I'm recently reading the book "Solitons and Instantons" written by R. RAJARAMAN. However, for lacking of ability, I couldn't figure out how to derivate the static solution for energy with this Lagrangian density in 2+1D. Here's the Lagrangian density and the energy. $$ {\cal L}=\frac{1}{2}(\partial_\mu\mathbf{\phi})\cdot(\partial^\mu\mathbf{\phi}) \\ E=\frac{1}{2}\int(\partial_\sigma\mathbf{\phi})\cdot(\partial_\sigma\mathbf{\phi})d^2x $$
As for the partial part, they are all {1,2}. Should I use metric tensor or something else to solve this?
