论文标题
bialynicki-birula和Landau-Peierls Fock空间量化电磁场位于位置表示的同构
Isomorphism between the Bialynicki-Birula and the Landau-Peierls Fock space quantization of the electromagnetic field in position representation
论文作者
论文摘要
我们首先使用两种主要方法：基于Riemann-Silberstein Vector，我们首先介绍了位置空间表示中电磁场在位置空间表示中的量化。我们在一个从经典的哈密顿结构开始的框架中描述了这两者，并通过确切的对应关系原理在骨髓的Fock空间中构建量子模型。我们证明这两个批准是完全等效的。这是通过证明Fock空间之间存在统一图来提出的，这使它们成为同构。由于所有物理可测量的数量都可以用标量产品表示，因此这意味着两个量化导致了完全相同的物理特性。我们进一步表明，在时间演变中保存了同构。为了显示等效性，我们使用螺旋性和频率运算符的概念。这两个操作员的组合提供了一种公式，该公式可以以精确的方式在这两种量化方法之间建立链接。我们还表明，可以通过类似于麦克斯韦方程的规范变量的替代选择来执行双林基 - 双核量化的构造，该量子避免了哈密顿量中的负特征值的存在。
We first present a summary of the quantization of the electromagnetic field in position space representation, using two main approaches: the Landau-Peierls approach in the Coulomb gauge and the Bialynicki-Birula approach, based on the Riemann-Silberstein vector. We describe both in a framework that starts with a classical Hamiltonian structure and builds the quantum model in a bosonic Fock space by a precisely defined principle of correspondence. We show that the two approches are completly equivalent. This is formulated by showing that there is a unitary map between the Fock spaces that makes them isomorphic. Since all the physically measurable quantities can be expressed in terms of scalar products, this implies that the two quantizations lead to exactly the same physical properties. We show furthemore that the isomorphism is preserved in the time evolutions. To show the equivalence, we use the concepts of helicity and frequency operators. The combination of these two operators provides a formulation that allows one to make the link between these two methods of quantization in a precise way. We also show that the construction in the Bialynicki-Birula quantization that avoids the presence of negative eigenvalues in the Hamiltonian, in analogy with the one for the Dirac equation for electrons and positrons, can be performed through an alternative choice of the canonical variables for Maxwell's equations.
