What is fermionic fields: Definition and 1 Discussions

In quantum field theory, a fermionic field is a quantum field whose quanta are fermions; that is, they obey Fermi–Dirac statistics. Fermionic fields obey canonical anticommutation relations rather than the canonical commutation relations of bosonic fields.
The most prominent example of a fermionic field is the Dirac field, which describes fermions with spin-1/2: electrons, protons, quarks, etc. The Dirac field can be described as either a 4-component spinor or as a pair of 2-component Weyl spinors. Spin-1/2 Majorana fermions, such as the hypothetical neutralino, can be described as either a dependent 4-component Majorana spinor or a single 2-component Weyl spinor. It is not known whether the neutrino is a Majorana fermion or a Dirac fermion; observing neutrinoless double-beta decay experimentally would settle this question.

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    Charge-Conjugation property

    I'm probably just complicating things, but I'm a little bit stuck with this problem. I started with just plugging in the definitions for ##\bar{\Psi}_a^c## and ##\Psi_b^c##. So I get $$\bar{\Psi}_a^c\gamma^{\mu}\Psi_b^c=-\Psi_a^TC^{-1}\gamma^{\mu}C\bar{\Psi}_b^T$$. After this I used...
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