On the uniqueness of a purely elastic S-matrix in (1+1) dimensions
On the uniqueness of a purely elastic S-matrix in (1+1) dimensions
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(1 1)维纯弹性S矩阵的唯一性
DOI：
10.1016/0370-2693(77)90382-3
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发表时间：
1977
期刊：
影响因子：
--
通讯作者：
P. Weisz
中科院分区：
文献类型：
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作者：
M. Karowski;H. Thun;T. T. Truong;P. Weisz
本文证明了在不存在粒子产生、粒子-反粒子非零后向散射和分解为两体S-矩阵的条件下，（1+ 1）维单质量费米子模型f的S-矩阵是唯一确定的。粒子产生和因式分解的缺乏[2]被认为是由一组无限的守恒局部电流[3]的存在所暗示的。这样得到的S矩阵是最近由Zamolodchikov [4]提出的大质量Thirring模型（sine-Gordon理论）的S矩阵。然而，作者是在下列假设的基础上得出这一结果的：（a）在两个动量快度差的复平面上，所有两体散射振幅都是亚纯的。(b)准经典束缚态谱的精确性。(c)2体反射振幅在”耦合”常数X的整数值处消失。(d)没有共振。在这里，我们只采用假设（a）;可以看出，（B）、（c）和（d）是一般性质的结果。
In this letter we show that the S-matrix of a (1+ 1) dimensional model of a single massive fermion f is uniquely determined if we assume absence of particle production, non-vanishing backward particle-antiparticle scattering and factorization [1] into 2-body S-matrices. The absence of particle production and factorization [2] are known to be implied by the existence of an infinite set of conserved local currents [3]. The S-matrix thus obtained is that of the massive Thirring model (sine-Gordon theory) proposed recently by Zamolodchikov [4]. However, this author derives his result on the basis of the following assumptions:(a) Meromorphy of all 2-body scattering amplitudes in the complex plane of the rapidity difference of the two momenta.(b) Exactness of the quasi-classical bound state spectrum.(c) Vanishing of the 2-body reflection amplitude at integer values of the" coupling" constant X.(d) Absence of resonances. Here in our treatment only assumption (a) is adopted; it will be seen that (b),(c), and (d) are consequences of the general properties.