Hamiltonian formulation of exactly solvable models and their physical vacuum states

TL;DR

This paper explores the Hamiltonian structures of exactly solvable fermionic models in quantum field theory, revealing equivalences between different formulations and deriving the physical vacuum states using bosonization techniques.

Contribution

It demonstrates the equivalence of spacelike and light-front Hamiltonians in certain models and introduces a simplified bosonization approach for the Federbush model.

Findings

Spacelike and light-front Hamiltonians become equivalent when solutions are incorporated.

The physical vacuum of the Thirring model is obtained via a Bogoliubov transformation.

A simplified massive bosonization for the Federbush model is derived.

Abstract

We clarify a few conceptual problems of quantum field theory on the level of exactly solvable models with fermions. The ultimate goal of our study is to gain a deeper understanding of differences between the usual ("spacelike") and light-front forms of relativistic dynamics. We show that by incorporating solutions of the operator field equations to the canonical formalism the spacelike and light front Hamiltonians of the derivative-coupling model acquire an equivalent structure. The same is true for the massive solvable theory, the Federbush model. In the conventional approach, the physical predictions in the two schemes disagree. Moreover, the derivative-coupling model is found to be almost identical to a free theory, in contrast to the conventional canonical treatment. Physical vacuum state of the Thirring model is then obtained by a Bogoliubov transformation as a coherent state quadratic in composite boson operators. To perform the same task in the Federbush model, we derive a massive version of Klaiber's bosonization and show that its light-front form is much simpler.