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Physics

Rep theory

• Standard Model: \({\operatorname{SU}}_3 \times{\operatorname{SU}}_2 \times{\operatorname{U}}_1\)

• \({\operatorname{SO}}(n)\) and its relativistic analog \({\operatorname{SO}}(1,n)\) define symmetries of space time.

  • Irreducible reps of \({\operatorname{SO}}_3\) describe the periodic table

• \({\operatorname{SU}}(n)\) defines fundamental quantum mechanical phase space symmetries.

  • Irreducible reps of \({\operatorname{SU}}_2\) lead to Dirac equations of the electron

• \(\SP(n)\) defines symmetries in cases where there is a quaternionic structure.

Spacetime

See Ricci tensor and Riemannian curvature