T>T_c弱磁场中伊辛场论的非弹性散射和弹性振幅。微扰分析
Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at T>T_c. Perturbative analysis
摘要：
本文用微扰理论研究了弱磁场h中T>T_c的伊辛场论中的两粒子散射。我们明确地计算了过程2->3的h^2阶的截面。在这个量级上，在所有能量E下，相应的横截面支配着总横截面（所有非弹性过程的概率）。我们证明了在高能量下，总截面中的h^2项增长为16 G_3 h^2 log（E），其中G_3正好是欧几里得自旋-自旋关联函数的三阶矩。超越首阶，我们认为在小h^2时，2->2过程的概率随着E^（-16G_3 h^2）衰减为E->无穷大。
英文摘要：
Two-particle scattering in Ising field theory in a weak magnetic field h is studied in the regime T>T_c, using perturbation theory in h^2. We calculate explicitly the cross-section of the process 2->3 to the order h^2. To this order, the corresponding cross-section dominates the total cross-section (the probability of all inelastic processes) at all energies E. We show that at high energies the h^2 term in the total cross-section grows as 16 G_3 h^2 log(E) where G_3 is exactly the third moment of the Euclidean spin-spin correlation function. Going beyond the leading order, we argue that at small h^2 the probability of the 2->2 process decays as E^(-16G_3 h^2) as E->infinity.
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