A Variational Principle for Gauge-Independent Electrodynamics

Abstract

A new lagrangian for the maxwell field is defined, expressed completely in terms of gauge-independent transverse field-strengths ($\mathfrak{E},\mathfrak{B}$) and matter variables (${\mathbf{x}}_i$, ${\mathbf{v}}_i$, and ${\mathbf{p}}_i$ in the classical theory; $\psi$ and ${\psi }^{†}$ in the wave-mechanical theory). The coulomb field is defined in terms of matter variables, and a (solenoidal) vector potential is defined in terms of the magnetic field strength $\mathfrak{B}$. The variational principle gives the usual equations of motion and field equations. Quantization leads automatically to the formulas of gauge-independent quantum electrodynamics.