The canonical quantization of a massive spinor-like spin $j=1$ field belonging to the $(1,0)\oplus(0,1)$ representation of the HLG, whose dynamics satisfy only the Klein-Gordon equation, is studied. The conventional quantization yields ghosts in the spectrum; however, it is shown that a suitable redefinition of the dual field by introducing an operator that modifies the inner product of states in Hilbert space leads to a well-defined theory. This redefinition renders the theory pseudo-Hermitian, while preserving a real energy spectrum and unitary evolution.

The canonical quantization of a massive spinor-like spin $j=1$ field belonging to the $(1,0)\oplus(0,1)$ representation of the HLG, whose dynamics satisfy only the Klein-Gordon equation, is studied. The conventional quantization yields ghosts in the spectrum; however, it is shown that a suitable redefinition of the dual field by introducing an operator that modifies the inner product of states in Hilbert space leads to a well-defined theory. This redefinition renders the theory pseudo-Hermitian, while preserving a real energy spectrum and unitary evolution.