Domain 10 · Mathematics Codex

Mathematical Physics & Modelling

The deep mathematical structures that describe physical reality — from Lagrangians to gauge fields.

Scope

Classical mechanics (Lagrangian and Hamiltonian formulations), electromagnetism, special and general relativity, quantum mechanics, quantum field theory, gauge theory, chaos theory, dynamical systems.

Mathematical physics is not physics using mathematics — it is the discovery that physical law has deep mathematical structure. The unreasonable effectiveness of mathematics in the natural sciences (Eugene Wigner's phrase) is most visible here: differential geometry developed for abstract reasons turns out to be exactly the right language for general relativity; group theory developed for pure algebraic reasons turns out to classify elementary particles.

Entries in this domain

Build status: This domain is in active build. Live entries are marked below. All other entries are planned and pending — see build status for the full picture.
  • Lagrangian Mechanics Pending
    A reformulation of classical mechanics using the principle of least action — more powerful and geometrically natural than Newton's original formulation.
  • Chaos Theory Pending
    The study of dynamical systems extremely sensitive to initial conditions — where tiny differences grow exponentially, making long-term prediction impossible.

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