# Symmetrized trace

1. Jun 3, 2005

### wac03

my question is pretty technical,
in the course of studying the non-abelian Born-Infeld, i have tried to write out the Born-Infeld langrangian written using the symmetrized trace formalism, i have met at the fourth order of field strength the term
sTr(F^4) =F_{mn}F_{rn}F_{ml}F_{rl}+1/2F_{mn}F_{rn}F_{rl}F_{ml}
which looks at leat for me so involved to get proved.

My given is,
F is field strength of nonabelian gauge field
F is g-valued (g is Lie algbra of nonabelian compact gauge group G)
Fi is in the fundamental representation of g.
i will be so grateful if someone could give me hints or something which could hel to verify the relation in question
thx