Duality In Equations of Motion from Spacetime Dependent Lagrangians

Starting from lagrangian field theory and the variational principle, we show that duality in equations of motion can also be obtained by introducing explicit spacetime dependence of the lagrangian. Poincare invariance is achieved precisely when the duality conditions are satisfied in a particular way. The same analysis and criteria are valid for both abelian and nonabelian dualities. We illustrate how (1)Dirac string solution (2)Dirac quantisation condition (3)t'Hooft-Polyakov monopole solutions and (4)a procedure emerges for obtaining {\it new} classical solutions of Yang-Mills (Y-M) theory. Moreover, these results occur in a way that is strongly reminiscent of the {\it holographic principle}.