follows is that Poincare generators are orthogonal to the gauge
generators.

High Energy Physics - Theory