Running Coupling in pure gauge theories using the Schr\"odinger functional

Schr"odinger functional, the propagation kernel for going from some field configuration at time $x^0=0$ to some other configuration at $x^0=T$, is used to define a running coupling, ${\bar{g}}^2(L)$, at a length scale, $L$, in pure gauge theories. Using a lattice formulation and finite size scaling techniques, this running coupling is calculated non-perturbatively in the continuum for a wide range of $L$, that extends from the perturbative scales to non-perturbative scales, for the specific case of pure SU(2) gauge theory.