Ghost free boson-fermion co-existence system
arXiv:1704.02717 · doi:10.1103/PhysRevD.96.044015
Abstract
We study co-existence system of both bosonic and fermionic degrees of freedom. For such system with up to first derivatives in Lagrangian, we find Ostrogradsky-type 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 evolution of system.
21 pages, v2 : a field theoretical example is added in Appendix, v3: published in PRD
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- Stable cosmological solutions in degenerate theory of gravity
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- On Lorentz-invariant spin-2 theories