尺度不变性的作用原理及其应用(第一部分)

IF 2.2 3区 综合性期刊 Q2 MULTIDISCIPLINARY SCIENCES Symmetry-Basel Pub Date : 2023-10-24 DOI:10.3390/sym15111966
Andre Maeder, Vesselin G. Gueorguiev
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引用次数: 1

摘要

在一般作用原理的基础上,我们用狄拉克(1973)的协张量关系重新讨论了尺度不变场方程。这一作用原理也导致了尺度因子λ的表达式,它对应于测量条件,假设宏观空间是尺度不变的,均匀的,各向同性。这些结果加强了尺度不变真空(SIV)范式的基础。从场方程和测地线方程中,我们以当前的时间单位(年、秒)推导出类牛顿方程、二体问题方程及其长期变化。在双体系统中,轨道会轻微膨胀,而在膨胀过程中轨道速度保持恒定。有趣的是,开普勒第三定律是一个显著的尺度不变性质。
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Action Principle for Scale Invariance and Applications (Part I)
On the basis of a general action principle, we revisit the scale invariant field equation using the cotensor relations by Dirac (1973). This action principle also leads to an expression for the scale factor λ, which corresponds to the one derived from the gauging condition, which assumes that a macroscopic empty space is scale-invariant, homogeneous, and isotropic. These results strengthen the basis of the scale-invariant vacuum (SIV) paradigm. From the field and geodesic equations, we derive, in current time units (years, seconds), the Newton-like equation, the equations of the two-body problem, and its secular variations. In a two-body system, orbits very slightly expand, while the orbital velocity keeps constant during expansion. Interestingly enough, Kepler’s third law is a remarkable scale-invariant property.
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来源期刊
Symmetry-Basel
Symmetry-Basel MULTIDISCIPLINARY SCIENCES-
CiteScore
5.40
自引率
11.10%
发文量
2276
审稿时长
14.88 days
期刊介绍: Symmetry (ISSN 2073-8994), an international and interdisciplinary scientific journal, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish their experimental and theoretical research in as much detail as possible. There is no restriction on the length of the papers. Full experimental and/or methodical details must be provided, so that results can be reproduced.
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