Four-momentum operator
= Four-momentum operator
{title2=$P^\mu=(H,\mathbf P)$}
The generators of spacetime translations in a <quantum field theory>. With the mostly-minus <Minkowski metric>, $P\cdot a=Ha^0-\mathbf P\cdot\mathbf a$. A <momentum eigenstate> satisfies $P^\mu|p\rangle=p^\mu|p\rangle$, where $p^\mu$ is its <four-momentum>. After subtracting the <vacuum energy>, a translation-invariant <vacuum state> has eigenvalue zero.