Classical field theory is a research area in theoretical physics that studies continuous fields, such as electromagnetic, gravitational, and scalar fields, within a pre-quantum, typically relativistic or Galilean-invariant framework. It formulates dynamics via Lagrangian and Hamiltonian densities, leading to Euler–Lagrange field equations and conservation laws derived from spacetime and internal symmetries through Noether’s theorem. The discipline underpins general relativity and classical electrodynamics, and provides the mathematical and conceptual foundation for quantum field theory, emphasizing variational principles, gauge invariance, and the structure of classical solutions including waves, solitons, and topological defects.
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