Thanks. This is what I was looking for when I originally posed the question. So, if I understood you correctly, the restriction of Lorentz symmetry on the Hami

Thanks. This is what I was looking for when I originally posed the question. So, if I understood you correctly, the restriction of Lorentz symmetry on the Hamiltonian in turn requires QFT creation and annihilation operators to commute/anticommute (the anticommute part what then ultimately drives a negative energy contribution from fermionic fields when summing over all possible energy states). What causes the anticommute properties? Is there a non-abelian symmetry group backing fermion fields somewhere?