论文标题
QFT中的交叉对称分散关系
Crossing Symmetric Dispersion Relations in QFTs
论文作者
论文摘要
对于量子场理论中的2-2个散射，通常的固定$ t $色散关系仅表现出两道通道对称性。本文考虑了交叉对称的分散关系，在1970年代恢复了某些旧思想。这不是固定的$ t $分散关系，而是在不同的变量$ z $中具有分散关系，这与曼德尔斯坦不变性$ s，t，u $有关，通过参数立方关系，使复杂$ z $ z $ z $平面的交叉对称性成为几何旋转。所得的分散体显然是三通道交叉对称的。我们为有效场理论（包括无效的限制条件）提供了某些已知阳性条件的简单推导，这些条件导致了两个方面的边界并得出了一系列新的非扰动不平等。我们展示了这些不平等现象如何使我们能够从II型字符串理论中四个DILATON振幅的低能量扩展中找到第一个巨大的弦状态。我们还展示了如何从这种方法中获得广义的（数值）Froissart结合，对所有能量有效。
For 2-2 scattering in quantum field theories, the usual fixed $t$ dispersion relation exhibits only two-channel symmetry. This paper considers a crossing symmetric dispersion relation, reviving certain old ideas in the 1970s. Rather than the fixed $t$ dispersion relation, this needs a dispersion relation in a different variable $z$, which is related to the Mandelstam invariants $s,t,u$ via a parametric cubic relation making the crossing symmetry in the complex $z$ plane a geometric rotation. The resulting dispersion is manifestly three-channel crossing symmetric. We give simple derivations of certain known positivity conditions for effective field theories, including the null constraints, which lead to two sided bounds and derive a general set of new non-perturbative inequalities. We show how these inequalities enable us to locate the first massive string state from a low energy expansion of the four dilaton amplitude in type II string theory. We also show how a generalized (numerical) Froissart bound, valid for all energies, is obtained from this approach.
