Hopf algebras and renormalization in physics Alessandra Frabetti

Hopf algebras and renormalization in physics Alessandra Frabetti Banff, september 1st, 2004 Contents Renormalization Hopf algebras 2 Matter and forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Standard Model and Feynman graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Quantum = quantization of classical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 From classical to quantum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Free theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Interacting theories .

• path integrals


• quantum self-adjoint operators


• e? particles


• residual strong


• hopf algebras


• e?


• dyson renormalization