论文标题
分散关系，打结多项式和$ Q $形式的谐波振荡器
Dispersion relations, knot polynomials and the $q$-deformed harmonic oscillator
论文作者
论文摘要
我们表明，用于2-2个散射的交叉对称分散关系（CSDR）导致与打结多项式和Q呈现的代数的迷人联系。特别是，可以自然地通过与圆环结$（2,2n+1）$相对应的亚历山大多项式的生成函数来自然识别。振幅低能膨胀系数的某些线性组合可以根据结的不变性而界定。 PION S-MATRIX Bootstrap数据尊重所获得的分析界限。我们将$ q $ formed的谐波振荡器与CSDR结图片相关联。特别是，可以将散射振幅视为涉及$ Q $ $ Q $变形的谐波振荡器的$ Q $平均热两个点功能。低温膨胀系数正是$ q $平均的亚历山大结多项式。
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.
