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Dispersion relations, knots polynomials, and the q -deformed harmonic oscillator

Sinha, A (2022) Dispersion relations, knots polynomials, and the q -deformed harmonic oscillator. In: Physical Review D, 106 (12).

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Official URL: https://doi.org/10.1103/PhysRevD.106.126019


We show that the crossing symmetric dispersion relation (CSDR) for 2-2 scattering leads to a fascinating connection with knot polynomials and q-deformed algebras. In particular, the dispersive kernel can be identified naturally in terms of the generating function for the Alexander polynomials corresponding to the torus knot (2,2n+1) arising in knot theory. Certain linear combinations of the low energy expansion coefficients of the amplitude can be bounded in terms of knot invariants. Pion S-matrix bootstrap data respect the analytic bounds so obtained. We correlate the q-deformed harmonic oscillator with the CSDR-knot picture. In particular, the scattering amplitude can be thought of as a q-averaged thermal two-point function involving the q-deformed harmonic oscillator. The low temperature expansion coefficients are precisely the q-averaged Alexander knot polynomials. © 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.

Item Type: Journal Article
Publication: Physical Review D
Publisher: American Physical Society
Additional Information: The copyright for this article belongs to the Authors.
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Date Deposited: 27 Jan 2023 09:15
Last Modified: 27 Jan 2023 09:15
URI: https://eprints.iisc.ac.in/id/eprint/79544

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