Publications at the Riemann Center
Coupling and particle number intertwiners in the Calogero model
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.
Details
- Organisation(s)
-
Institute of Theoretical Physics
Riemann Center for Geometry and Physics
- External Organisation(s)
-
Universidad de Santiago de Chile
- Type
- Article
- Journal
- Journal of high energy physics
- Volume
- 2025
- ISSN
- 1029-8479
- Publication date
- 10.07.2025
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Electronic version(s)
-
https://doi.org/10.1007/JHEP07(2025)128 (Access:
Open
)
