论文标题
正常排序正常模式
Normal Ordering Normal Modes
论文作者
论文摘要
在量子场理论的孤儿扇区中，通常以正常模式扩展量子场通常很方便。正常的模式创建和歼灭操作员可以正常排序，其正常有序的产品在单环孤子基态中的期望值消失了。然而，该理论的哈密顿量通常是基于创建平面波的运算符的正常秩序。在本文中，我们找到了两个正常订单之间的ick映射。出于具体性，我们将注意力限制在1+1个维度上的Schrodinger图片标量字段，尽管我们期望我们的结果很容易概括此案。我们发现，平面波订购的$ n $ - 点功能是术语的总和，将零模式，呼吸和连续性常规模式的$ j $点功能分解为$ j $ - 点函数。我们在$ j $中找到一个递归公式，对于同一时刻的田野产品，我们在所有$ j $上解决了递归公式。
In a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have vanishing expectation values in the one-loop soliton ground state. The Hamiltonian of the theory, however, is usually normal ordered in the basis of operators which create plane waves. In this paper we find the Wick map between the two normal orderings. For concreteness, we restrict our attention to Schrodinger picture scalar fields in 1+1 dimensions, although we expect that our results readily generalize beyond this case. We find that plane wave ordered $n$-point functions of fields are sums of terms which factorize into $j$-point functions of zero modes, breather and continuum normal modes. We find a recursion formula in $j$ and, for products of fields at the same point, we solve the recursion formula at all $j$.
