= Classical field theory
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Classical field theory describes physical quantities assigned throughout space and time, with field values that are ordinary numerical or geometric objects. A <scalar field> assigns a scalar to each point; the <electromagnetic field> assigns electric and magnetic components. Initial and <boundary conditions> together with field equations determine their evolution.
A local <action> $S=\int\mathcal L(\phi,\partial\phi,x)\,d^dx$ provides a systematic formulation. Varying the fields gives the <Euler Lagrange equations>, while continuous symmetries lead through <Noether theorem> to conserved currents. <Maxwell equations> and the classical <Klein-Gordon equation> are examples. The field description makes finite-speed propagation and local energy transfer explicit. In <quantum field theory>, the corresponding fields become operator-valued objects and their correlations determine quantum predictions.
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