Angular Momentum Operator in Quantum Field Theory

The problem here was when doing the integration by parts. One has to be very careful when remembering which operators act on which expressions. In my case, it turned out that the derivative was acting on the wrong terms when doing the integration by parts, which indeed did add an extra minus sign.

It looks like you've missed a sign: \begin{align} Q_i &= \epsilon_{ijk} \int_{p,q} \sqrt{\frac{E_q}{E_p}}p^k \int d^3x (a_qe^{iq\cdot x}-a_q^\dagger e^{-iq\cdot x}) \left(a_p (-i\frac{\partial}{\partial p^j})e^{ip\cdot x} -a_p^\dagger (i\frac{\partial}{\partial p^j})e^{-ip\cdot x}\right). \end{align} Then it looks like the term that goes like $a_q^\dagger a_p^\dagger$ should have the opposite sign.