https://doi.org/10.1140/epjc/s10052-020-8098-0
Regular Article - Theoretical Physics
A semi-infinite matrix analysis of the BFKL equation
1
Instituto de Física Teórica UAM/CSIC, Nicolás Cabrera 15, and Universidad Autónoma de Madrid, 28049, Madrid, Spain
2
LIP, Av. Prof. Gama Pinto, 2, 1649-003, Lisbon, Portugal
3
Centre de recherche sur l’inflammation UMR 1149, Inserm, Université Paris Diderot, 75018, Paris, France
4
Data Team, Département d’informatique de l’ENS, École normale supérieure, CNRS, PSL Research University, 75005, Paris, France
5
CERN, Theoretical Physics Department, Geneva, Switzerland
* e-mail: agustin.sabio@uam.es
Received:
31
March
2020
Accepted:
29
May
2020
Published online:
17
June
2020
The forward BFKL equation is discretised in virtuality space and it is shown that the diffusion into infrared and ultraviolet momenta can be understood in terms of a semi-infinite matrix. The square truncation of this matrix can be exponentiated leading to asymptotic eigenstates sharing many features with the BFKL gluon Green’s function in the limit of large matrix size. This truncation is closely related to a representation of the XXX Heisenberg spin 
chain with SL(2) invariance where the Hamiltonian acts on a symmetric double copy of the harmonic oscillator. A simple modification of the BFKL matrix suppressing the infrared modes generates evolution more compatible with the Froissart bound.
© The Author(s), 2020
