Integrability properties of Motzkin polynomials

Gahramanov, Ilmar; Musaev, Edvard T.

doi:10.1063/1.5018372

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Integrability properties of Motzkin polynomials

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Gahramanov, Ilmar
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Musaev, Edvard T.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Gahramanov, I., & Musaev, E. T. (2020). Integrability properties of Motzkin polynomials. Journal of Mathematical Physics, 61(3): 033509. doi:10.1063/1.5018372.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-8CAE-9

Abstract

We consider the Polchinski RG equation for a theory of matrix scalar fields
interacting with single trace operators and show that it can be written in a
Hamiltonian form for a specific choice of the cut-off function. The obtained
Hamiltonian equations are a non-linear generalization of the shock-wave
equation that is known to be integrable. We present an infinite tower of
conserved quantities and recover their relation to Motzkin polynomials.