Algebra of Classical and Quantum Binary Measurements

• 作者: Carl A. Brannen
• 来源期刊: 现代物理(英文)
• 学科: 数学
• 关键词: QUANTUM MECHANICS SCHWINGER Measurement ALGEBRA QUANTUM THERMODYNAMICS
• 年，卷（期）: 2018,（4）
• 页码范围: 628-650
• 页数: 23页
• 分类号: O1

摘要

The simplest measurements in physics are binary;that is, they have only two possible results. An example is a beam splitter. One can take the output of a beam splitter and use it as the input of another beam splitter. The compound measurement is described by the product of the Hermitian matrices that describe the beam splitters. In the classical case, the Hermitian matrices commute (are diagonal) and the measurements can be taken in any order. The general quantum situation was described by Julian Schwinger with what is now known as “Schwinger’s Measurement Algebra”. We simplify his results by restriction to binary measurements and extend it to include classical as well as imperfect and thermal beam splitters. We use elementary methods to introduce advanced subjects such as geometric phase, Berry-Pancharatnam phase, superselection sectors, symmetries and applications to the identities of the Standard Model fermions.