In Peskin and Schroeder, after having derived a conserved tensor $T^{\mu \nu}$ associated with translations in space-time (the stress-energy tensor), it is said that the charges $\int d^3 x T^{0i}$: $$P^{i} = -\int d^3 \mathbf{x} \hphantom{ii} \pi(\mathbf{x}) \partial_i \phi(\mathbf{x}) $$ are to be "interpreted" as the physical momentum, as opposed to the canonical momentum, whose density is
$$\pi(\mathbf{x})~=~\frac{\partial{\cal L}}{\partial \dot{\phi}(\mathbf{x})}.$$
Is there a way of showing that the above equation does indeed correspond to the physical momentum?
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