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However, for the Dirace field with Lagrangian [itex]{\cal L}=\bar{\psi}({i\gamma}^{\mu}{\partial}_{\mu}+m) \psi[/itex], it's impossible to write [itex]\dot{q}[/itex] as a function of [itex]p[/itex], because the conjugate momentum is [itex]i{\psi}^{\dagger}[/itex], this means the Hamitonian has to contain [itex]\dot{\psi}[/itex]? How do we make sense of it?