Four-particle solutions to Baxter equation of SL(2,C) Heisenberg spin magnet for integer conformal Lorentz spin and their normalizability

TL;DR

This paper investigates four-particle solutions to the Baxter equation in the SL(2,C) Heisenberg spin magnet, identifying both normalizable and non-normalizable states for non-zero conformal Lorentz spin using the Q-Baxter method.

Contribution

It provides a detailed analysis of the spectrum of four-reggeized gluon states with non-zero Lorentz conformal spin, highlighting the existence of normalizable and non-normalizable solutions and their symmetry properties.

Findings

Normalizable trajectory-like states form a continuous spectrum.

Discrete point-like solutions are non-normalizable.

Symmetry of the Casimir operator explains the existence of certain solutions.

Abstract

The four reggeized gluon states for non-vanishing Lorentz conformal spin $n_h$ are considered. To calculate their spectrum the Q-Baxter method is used. As a result we describe normalizable trajectory-like states, which form continuous spectrum, as well as discrete point-like solutions, which turn out to be non-normalizable. The point-like solutions exist due to symmetry of the Casimir operator where conformal weights $(h,\bar h) \to (h,1-\bar h)$.