The Quantum Theory of Fields: THE CLUSTER DECOMPOSITION PRINCIPLE
The Quantum Theory of Fields: THE CLUSTER DECOMPOSITION PRINCIPLE
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DOI：
10.1017/cbo9781139644167.006
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发表时间：
1995-06
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影响因子：
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通讯作者：
S. Weinberg
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文献类型：
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作者：
S. Weinberg
到目前为止，我们还没有太多关于哈密顿算子H的详细结构的讨论。这个算子可以通过给出任意数量粒子的状态之间的所有矩阵元素来定义。等价地，正如我们将在这里展示的，任何这样的算符都可以表示为某些产生和消灭单个粒子的算符的函数。我们在第一章中已经看到，在量子力学的早期，在电磁场和其他场的正则量子化中，我们第一次遇到了这种创造和湮灭算符。他们为理论提供了一种自然的形式主义，在这种理论中，大质量粒子和光子可以产生和毁灭，始于20世纪30年代初的费米β衰变理论。然而，用产生和湮灭算符来构造哈密顿量还有更深层次的原因，这超出了对任何先前存在的场论（如电动力学）的解释，与粒子是否真的能产生或消灭无关。这种形式主义的最大优点是，如果我们将哈密顿量表示为产生算符和湮灭算符的乘积之和，加上适当的非奇异系数，那么S矩阵将自动满足一个关键的物理要求，即集团分解原理，这实际上表明，远距离实验产生不相关的结果。事实上，正是由于这个原因，创造和湮灭算符的形式主义被广泛用于非相对论量子统计力学，其中粒子的数量通常是固定的。
Up to this point we have not had much to say about the detailed structure of the Hamiltonian operator H . This operator can be defined by giving all its matrix elements between states with arbitrary numbers of particles. Equivalently, as we shall show here, any such operator may be expressed as a function of certain operators that create and destroy single particles. We saw in Chapter 1 that such creation and annihilation operators were first encountered in the canonical quantization of the electromagnetic field and other fields in the early days of quantum mechanics. They provided a natural formalism for theories in which massive particles as well as photons can be produced and destroyed, beginning in the early 1930s with Fermi's theory of beta decay. However, there is a deeper reason for constructing the Hamiltonian out of creation and annihilation operators, which goes beyond the need to quantize any pre-existing field theory like electrodynamics, and has nothing to do with whether particles can actually be produced or destroyed. The great advantage of this formalism is that if we express the Hamiltonian as a sum of products of creation and annihilation operators, with suitable non-singular coefficients, then the S -matrix will automatically satisfy a crucial physical requirement, the cluster decomposition principle, which says in effect that distant experiments yield uncorrelated results. Indeed, it is for this reason that the formalism of creation and annihilation operators is widely used in non-relativistic quantum statistical mechanics, where the number of particles is typically fixed.