Variations on Symmetry

A work in progress on the wave description of nature that emerges from physical principles, stipulated symmetry, and seminal observations.

Contents

1. IntroductionComing soon

   How symmetry, locality, variational reasoning, and superposition form physical theories

   Outline

   1. Invariant structure
   2. State, law, and observation
2. SymmetryNEW

   Symmetry, representations, waves, and the connection to quantum mechanics.

   Outline

   1. Discrete symmetries
   2. Continuous symmetries
   3. The Fourier Structure of Waves
   4. From Wave Mechanics to Quantum Mechanics
3. SpacetimeComing soon

   The geometry of events and causality.

   Outline

   1. Galilean structure
   2. Relativistic structure
4. Variational ApproachesNEW

   The Principle of Least Action

   Outline

   1. The Lagrangian Function
   2. Curvature and the Relativistic Source of Acceleration
   3. Using Variational Calculus to Find Geodesics
   4. From Action to Momentum and Energy
   5. Fermat's Theorem
   6. Lagrangians of Fields
5. Fields and InteractionsComing soon

   General Relativity and Gauge Fields.

6. State spaceNEW

   The evolution of ensembles

   Outline

   1. The Evolution of Ensembles in Physical Systems
   2. Phase Space
   3. Generating Time Evolution
   4. The Algebra of Hamiltonian Mechanics
7. Quantum MechanicsComing soon

   Shifting to an information perspective

   Outline

   1. State and measurement
   2. Operators
   3. Commutators
   4. Fields
   5. Quantization
   6. Particle interpretation