Bound State Spectrum of Massive Thirring Model in Rest Frame

TL;DR

This paper analytically investigates the bound state spectrum of the massive Thirring model using canonical quantization and Bogoliubov transformation, confirming only one bound state exists with consistent behavior across coupling regimes.

Contribution

It provides an analytical solution for the bound state spectrum in the massive Thirring model using a self-consistent regularization method and confirms the existence of only one bound state.

Findings

Spectrum behaves correctly in weak and strong coupling limits

Interaction between qar{q} bosons is always repulsive

Only one bound state exists in the model

Abstract

The bound state spectrum of the massive Thirring model is studied in the framework of the canonical quantization in the rest frame. First, we quantize the field with the massless free fermion basis states. Then, we make a Bogoliubov transformation. This leads to the natural mass renormalization. The bound state spectrum is analytically solved by the $q\bar{q}$ Fock space. It is found that the spectrum has the right behaviors both for the weak and for the strong coupling limits after the appropriate wave function regularization. This regularization is quite clear and the treatment is self-consistent for the bound state problem compared to other regularizations. Further, we show that the interaction between $q\bar{q}$ bosons is always repulsive and therefore there is no bound state in the four fermion ($qq \bar q \bar q$) Fock space. This confirms that there is only one bound state in the massive Thirring model.