How Anomalous is the Electron’s Magnetic Moment?

IF 1 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2025-06-07 DOI:10.1007/s10701-025-00846-1

Charles T. Sebens

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Abstract

The electron’s spin magnetic moment is ordinarily described as anomalous in comparison to what one would expect from the Dirac equation. But, what exactly should one expect from the Dirac equation? The standard answer would be the Bohr magneton, which is a simple estimate of the electron’s spin magnetic moment that can be derived from the Dirac equation either by taking the non-relativistic limit to arrive at the Pauli equation or by examining the Gordon decomposition of the electron’s current density. However, these derivations ignore two effects that are central to quantum field theoretic calculations of the electron’s magnetic moment: self-interaction and mass renormalization. Those two effects can and should be incorporated when analyzing the Dirac equation, to better isolate the distinctive improvements of quantum field theory. Either of the two aforementioned derivations can be modified accordingly. Doing so yields a magnetic moment that depends on the electron’s state (even among z-spin up states). This poses a puzzle for future research: How does the move to quantum field theory take you from a state-dependent magnetic moment to a fixed magnetic moment?

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电子的磁矩有多反常？

与狄拉克方程相比，电子的自旋磁矩通常被描述为异常。但是，我们应该从狄拉克方程中期待什么呢？标准的答案是玻尔磁子，它是对电子自旋磁矩的一个简单估计，可以从狄拉克方程中推导出来，或者通过非相对论极限得到泡利方程，或者通过检查电子电流密度的戈登分解。然而，这些推导忽略了两个对电子磁矩量子场论计算至关重要的效应：自相互作用和质量重整化。在分析狄拉克方程时，可以也应该把这两种效应结合起来，以更好地区分量子场论的显著改进。上述两个推导中的任何一个都可以进行相应的修改。这样做会产生一个磁矩，这个磁矩取决于电子的状态（即使是在z自旋向上的状态中）。这给未来的研究提出了一个难题：量子场论是如何把你从一个依赖状态的磁矩带到一个固定的磁矩的？

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.