The anti-commutation relation between the components of a fermion field ψ is given by [ψα(x),ψ†β(y)]+=δαβδ(3)(x−y).
In case of two different and independent fermion fields, should I impose commutation or anticommutation between them?
If we continue to use anticommutation, how should the RHS change for two different fermion fields ψ1 and ψ2? [ψ1α(x),ψ2†β(y)]+=?
[ψ1α(x),ψ2β(y)]+=?[ψ1†α(x),ψ2†β(y)]+=?
Answer
We use anticommutation relations:
[ψ1α(x),ψ2†β(y)]+=0
[ψ1α(x),ψ2β(y)]+=0
[ψ1†α(x),ψ2†β(y)]+=0
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