论文标题
不断发展的Stueckelberg-Horwitz-Piron指标的4+1形式主义
A 4+1 Formalism for the Evolving Stueckelberg-Horwitz-Piron Metric
论文作者
论文摘要
我们提出了一种在Stueckelberg--Horwitz--piron（SHP）一般相对论的本地指标的现场理论，在该框架中，经典的四维（4D）Worldlines $ X^μ\ x^μ\ weft（τ\ \ right）$（$μ= 0,1,1,2,3 $）的演变是由外部时间$ $ $ $ $。将SHP电动力学和ADM形式主义的见解结合在一起，我们将4D时空$ \ Mathcal {M} $的概念推广到正式的歧管$ \ Mathcal {M} _5 = \ Mathcal {M Mathcal {M} $ \ MATHCAL {M} $）和DYNAMICS（$ \ Mathcal {M} \ left（τ\ right）$的系统演变具有$τ\ in R $的单调提前）。从策略上破坏公制$ g_ {αβ}（x，τ）$（$α，β= 0,1,2,3,5 $）的正式5D对称性，在$ \ Mathcal {m} _5 $上构成了$ \ Mathcal {m}最初条件应满足的约束。所产生的理论与五维（5D）的引力不同，与SHP U（1）仪表理论不同于5D电动力学。
We propose a field theory for the local metric in Stueckelberg--Horwitz--Piron (SHP) general relativity, a framework in which the evolution of classical four-dimensional (4D) worldlines $x^μ\left( τ\right)$ ($μ= 0,1,2,3 $) is parameterized by an external time $τ$. Combining insights from SHP electrodynamics and the ADM formalism in general relativity, we generalize the notion of a 4D spacetime $\mathcal{M}$ to a formal manifold $\mathcal{M}_5 = \mathcal{M} \times R$, representing an admixture of geometry (the diffeomorphism invariance of $\mathcal{M}$) and dynamics (the system evolution of $\mathcal{M} \left( τ\right)$ with the monotonic advance of $τ\in R$). Strategically breaking the formal 5D symmetry of a metric $g_{αβ}(x,τ)$ ($α,β= 0,1,2,3,5 $) posed on $\mathcal{M}_5$, we obtain ten unconstrained Einstein equations for the $τ$-evolution of the 4D metric $γ_{μν}(x,τ)$ and five constraints that are to be satisfied by the initial conditions. The resulting theory differs from five-dimensional (5D) gravitation, much as SHP U(1) gauge theory differs from 5D electrodynamics.
