Partial bosonization: The formalism of Cheshire Cat bag models

By bosonizing fermionic theories on only a part of space-time, one obtains idealized bag models where the physics is independent of the bag radius. Such ''Cheshire Cat Models (CCM's)'' were introduced in an earlier paper, where it was suggested that realistic bag models are in fact approximate CCM's. The present paper further explores Abelian CCM's in 1+1 dimensions. First, the boundary action for CCM's is derived in the Lagrangian formalism by demanding invariance under parity and chiral rotations. Next, a quantum reinterpretation of the classical Lagrangian bag boundary conditions is used to obtain the bosonic representation of fermions as soliton operators. Last, these soliton operators are used to construct CCM's in the Hamiltonian framework. The Cheshire Cat criterion - independence of the energy spectrum on the bag radius - is presented as the commuting of the energy and momentum operators for the model. (orig.)