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Journal Article

Integrability properties of Motzkin polynomials

MPS-Authors
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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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1706.00197.pdf
(Preprint), 548KB

1706.00197v2.pdf
(Preprint), 137KB

1.5018372.pdf
(Publisher version), 5MB

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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: http://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.