论 De Donder-Weyl 哈密顿表述下变形 Einstein-Cartan 规范引力中的宇宙学常数
On the cosmological constant in the deformed Einstein-Cartan gauge gravity in De Donder-Weyl Hamiltonian formulation
AI总结：
本文基于 De Donder-Weyl 哈密顿表述的协变正则规范引力理论，通过引入二次 Riemann-Cartan 项修改 Einstein-Hilbert 作用量，导出时空真空能量可抵消物质真空能量，从而为解决“宇宙学常数问题”提供了自然贡献。
摘要：
作为 Einstein-Hilbert 理论的一种修改，协变正则规范引力（CCGG）导出了一个宇宙学常数，该常数表示时空连续体从其 (A)dS 基态变形为平坦几何时的能量。CCGG 基于 De Donder-Weyl (DW) 哈密顿表述中的正则变换理论。该框架通过一个二次 Riemann-Cartan 伴随式修改了自由引力场的 Einstein-Hilbert 拉格朗日量。该理论预测时空与物质系统的总能量-动量消失，这与可追溯至 Lorentz (1916) 和 Levi-Civita (1917) 的“零能宇宙”猜想一致。因此，平坦几何只能在物质存在的情况下存在，此时物质的体真空能量，无论其值为何，都会被时空的真空能量抵消。观测到的宇宙学常数 $Λ_{\mathrm{obs}}$ 被发现仅是一个量级为 $10^{-120} \,λ_0$ 的小修正，归因于偏离平坦几何以及时空复杂动力学几何（即挠率）的效应，可能还包括物质和时空的真空涨落。广义相对论的这一二次扩展，早在 1918 年就由 Einstein 预见，因此为解决被称为“宇宙学常数问题”的 120 个数量级的错误估计提供了一个重要且自然的贡献。
英文摘要：
A modification of the Einstein-Hilbert theory, the Covariant Canonical Gauge Gravity (CCGG), leads to a cosmological constant that represents the energy of the space-time continuum when deformed from its (A)dS ground state to a flat geometry. CCGG is based on the canonical transformation theory in the De Donder-Weyl (DW) Hamiltonian formulation. That framework modifies the Einstein-Hilbert Lagrangian of the free gravitational field by a quadratic Riemann-Cartan concomitant. The theory predicts a total energy-momentum of the system of space-time and matter to vanish, in line with the conjecture of a "Zero-Energy-Universe" going back to Lorentz (1916) and Levi-Civita (1917). Consequently a flat geometry can only exist in presence of matter where the bulk vacuum energy of matter, regardless of its value, is eliminated by the vacuum energy of space-time.% $λ_0$. The observed cosmological constant $Λ_{\mathrm{obs}}$ is found to be merely a small correction %of the order $10^{-120} \,λ_0$ attributable to deviations from a flat geometry and effects of complex dynamical geometry of space-time, namely torsion and possibly also vacuum fluctuations of matter and space-time. That quadratic extension of General Relativity, anticipated already in 1918 by Einstein \cite{einstein18}, thus provides a significant and natural contribution to resolving the %$120$ orders of magnitude miss-estimate called the "cosmological constant problem".
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