Sine-Gordon field theory vs relativistic Calogero-Moser N-particle systems: an overview

by Prof. Simon Ruijsenaars (University Leeds UK)

Tuesday 28 Mar 2017, 14:00 → 15:00 Europe/Budapest

Bldg.1. Meeting Room (KFKI campus)

The sine-Gordon equation φ_xx −φ_tt = sin(φ), describes an integrable 2D relativistic field theory, both at the classical and at the quantum level. The classical soliton, antisoliton and breather solutions turn into solitonic fermions, antifermions and their bound states at the quantum level, with particle number preservation under scattering and factorized amplitudes governed by the Yang-Baxter equations. We survey the relation between the sine-Gordon model and (a special case of) the hyperbolic relativistic integrable N-particle systems of A(N−1) Calogero-Moser type. In particular, we present compelling evidence that the intimate link of the classical version of the latter and the classical particle-like sine-Gordon solutions turns into a physical equivalence on the quantum level, in the sense that the same scattering amplitudes and bound state energies arise in the quantum field-theoretic and N-particle models.