Dynamical Mass Generation in QED: Miransky scaling and Schrödinger-like infinite well and barrier potentials supporting a bound state

IF 1.8 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Few-Body Systems Pub Date : 2025-09-22 DOI:10.1007/s00601-025-02010-x

Juan D. García-Muñoz, A. Alfaro, L. X. Gutiérrez-Guerrero, A. Raya

引用次数: 0

Abstract

In this study, we revisit the Schwinger–Dyson equation for the electron propagator in QED in three- and four-space–time dimensions. Our analysis addresses the non-perturbative phenomenon of dynamical chiral symmetry breaking which demands a critical value of the coupling for the dynamical generation of electron masses, encoded in the infrared behavior of the said Green function. With a minimalistic truncation of the infinite tower of equations and adopting standard assumptions, the resulting gap equation is linearized and transformed into a Schrödinger-like equation with an auxiliary potential barrier (well) subjected to boundary conditions for both high and low momenta. Then, the dynamical mass is associated with the zero mode of the corresponding Schrödinger-like operator and adheres to the Miransky scaling law, as expected.

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QED中的动态质量生成：Miransky标度和Schrödinger-like支持束缚态的无限阱势和势垒势

在这项研究中，我们在三维和四维时空中重新审视了QED中电子传播子的Schwinger-Dyson方程。我们的分析解决了动态手性对称破缺的非摄动现象，这需要一个电子质量动态产生的耦合临界值，编码在上述格林函数的红外行为中。通过对无限塔方程的极简截断并采用标准假设，将所得的间隙方程线性化并转换为具有高动量和低动量边界条件的辅助势垒（井）的Schrödinger-like方程。然后，将动态质量与相应Schrödinger-like算符的零模相关联，并如预期的那样遵循Miransky标度定律。

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

Few-Body Systems 物理-物理：综合

CiteScore

2.90

自引率

18.80%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal Few-Body Systems presents original research work – experimental, theoretical and computational – investigating the behavior of any classical or quantum system consisting of a small number of well-defined constituent structures. The focus is on the research methods, properties, and results characteristic of few-body systems. Examples of few-body systems range from few-quark states, light nuclear and hadronic systems; few-electron atomic systems and small molecules; and specific systems in condensed matter and surface physics (such as quantum dots and highly correlated trapped systems), up to and including large-scale celestial structures. Systems for which an equivalent one-body description is available or can be designed, and large systems for which specific many-body methods are needed are outside the scope of the journal. The journal is devoted to the publication of all aspects of few-body systems research and applications. While concentrating on few-body systems well-suited to rigorous solutions, the journal also encourages interdisciplinary contributions that foster common approaches and insights, introduce and benchmark the use of novel tools (e.g. machine learning) and develop relevant applications (e.g. few-body aspects in quantum technologies).