量子电动力学的乘积图

IF 4.2 Q2 QUANTUM SCIENCE & TECHNOLOGY
B. S. Kay
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引用次数: 3

摘要

我们简要介绍了我们的工作,以提供量子电动力学(QED)的产品图片。我们的目标是补充最近在《物理学基础》上发表的一篇论文中的较长论述,并帮助使这项工作更容易获得。乘积图是QED的一个公式,等价于标准库仑规范QED,其中希尔伯特空间作为电磁场的希尔伯特空间和带电物质(即狄拉克场)的Hilbert空间的乘积(的某个物理子空间)产生,哈密顿量作为电磁哈密顿量、带电物质哈密顿量,以及交互项。(QED的库仑规范公式不是一个乘积图,因为在它中,电磁场的纵向部分是由带电物质算符组成的。)我们还记得QED的“矛盾交换子定理”,它暴露了以前QED的时间规范量化尝试中的缺陷,我们解释了我们的产品图片是如何提供克服这些缺陷的方法的。此外,我们还讨论了该定理可以推广到杨-米尔斯域的程度。我们还开发了与电磁场相互作用的非相对论带电粒子的乘积图,并指出这如何导致对具有库仑相互作用的许多非相对论电荷粒子理论的一种新的思考方式。在后记中,我们解释了为QED提供乘积图是如何给人们带来希望的,即人们将能够同样获得(杨·米尔斯和)量子引力的乘积图——后者是理解作者的物质-引力纠缠假说所必需的。此外,我们还简要讨论了这一假设与罗杰·彭罗斯的预测和想法之间的一些异同,这些预测和想法与引力在量子态还原中的可能作用有关,也与宇宙学熵有关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A product picture for quantum electrodynamics
We present a short account of our work to provide quantum electrodynamics (QED) with a product picture. We aim to complement the longer exposition in a recent paper in Foundations of Physics and to help to make that work more accessible. The product picture is a formulation of QED, equivalent to standard Coulomb gauge QED, in which the Hilbert space arises as (a certain physical subspace of) a product of a Hilbert space for the electromagnetic field and a Hilbert space for charged matter (i.e., the Dirac field) and the Hamiltonian arises as the sum of an electromagnetic Hamiltonian, a charged matter Hamiltonian, and an interaction term. (The Coulomb gauge formulation of QED is not a product picture because, in it, the longitudinal part of the electromagnetic field is made out of charged matter operators.) We also recall a “Contradictory Commutator Theorem” for QED, which exposes flaws in previous attempts at temporal gauge quantization of QED, and we explain how our product picture appears to offer a way to overcome those flaws. Additionally, we discuss the extent to which that theorem may be generalized to Yang–Mills fields. We also develop a product picture for nonrelativistic charged particles in interaction with the electromagnetic field and point out how this leads to a novel way of thinking about the theory of many nonrelativistic electrically charged particles with Coulomb interactions. In an afterword, we explain how the provision of a product picture for QED gives hope that one will be able likewise to have a product picture for (Yang Mills and for) quantum gravity—the latter being needed to make sense of the author's matter-gravity entanglement hypothesis. Also, we briefly discuss some similarities and differences between that hypothesis and its predictions and ideas of Roger Penrose related to a possible role of gravity in quantum state reduction and related to cosmological entropy.
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CiteScore
9.90
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