关于导致具有不定度量和非平凡S-矩阵的局部相对论QFT的SPDE的公式化
On the formulation of SPDEs leading to local, relativistic QFTs with indefinite metric and nontrivial S-matrix
摘要：
本文讨论欧氏协变向量随机场作为$DA=η$形式的随机偏微分方程的解，其中$D$是一个协变（w.r.t.具有“正质谱”的$SO(d)$）微分算子和$η$的表示τ是非高斯白噪声。利用Becker，Gielerak和Lugewicz讨论的Schwinger函数的解析延拓，得到了Fourier变换截断Wightman函数的显式公式.基于这些公式，我们给出了$D$的质量谱的充分必要条件，这些条件意味着相对论量子矢量场对给定的Wightman函数序列的非平凡散射行为.我们明确地计算散射振幅，我们发现，在所获得的理论中的粒子的质量是由$D$的质谱。
英文摘要：
We discuss Euclidean covariant vector random fields as the solution of stochastic partial differential equations of the form $DA=η$, where $D$ is a covariant (w.r.t. a representation τof $SO(d)$) differential operator with "positive mass spectrum" and $η$ is a non-Gaussian white noise. We obtain explicit formulae for the Fourier transformed truncated Wightman functions, using the analytic continuation of Schwinger functions discussed by Becker, Gielerak and Lugewicz. Based on these formulae we give necessary and sufficient conditions on the mass spectrum of $D$ which imply nontrivial scattering behaviour of relativistic quantum vector fields associated to the given sequence of Wightman functions. We compute the scattering amplitudes explicitly and we find that the masses of particles in the obtained theory are determined by the mass spectrum of $D$.
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