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