Details
| Original language | English |
|---|---|
| Article number | 128 |
| Journal | Journal of high energy physics |
| Volume | 2025 |
| Issue number | 7 |
| Publication status | Published - 10 Jul 2025 |
Abstract
It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as “horizontal” and construct “vertical” intertwiners, which change the number of interacting particles for a fixed but integer value of the coupling constant. The emerging structure of a grid of intertwiners exists only in the algebraically integrable situation (integer coupling) and allows one to obtain each Liouville charge from the free power sum in the particle momenta by iterated intertwining either horizontally or vertically. We present recursion formulæ for the intertwiners as a factorization problem for partial differential operators and prove their existence for small values of particle number and coupling. As a byproduct, a new basis of non-symmetric Liouville integrals appears, algebraically related to the standard symmetric one.
Keywords
- Conformal and W Symmetry, Discrete Symmetries, Integrable Field Theories, Integrable Hierarchies
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of high energy physics, Vol. 2025, No. 7, 128, 10.07.2025.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Coupling and particle number intertwiners in the Calogero model
AU - Correa, Francisco
AU - Inzunza, Luis
AU - Lechtenfeld, Olaf
N1 - Publisher Copyright: © The Author(s) 2025.
PY - 2025/7/10
Y1 - 2025/7/10
N2 - It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as “horizontal” and construct “vertical” intertwiners, which change the number of interacting particles for a fixed but integer value of the coupling constant. The emerging structure of a grid of intertwiners exists only in the algebraically integrable situation (integer coupling) and allows one to obtain each Liouville charge from the free power sum in the particle momenta by iterated intertwining either horizontally or vertically. We present recursion formulæ for the intertwiners as a factorization problem for partial differential operators and prove their existence for small values of particle number and coupling. As a byproduct, a new basis of non-symmetric Liouville integrals appears, algebraically related to the standard symmetric one.
AB - It is long known that quantum Calogero models feature intertwining operators, which increase or decrease the coupling constant by an integer amount, for any fixed number of particles. We name these as “horizontal” and construct “vertical” intertwiners, which change the number of interacting particles for a fixed but integer value of the coupling constant. The emerging structure of a grid of intertwiners exists only in the algebraically integrable situation (integer coupling) and allows one to obtain each Liouville charge from the free power sum in the particle momenta by iterated intertwining either horizontally or vertically. We present recursion formulæ for the intertwiners as a factorization problem for partial differential operators and prove their existence for small values of particle number and coupling. As a byproduct, a new basis of non-symmetric Liouville integrals appears, algebraically related to the standard symmetric one.
KW - Conformal and W Symmetry
KW - Discrete Symmetries
KW - Integrable Field Theories
KW - Integrable Hierarchies
UR - http://www.scopus.com/inward/record.url?scp=105010580463&partnerID=8YFLogxK
U2 - 10.1007/JHEP07(2025)128
DO - 10.1007/JHEP07(2025)128
M3 - Article
AN - SCOPUS:105010580463
VL - 2025
JO - Journal of high energy physics
JF - Journal of high energy physics
SN - 1029-8479
IS - 7
M1 - 128
ER -