On the quantization of a theory arising from a variational principle for multiple integrals with application to born's electrodynamics

Abstract

The transition from classical mechanics to quantum mechanics has been formulated in various ways. But all these ways have the common feature that they use as starting point mechanics not in its Newtonian form, but in the form which it was given by Lagrange and Hamilton. The essence of this form consists in the fact that the differential equations are represented as Euler equations of a variational principle for v functions, the generalized coordinates, of one variable, the time. In its purely mathematical aspect the quantization method may, therefore, be regarded as a mode of taking certain notions and certain relations arising from a variational principle for several dependent and one independent variable and of giving them a new meaning.