Coherent Soft‐Photon States and Infrared Divergences. I. Classical Currents
Coherent Soft‐Photon States and Infrared Divergences. I. Classical Currents
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相干软光子态和红外发散 I. 经典电流。
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发表时间：
1968
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通讯作者：
T. Kibble
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作者：
T. Kibble
作为处理无红外发散和避免引入虚光子质量的软光子过程的第一步，讨论了属于非Fock表示的渐近光子态的规范。与钟的工作一样，使用了由广义相干态组成的基，但与他的工作不同的是，这些态是根据冯·诺伊曼的无限张量积严格定义的。结果表明，必须给这些态一个附加的标号，这个标号用来区分各种“弱等价”的矢量，并且形式上对应于一个无限大的相因子。定义了一个不可分的Hilbert空间HIR(无限张量积空间的一个子空间)，它可以看作是所有可能的渐近光子态的空间。讨论了电磁场与给定的经典电流分布之间的相互作用，并证明了矩阵元素为有限的么正S算子可以是有限的。
As a first step toward a treatment of soft‐photon processes which is free of infrared divergences and avoids the necessity of introducing a fictitious photon mass, the specification of asymptotic photon states belonging to non‐Fock representations is discussed. As in the work of Chung, a basis consisting of generalized coherent states is used, but in contrast to his work, these states are rigorously defined in terms of von Neumann's infinite tensor product. It is shown that the states must be given an additional label which serves to distinguish various ``weakly equivalent'' vectors, and which corresponds formally to an infinite phase factor. A nonseparable Hilbert space HIR is defined (as a subspace of the infinite tensor‐product space) which may be regarded as the space of all possible asymptotic photon states. The interaction of the electromagnetic field with a prescribed classical current distribution is discussed, and it is shown that a unitary S operator, all of whose matrix elements are finite, may...