# fermion field

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## fermion field

[′fer·mē‚än ‚fēld]
(quantum mechanics)
An operator defined at each point in space-time that creates or annihilates a particular type of fermion and its antiparticle.
References in periodicals archive ?
These observables can then be inputted in phenomenological models and offer guidance in further developments with extended gauge theory and fermionic field content.
The fermionic field operators with equal time arguments satisfy the anticommutation relations 
In particular, the fermionic field operators can be written as
Furthermore, we can define the equation of state parameter of the fermionic field by using the energy density (26) and pressure (23) as [[omega].sub.f] = [p.sub.f]/[[rho].sub.f] to search whether the fermionic field can provide alternative for dark energy or not.
Therefore, the results show that the fermionic field may behave like both the quintessence and the phantom dark energy field in the late-time universe.
This solution is the same as the results obtained in the context of nonminimal coupling of the fermionic field to the torsion in 3+1 dimensional teleparallel gravity .
It is interesting to note that this solution is the same as the results obtained in the context of nonminimal coupling of the fermionic field to the torsion in 3+1 dimensional teleparallel gravity .
The usual one-loop effective action for a fermionic field in a gauge field background is given by
where [[psi].sub.a] is the fermionic field corresponding to baryon [alpha].
However, I would like to propose here a different, more general argument, which avoids the difficulties given by the necessity that the field equations should satisfy at the singularities special conditions like the sufficient conditions found in  and also the open problem of which are the conditions to be satisfied by the fermionic fields at singularities.
Consider functions (equipped with engineering dimensions) {[[phi].sub.1], ..., [[phi].sub.m]} (the bosonic fields or bosons) and {[[psi].sub.1], ..., [[psi].sub.m]} (the fermionic fields or fermions), collectively called the component fields.
[+ or -] is sign for bosonic and fermionic fields ([phi]), respectively.

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