Commutator for fermion operators?

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SUMMARY

The discussion focuses on the behavior of fermion operators in quantum mechanics, specifically addressing the anti-commutation relations. When given two fermion operators A and B, the anti-commutator is defined as AB + BA. The equation AB - BA does not automatically vanish for fermions; instead, it can be expressed as 2AB - C, where C is the result of the anti-commutator. This highlights the importance of understanding the implications of these relations in quantum field theory.

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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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