The Special Relativistic Classical Field Theory

Abstract

We shall define the Lagrangian function for a relativistic classical field. Let $\bar D \subset \mathbb{R}^4$ be a bounded region corresponding to a region $\bar U$ in space-time M₄. Let F: $\bar D \to \mathbb{R}^\rho$ be a twice differentiable function, i.e., $F \in \ell ^2 (\bar D;\mathbb{R}^\rho )$ (see Figure 24).