Hamiltonians and physical vacua of exactly solvable models

TL;DR

This paper derives correct quantum Hamiltonians for exactly solvable 2D models, revealing new insights into their vacua and showing equivalences and differences with free theories and across formulations.

Contribution

It provides a detailed derivation of Hamiltonians considering operator solutions, and clarifies the structure of vacua and model equivalences in exactly solvable 2D models.

Findings

Correct Hamiltonians derived considering operator solutions

Vacua of massless Thirring and Federbush models obtained via Bogoliubov transformation

Federbush model has identical interacting structure in space-like and light-front formulations

Abstract

Correct quantum Hamiltonians of a few exactly solvable models in two space-time dimensions are derived by taking into account operator solutions of the field equations. While two versions of the model with derivative coupling are found to be equivalent in many respects to a free theory, physical vacua of the massless Thirring and Federbush models are obtained by means of a Bogoliubov transformation in the form of a coherent state quadratic in composite boson operators. Contrary to the conventional treatment, the Federbush model is shown to have the same interacting structure in both space-like and light-front formulations.