Relationship between Φ⁴-matrix model and N-body harmonic oscillator or Calogero-Moser model

Autor(en)

H. Grosse, N. Kanomata, A. Sako, R. Wulkenhaar

Abstrakt

We study some Hermitian Φ⁴-matrix model and some real symmetric Φ⁴-matrix model whose kinetic terms are given by Tr(EΦ²), where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition functions of these matrix models correspond to zero-energy solutions of a Schödinger type equation with N-body harmonic oscillator Hamiltonian and Calogero-Moser Hamiltonian, respectively. The first half of this paper is primarily a review of previous work of us. The discussion of the properties of zero-energy solutions and the discussion of systems of differential equations satisfied by partition functions derived from the Virasoro algebra in the latter half of this paper contain novel material.

Organisation(en)

Forschungsplattform Internationales Erwin Schrödinger Institut für Mathematik und Physik, Mathematische Physik

Externe Organisation(en)

Tokyo University of Science, Universität Münster

Journal

Journal of Physics: Conference Series

Band

2912

Anzahl der Seiten

8

ISSN

1742-6588

DOI

https://doi.org/10.1088/1742-6596/2912/1/012014

Publikationsdatum

2024

Peer-reviewed

Ja

ÖFOS 2012

103019 Mathematische Physik

ASJC Scopus Sachgebiete

Allgemeine Physik und Astronomie

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/baf7d951-266d-449b-a7f1-4afcf86308af