Wick-Cutkosky模型非线性推广中的约束相互作用
Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model
摘要：
我们考虑Wick-Cutkosky模型的非线性介导场推广。使用迭代的方法和消除介导场的协变格林函数的装置，我们到达一个拉格朗日密度包含多点的时间非局部相互作用项。在$ϕ^3{+}ϕ^4$理论的低阶近似下，我们得到了通常的两个电流相互作用以及限制型的三个电流相互作用。对于偶极模型的一个版本，在没有近似的情况下获得相同的结果。过渡到哈密顿形式主义和随后的正则量子化进行与时间非局域性考虑近似。利用三粒子Fock空间试探态，变分导出了相对论性三粒子波动方程。得到了该方程的非相对论极限，并对其性质进行了分析和讨论。
英文摘要：
We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky model. Using an iterative approach and eliminating the mediating field by means of the covariant Green function we arrive at a Lagrangian density containing many-point time-nonlocal interaction terms. In low-order approximations of $ϕ^3{+}ϕ^4$ theory we obtain the usual two-current interaction as well as a three-current interaction of a confining type. The same result is obtained without approximation for a version of the dipole model. The transition to the Hamiltonian formalism and subsequent canonical quantization is performed with time non-locality taken into account approximately. A relativistic three-particle wave equation is derived variationally by using a three-particle Fock space trial state. The non-relativistic limit of this equation is obtained and its properties are analyzed and discussed.
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