Thursday, 22 June 2017

second quantization - How will the (anti)commutation relation between two different fermion fields look like?


The anti-commutation relation between the components of a fermion field ψ is given by [ψα(x),ψβ(y)]+=δαβδ(3)(xy).




  1. In case of two different and independent fermion fields, should I impose commutation or anticommutation between them?





  2. If we continue to use anticommutation, how should the RHS change for two different fermion fields ψ1 and ψ2? [ψ1α(x),ψ2β(y)]+=?

    [ψ1α(x),ψ2β(y)]+=?
    [ψ1α(x),ψ2β(y)]+=?





Answer



We use anticommutation relations:


[ψ1α(x),ψ2β(y)]+=0

[ψ1α(x),ψ2β(y)]+=0
[ψ1α(x),ψ2β(y)]+=0


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