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The local Lorentz transformation are acting on the tangent space $T_p(M)$ to the curved GR manifold at each point $p$. The idea of a "tangent space" is a formal way of ascribing a flat space to th …

This just the representation theory pf the group. There no time involved. In applications the representation states are in the Heisenberg picture, in which neither they nor the Hilbert space depend …

Consider a state with with a unit charge that is is spread uniformly over a volume $V$. The total charge is unity so, $$ \int_V d x j_0(x) =1. $$ but as $V$ becomes large $j_0(x)=1/V$ tends to zero. …

The problem is that while the total angular momentum $$ M_{\mu\nu}= x_\mu p_\nu - x_\nu p_\mu +S_{\mu\nu} $$ about the point $x=0$ is well defined, the seperation between the orbital part and the int …

One can make a Poincare-Lie-Algebra-valued Cartan Connection by setting $$ \eta = \tau_a {\bf e}^{*a} + \frac 12 \sigma^{ab} \omega_{ab} $$ where $\tau_a$ and $\sigma^{ab}$ are the Lie algebra genera …

The third law states that momentum is conserved. From Noether we know that momentum consrevation is a consequence of translational symmetry. The tranlations are a subgroup of Poincare. So Yes.