发表机构
Shinshu University; Komatsu University（信州大学; 小松大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究含外势的克莱因-戈登方程量子化产生的正则对易关系的Weyl表示，发现质量不同时表示不等价，质量相同时等价性转变在势差衰减率-3/2处，与散射理论短程条件的-1衰减率不同。
AI 中文摘要
我们研究描述受外势影响的量子化有质量标量场模型的正则对易关系的Weyl表示。主要问题是确定当质量和/或势发生变化时，Weyl表示是否仍等价于原始表示或变得不等价。该问题被简化为对Schrödinger算子的研究。结果表明，当质量不同时，Weyl表示是不等价的；当质量相同时，等价与不等价之间的转变发生在势差的衰减率为-3/2处，这与散射理论中定义短程条件的衰减率-1形成对比。
英文摘要
We investigate the Weyl representation of the canonical commutation relations for a model describing a quantized massive scalar field under the influence of an external potential. The main problem is to determine whether the Weyl representation remains equivalent to or becomes inequivalent to the original one when the mass and/or potential are changed. This problem is reduced to the study of Schrödinger operators. It turns out that the Weyl representations are inequivalent when the masses differ. Moreover, when the masses are the same, the transition between equivalence and inequivalence occurs at the decay rate $-3/2$ of the difference between the potentials. This contrasts with the decay rate $-1$ that defines the short-range condition in scattering theory.
Comments29 pages
