We study co-existence system of both bosonic and fermionic degrees of freedom. Even if Lagrangian does not include higher derivatives, fermionic ghosts exist. For Lagrangian with up to first derivatives, we find the fermionic ghost-free condition in Hamiltonian analysis, which is found to be the same with requiring that the equations of motion of fermions are first-order in Lagrangian formulation. When fermionic degrees of freedom are present, uniqueness of time evolution is not guaranteed a priori because of the Grassmann property. We confirm that the additional condition, which is introduced to close Hamiltonian analysis, also ensures the uniqueness of the time evolutionof system.
|Publication status||Published - 2017 Apr 10|
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