Modern Theoretical Physics From Classical Mechanics to Quantum Field Theory

A wiki for understanding theoretical physics with emphasis on precise mathematical foundations — from Classical Mechanics through Quantum Field Theory, the Standard Model, and General Relativity. Written for readers with a mathematical background who want to build physical intuition.

Bohr's Atomic Model and Spectral Lines
Quantum MechanicsHistoryAtomic PhysicsFoundations
Electroweak Unification: How Electromagnetism Emerges
Standard ModelGauge TheorySymmetry BreakingHiggs
What are Fiber Bundles and why do they matter in physics?
MathematicsFiber BundlesGauge Theory
Force, Energy, and Conservative Forces
Classical MechanicsFoundations
Gauge Theory vs General Relativity: The Deep Unity
Gauge TheoryGeneral RelativityGeometryFoundations
Why can't gravity be unified with Quantum Mechanics?
GravityQFTFoundationsOpen Problems
The Harmonic Oscillator
Quantum MechanicsClassical MechanicsFoundationsExamples
How does the Heisenberg uncertainty relation relate to Lie algebras?
Quantum MechanicsLie AlgebrasMathematics
Lagrangian and Hamiltonian Formalism
Classical MechanicsFoundationsLagrangian Mechanics
Linear Algebra in Physics: Why It Matters
MathematicsFoundationsClassical MechanicsQuantum Mechanics
Newton's Laws of Motion
Classical MechanicsFoundations
Particle Types Overview
Standard ModelParticles
How do particle types relate to mathematical objects?
MathematicsStandard ModelRepresentation Theory
Is QFT based on Riemannian Geometry?
QFTGeometryFoundationsFiber Bundles
How does QFT differ from Quantum Mechanics?
QFTQuantum MechanicsFoundations
Quantum Mechanics and Functional Analysis
Quantum MechanicsMathematicsFoundationsHilbert Spaces
The Schrodinger Equation
Quantum MechanicsFoundations
Symmetries and Conservation Laws
Classical MechanicsFoundationsSymmetry
What is a Lagrangian?
FoundationsClassical MechanicsQFT
What is Wick Rotation and why does it work?
QFTPath IntegralsMathematics