Exactly solvable models and spontaneous symmetry breaking

TL;DR

This paper explores exactly solvable two-dimensional fermionic models using a modified Hamiltonian approach that incorporates solutions of operator field equations, comparing different formulations and extending to related models.

Contribution

It introduces a novel Hamiltonian method accounting for operator solutions, applies it to various 2D models, and discusses vacuum structure and symmetry breaking.

Findings

Modified Hamiltonian approach effectively solves 2D models.

Comparison of conventional and light-front formulations reveals differences.

New insights into vacuum degeneracy and symmetry breaking in the Schwinger model.

Abstract

We study a few two-dimensional models with massive and massless fermions in the hamiltonian framework and in both conventional and light-front forms of field theory. The new ingredient is a modification of the canonical procedure by taking into account solutions of the operator field equations. After summarizing the main results for the derivative-coupling and the Thirring models, we briefly compare conventional and light-front versions of the Federbush model including the massive current bosonization and a Bogoliubov transformation to diagonalize the Hamiltonian. Then we sketch an extension of our hamiltonian approach to the two-dimensional Nambu--Jona-Lasinio model and the Thirring--Wess models. Finally, we discuss the Schwinger model in a covariant gauge. In particular, we point out that the solution due to Lowenstein and Swieca implies the physical vacuum in terms of a coherent state of massive scalar field and suggest a new formulation of the model's vacuum degeneracy.