Non-abelian Cheshire cat bag models in 1+1 dimensions

Abstract

Non-abelian Cheshire cat models are investigated in their lagrangian and hamiltonian formulations. The lagrangian bag boundary conditions are used to derive the form of non-abelian soliton operators, through which fermions are represented in bosonic language. These soliton operators are then used to construct the boundary interaction in the hamiltonian picture, wherein the bosonic sector is formulated by means of a current algebra involving anomalous commutators. The hamiltonian and the momentum operator are shown to commute, thus implying that the Cheshire cat criterion — the independence of the energy spectrum on the bag wall position — is fulfilled by the system.