Real symmetric Φ⁴-matrix model as Calogero-Moser model

2023/11/18 by Harald Grosse, Grosse, Harald, Naoyuki Kanomata +5 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics

paper · pdf · doi:10.48550/arxiv.2311.10974

openalex publication_date 2023/11/18 · openalex created_date 2023/11/22 · openalex updated_date 2026/07/28

Abstract

We study a real symmetric Φ⁴-matrix model whose kinetic term is given by Tr( E Φ²), where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Schödinger type equation with Calogero-Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.

Cited by

• Relationship between a Φ⁴ matrix model and harmonic oscillator systems

Related

• Relationship between a Φ⁴ matrix model and harmonic oscillator systems
• Integrability of Φ⁴ Matrix Model as N-body Harmonic Oscillator System
• Classical dynamical r-matrices for Calogero-Moser systems and their generalizations
• Matrix Versions of the Calogero Model
• Conformal mechanical treatment of Calogero-Moser model and infinite dimensional Lie algebra of conformal Galilei type