my question is pretty technical,(adsbygoogle = window.adsbygoogle || []).push({});

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

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# Symmetrized trace

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