Poincare invariance in temporal gauge canonical quantization and $θ$-vacua

The Poincare invariance in the temporal gauge canonical quantization of QCD is shown manifestly by verifying the energy-momentum-vector and angular-momentum-tensor satisfy the Poincare algebra in the physical Hilbert space. Two different values of $θ$ for the $θ$-term in QCD lagrangian lead to different representations of the Poincare group, which are, however, connected by an unitary transformation. Thus the parameter $θ$ becomes physically irrelevant unless we can further restrict the physical Hilbert space.

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