- #1
GoldPheonix
- 85
- 0
Right, so in Yang-Mills theory, the vector potential is modified from:
To:
However, it is my understanding that the exterior/wedge product is anticommutitive, so that for a given exterior algebra over a vector space, V:
Why then is the second term in the curvature, F, not non-zero? I assume I'm missing something, could someone fill me in?
(Sorry, this probably fits better in Topology & Geometry section, but the question technically is a question about multilinear algebra)
[tex]F = dA[/tex]
To:
[tex]F = dA + A\wedge A[/tex]
However, it is my understanding that the exterior/wedge product is anticommutitive, so that for a given exterior algebra over a vector space, V:
[tex]\omega \wedge \omega = 0, \forall \omega \epsilon \Lambda(V) [/tex]
Why then is the second term in the curvature, F, not non-zero? I assume I'm missing something, could someone fill me in?
(Sorry, this probably fits better in Topology & Geometry section, but the question technically is a question about multilinear algebra)