一些经典粒子模型和量子规范理论

Q2 Physics and Astronomy Quantum Reports Pub Date : 2022-11-03 DOI:10.3390/quantum4040035
A. Akhmeteli
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引用次数: 0

摘要

本文综述了一些与量子力学解释和模拟著名量子规范理论相关的数学模型,如标量电动力学(Klein–Gordon–Maxwell电动力学)、旋量电动力学(Dirac–Maxwell电动力学)等。在这些模型中,进化通常用修正的Maxwell方程来描述。在标量电动力学的情况下,标量复波函数可以通过规范变换变为实,波函数可以从标量电动力学方程中代数消去,由此得到的修正麦克斯韦方程描述了电磁场的独立演化。旋量电动力学也得到了类似的结果。狄拉克旋量的四分之三分量可以从狄拉克方程中代数消去,剩下的分量可以通过规范变换变为实数。杨-米尔斯场中的狄拉克方程也得到了类似的结果。由于量子规范理论在现代物理学中发挥着核心作用,本文的方法可能足够通用。单粒子波函数可以建模为大量粒子和反粒子的类等离子体集合。这似乎能够模拟量子相空间分布函数,例如Wigner分布函数,这些函数不一定是非负的。
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Some Classical Models of Particles and Quantum Gauge Theories
The article contains a review and new results of some mathematical models relevant to the interpretation of quantum mechanics and emulating well-known quantum gauge theories, such as scalar electrodynamics (Klein–Gordon–Maxwell electrodynamics), spinor electrodynamics (Dirac–Maxwell electrodynamics), etc. In these models, evolution is typically described by modified Maxwell equations. In the case of scalar electrodynamics, the scalar complex wave function can be made real by a gauge transformation, the wave function can be algebraically eliminated from the equations of scalar electrodynamics, and the resulting modified Maxwell equations describe the independent evolution of the electromagnetic field. Similar results were obtained for spinor electrodynamics. Three out of four components of the Dirac spinor can be algebraically eliminated from the Dirac equation, and the remaining component can be made real by a gauge transformation. A similar result was obtained for the Dirac equation in the Yang–Mills field. As quantum gauge theories play a central role in modern physics, the approach of this article may be sufficiently general. One-particle wave functions can be modeled as plasma-like collections of a large number of particles and antiparticles. This seems to enable the simulation of quantum phase-space distribution functions, such as the Wigner distribution function, which are not necessarily non-negative.
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来源期刊
Quantum Reports
Quantum Reports Physics and Astronomy-Physics and Astronomy (miscellaneous)
CiteScore
3.30
自引率
0.00%
发文量
33
审稿时长
10 weeks
期刊最新文献
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