Integrability of Φ4 matrix model as N-body harmonic oscillator system

Harald Grosse; Akifumi Sako

doi:10.1007/s11005-024-01783-2

Integrability of Φ4 matrix model as N-body harmonic oscillator system

Harald Grosse, Akifumi Sako

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We study a Hermitian matrix model with a kinetic term given by Tr(HΦ²), where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential Φ³ replaced by Φ⁴. We show that its partition function solves an integrable Schrödinger-type equation for a non-interacting N-body Harmonic oscillator system.

Original language	English
Article number	48
Journal	Letters in Mathematical Physics
Volume	114
Issue number	2
DOIs	https://doi.org/10.1007/s11005-024-01783-2
Publication status	Published - Apr 2024

Keywords

81R10
81R12
81T32
81T75
Harmonic oscillator
Integrable model
Matrix model
Noncommutative geometry

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10.1007/s11005-024-01783-2

Cite this

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abstract = "We study a Hermitian matrix model with a kinetic term given by Tr(HΦ2), where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential Φ3 replaced by Φ4. We show that its partition function solves an integrable Schr{\"o}dinger-type equation for a non-interacting N-body Harmonic oscillator system.",

keywords = "81R10, 81R12, 81T32, 81T75, Harmonic oscillator, Integrable model, Matrix model, Noncommutative geometry",

author = "Harald Grosse and Akifumi Sako",

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AU - Sako, Akifumi

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N2 - We study a Hermitian matrix model with a kinetic term given by Tr(HΦ2), where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential Φ3 replaced by Φ4. We show that its partition function solves an integrable Schrödinger-type equation for a non-interacting N-body Harmonic oscillator system.

AB - We study a Hermitian matrix model with a kinetic term given by Tr(HΦ2), where H is a positive definite Hermitian matrix, similar as in the Kontsevich Matrix model, but with its potential Φ3 replaced by Φ4. We show that its partition function solves an integrable Schrödinger-type equation for a non-interacting N-body Harmonic oscillator system.

KW - 81R10

KW - 81R12

KW - 81T32

KW - 81T75

KW - Harmonic oscillator

KW - Integrable model

KW - Matrix model

KW - Noncommutative geometry

UR - https://www.scopus.com/pages/publications/85188506836

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DO - 10.1007/s11005-024-01783-2

M3 - Article

AN - SCOPUS:85188506836

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VL - 114

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 2

M1 - 48

ER -

Integrability of Φ4 matrix model as N-body harmonic oscillator system

Abstract

Keywords

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