AN INTRODUCTION TO YANGIAN SYMMETRIES

Denis Bernard (1)

1 SPhT - Service de Physique Théorique

We review some aspects of the quantum Yangians as symmetry algebras of two-dimensional quantum field theories. The plan of these notes is the following: 1 — The classical Heisenberg model: •Non-Abelian symmetries; •The generators of the symmetries and the semi-classical Yangians; •An alternative presentation of the semi-classical Yangians; (Digression on Poisson-Lie groups. 2 — The quantum Heisenberg chain: •Non-Abelian symmetries and the quantum Yangians; •The transfer matrix and an alternative presentation of the Yangians.

Domaines: Mathématiques [math]; Matière Condensée [cond-mat]; Physique des Hautes Energies - Théorie [hep-th]

Denis Bernard. AN INTRODUCTION TO YANGIAN SYMMETRIES. International Journal of Modern Physics B, 2012, 07 (20n21), pp.3517-3530. ⟨10.1142/S0217979293003371⟩. ⟨hal-03370731⟩