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## Main Question or Discussion Point

As is well known, a Dirac Lagrangian can be written in a symmetric form:

L = i/2 (\bar\psi \gamma \partial (\psi) - \partial (\bar\psi) \gamma \psi ) - m \bar\psi \psi

Let \psi and \psi^\dagger be independent fields. The corresponding canonical momenta are

p = i/2 \psi^\dagger;

p^\dagger = - i/2 \psi.

The anticommutation relations would be

{(\psi)_k, i/2 (\psi^dagger)_m}= i delta_km,

{(\psi^\dagger)_k, - i/2 (\psi)_m}= i delta_km,

which are in contradiction with one another. How can this happen?

L = i/2 (\bar\psi \gamma \partial (\psi) - \partial (\bar\psi) \gamma \psi ) - m \bar\psi \psi

Let \psi and \psi^\dagger be independent fields. The corresponding canonical momenta are

p = i/2 \psi^\dagger;

p^\dagger = - i/2 \psi.

The anticommutation relations would be

{(\psi)_k, i/2 (\psi^dagger)_m}= i delta_km,

{(\psi^\dagger)_k, - i/2 (\psi)_m}= i delta_km,

which are in contradiction with one another. How can this happen?