The discussion revolves around the physical interpretation of the Lorentz invariant quantity \(\bar\psi\psi\) in the context of fermion fields. Participants explore whether this quantity can be interpreted as a probability density and seek to clarify the nature of fermion fields and their associated interpretations.
Participants do not reach a consensus on the interpretation of \(\bar\psi\psi\) as a probability density, with multiple competing views presented regarding its significance and the nature of fermion fields.
There are limitations in the discussion regarding the assumptions about the interpretations of fermion fields and the definitions of probability density in this context. The distinction between field operators and wave functions is also a point of contention.
blue2script said:Hmm.. right. But then, what is the physical interpretation of the product above? And what is the probability density of a fermion field?
Fermion field is an operator, so it does not have a probabilistic interpretation. However, one should distinguish the field operator from the wave function which is a c-number function representing a quantum state. For a 1-particle wave function \psi, the probability density isblue2script said:Hmm.. right. But then, what is the physical interpretation of the product above? And what is the probability density of a fermion field?
Demystifier said:Fermion field is an operator, so it does not have a probabilistic interpretation. However, one should distinguish the field operator from the wave function which is a c-number function representing a quantum state. For a 1-particle wave function \psi, the probability density is
\psi^{\dagger}\psi