Non-linear realizations,Goldstone bosons of broken Lorentz rotations and effective actions for p-branes

We consider the non-linear realizations of the Poincare group for p  -branes with local subgroup SO(1,p)×SO(D−(p+1))$\mathit{SO}(1,p)\times \mathit{SO}(D-(p+1))$. The Nambu–Goto p-brane action is constructed using the Maurer–Cartan forms of the unbroken translations. We perform a throughout phase space analysis of the action and show that it leads to the canonical action of a p-brane. We also construct some higher order derivative terms of the effective p-brane action using the MC forms of the broken Lorentz transformations.