Commutator for fermion operators?

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When dealing with two fermion operators, the expression AB-BA can be analyzed using the known anti-commutator AB+BA. This expression does not automatically vanish for fermions; instead, it can be rewritten as 2AB-C if AB+BA equals C. The discussion highlights the importance of understanding the relationships between these operators in quantum mechanics. Further clarification on the implications of AB-BA may be needed for a comprehensive understanding. The topic underscores the complexities involved in manipulating fermion operators.
pellman
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If we have two fermion operators with a known anti-commutator AB+BA, what do we do if we find ourselves with AB-BA in an equation? Does this automatically vanish for fermions? if not, is there anything we can say about in general?
 
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pellman said:
If we have two fermion operators with a known anti-commutator AB+BA, what do we do if we find ourselves with AB-BA in an equation? Does this automatically vanish for fermions? if not, is there anything we can say about in general?
Not much. If AB+BA=C, then AB-BA=2AB-C. :rolleyes:
 
silly me. I'll have to post the whole question later instead.
 

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