One-Loop Quantum Stress-Energy Tensor for the Kink and sine-Gordon Solitons

We compute the renormalized one-loop quantum corrections to the energy density $T_{00}(x)$ and pressure $T_{11}(x)$ for solitons in the $1+1$ dimensional scalar sine-Gordon and kink models. We show how precise implementation of counterterms in dimensional regularization resolves previously identified discrepancies between the integral of $T_{00}(x)$ and the known correction to the total energy.