Semiclassical energy density of kinks and solitons

We compute semiclassical corrections to the energy density of kinks in ${\ensuremath{\phi}}^{4}$ theory and solitons sine-Gordon model ($1+1$) dimensions, using local covariant renormalization techniques from quantum field curved spacetimes. For correction energy, we recover known results. Our analysis highlights a subtlety definition conserved stress tensor for scalar theories dimensions.