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
-
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.