Infinite Family of Integrable Sigma Models Using Auxiliary Fields
Christian Ferko, Liam Smith
Abstract
We introduce a class of 2D sigma models which are parametrized by a function of one variable. In addition to the physical field g, these models include an auxiliary field v_{α} which mediates interactions in a prescribed way. We prove that every theory in this family is classically integrable, in that it possesses an infinite set of conserved charges in involution, which can be constructed from a Lax representation for the equations of motion. This class includes the principal chiral model (PCM) and all deformations of the PCM by functions of the energy-momentum tensor.
Topics & Concepts
Integrable systemSigmaRepresentation (politics)PhysicsClass (philosophy)Mathematical physicsTensor (intrinsic definition)Field (mathematics)Pure mathematicsAlgebra over a fieldMathematicsQuantum mechanicsComputer scienceArtificial intelligenceLawPoliticsPolitical scienceBlack Holes and Theoretical PhysicsNonlinear Waves and SolitonsPhysics of Superconductivity and Magnetism