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- W4312121471 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 respects 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." @default.
- W4312121471 created "2023-01-04" @default.
- W4312121471 creator A5044975740 @default.
- W4312121471 date "2022-12-22" @default.
- W4312121471 modified "2023-09-25" @default.
- W4312121471 title "Dispersion relations, knots polynomials, and the <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML display=inline><mml:mi>q</mml:mi></mml:math> -deformed harmonic oscillator" @default.
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- W4312121471 doi "https://doi.org/10.1103/physrevd.106.126019" @default.
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