Mathematical Physics
Mathematically rigorous foundations of physical theories.
Mathematical Physics. Mathematically rigorous foundations of physical theories.
Foundations and canonical references
The standard treatments of mathematical physics approach the subject from complementary angles. Reed, Methods of Modern Mathematical Physics I: Functional Analysis (1980) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Arnold, Mathematical Methods of Classical Mechanics (1989) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for mathematical physics include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1980Methods of Modern Mathematical Physics I: Functional Analysisreed-1980, simon-1980
- textbook · primary · 1989Mathematical Methods of Classical Mechanicsarnold-1989
In context
Where this topic sits in the prerequisite graph. Click any node to jump.
Explore
- 01
Mathematical Classical Mechanics
Hamiltonian and Lagrangian formalism on symplectic manifolds.
- 02
Rigorous Quantum Mechanics
Self-adjoint operators, spectral theory, and the Schrödinger equation.
- 03
Constructive Quantum Field Theory
Wightman axioms, Φ^4_3, and Osterwalder–Schrader.
- 04
Topological Quantum Field Theory
Atiyah's axioms, Chern–Simons theory, and quantum invariants.
- 05
Integrable Systems
Lax pairs, inverse scattering, and quantum integrability.
- 06
Rigorous Statistical Mechanics
Gibbs measures, phase transitions, and lattice models.
- 07
Mathematical Fluid Dynamics
Euler/Navier–Stokes, vortex dynamics, and turbulence statistics.
- 08
Mathematical Gauge Theory
Yang–Mills equations, instantons, and moduli spaces of connections.
- 09
Mathematical String Theory
Calabi–Yau compactifications, vertex algebras, and topological strings.
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