Dilatation Covariance and Exact Solutions in Local Relativistic Field Theories

Consideration is given to the invariance of field equations under space-time dilatations with (induced) transformation of constant parameters therein. Analysis of such "dilatation covariance" facilitates the determination of rigorous closed-form singularity-free solutions to essentially nonlinear classical field equations. More over, for essentially nonlinear quantized (boson) field theories, dilatation-covariance considerations facilitate the determination of rigorous closed-form solutions to the Schr\"odinger stationary-state equation.