New | Sternberg Group Theory And Physics
You're interested in exploring the Sternberg group theory and its connections to physics. Let's dive into a detailed discussion.
- Work explicit computations: momentum map for particle on sphere, cotangent bundle reduction examples.
- Quantize simple coadjoint orbits: R^2, S^2 → harmonic oscillator, spin.
- Explore modern papers on quantization commutes with reduction and higher symplectic techniques.
- Introductory texts on Lie groups and representation theory for physicists.
- Reviews on symplectic geometry, moment maps, and coadjoint orbits.
- Papers on “quantization commutes with reduction” and geometric quantization primers.
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Why do we have quarks, leptons, and bosons? According to Sternberg’s teachings on representation theory, particles are essentially "labels" for different ways a symmetry group can act. If you know the symmetry group (like You're interested in exploring the Sternberg group theory
Unlike traditional groups, non-invertible symmetries (emerging in quantum field theories and condensed matter) do not form a group but a fusion category . Sternberg’s earlier work on groupoids and crossed modules is now being used as the mathematical scaffolding for these symmetries. A recent preprint titled "Sternberg’s Cocycles for Non-Invertible Defects" demonstrates that the "higher group" structures found in M-theory and string theory compactifications are direct applications of Sternberg’s generalized group extensions. Work explicit computations: momentum map for particle on