Group Theory And Physics New - Sternberg

Feature Title: Sternberg Gaugeoids for Topological Quantum Phases

Core Concept

Leverage Sternberg’s generalization of group actions to Lie algebroids and groupoids (from his work with Weinstein on “symplectic groupoids” and with Ratiu on “reduction of Lie algebroids”) to classify and simulate non-invertible symmetries and anyon condensation in (2+1)D topological orders.

Further reading (if you’re feeling brave): sternberg group theory and physics new

• Configuration: Q = SO(3); phase space TSO(3) ≅ SO(3) × so(3) via left trivialization.
• Hamiltonian H(Ω) = 1/2 Ω^T I Ω expressed on so(3)* (Ω body angular velocity, I inertia tensor).
• Coadjoint motion: Euler equations dotL = L × Ω where L = IΩ.
• Momentum map for left/right action gives body-space and space-space angular momentum.
• Reduction by left action yields dynamics on so(3)* (Lie–Poisson); integrals: energy and magnitude of L.
• Quantization: coadjoint orbits are 2-spheres with symplectic area proportional to spin; quantizing discrete allowed values → spin representations; leads to quantum rigid rotor spectrum.

, are introduced simultaneously with mathematical concepts like homomorphisms representation theory Advanced Topics : It covers compact groups Lie groups , and the significance of the elementary particle physics Historical Context Configuration: Q = SO(3); phase space T SO(3)

recommends the book as a graduate-level text, praising its "fairly lucid" exposition. PhilPapers Accessing the Material Group Theory and Physics Key Concepts and Mathematical Framework

4. Reduction (Marsden–Weinstein) and examples

Key Concepts and Mathematical Framework