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How does boson state operate on fermion state

Physics Asked by kolahalb on November 30, 2020

I have a naive question on how Bosons interact with Fermions.

In quantum field theory, it is stated that the Fermions interact with each other by exchanging Bosons. That means, at a given time, a given Fermion state $psi_f$ interacts with a Boson state $psi_B$. My naive question is: is there a direct way to model the interaction between them? I mean: can we say something like: the Boson state operates on the Fermion state as: $psi_f’rightarrow{e^{ipsi_B}}psi_f$?

I have seen How does a boson interact with a fermion? and I am not asking that question. My question is whether it is possible to conceive the interaction by such a direct method. I understand that $psi_B$ may not be Hermitian.

Regards,
Kolahal

One Answer

Well maybe I'm wrong but I think the main constraint is that the interaction term must be a Lorentz-scalar. Also its usually importamt that the system better be stable. So the intertaction term may not produce a wast amount of negative energy. And linearity in the fields is a plus for the mathematics.

Your term does not seem to be Lorentz invariant. Use gamma matrices to turn the spinor to Lorentz vector and multiply it with a dual vector.

Answered by RobertSzili on November 30, 2020

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