arXiv 1207.72632012-07gr-qc

四维洛伦兹量子引力的仿射群表示形式

Affine group representation formalism for four dimensional, Lorentzian, quantum gravity

Chou Ching-Yi, Eyo Ita, Chopin Soo

备注：: 13 pages. Revised version
发表信息：: Class. Quantum Grav. 30 (2013) 065013
DOI：: 10.1088/0264-9381/30/6/065013

摘要：

在Ashtekar变量的上下文中，四维纯广义相对论的哈密顿约束与宇宙学常数，$Λ$，被重新表示为仿射代数的交换子的虚部的Chern-Simons功能，$Q$，和正定体积元素。这表明Klauder的仿射代数量子化程序确实可以应用于具有非零宇宙学常数的量子引力的完整Lorentz签名理论;并且它便于构造所有约束的解。仿射群的酉不可约表示展现出自然的希尔伯特空间结构，并且相干态和其他物理态可以从基准态生成。同样有趣的是，将哈密顿约束或惠勒-德维特方程表述为仿射代数需要一个非零的宇宙学常数;而$\frac{Δ{V}}{<{V}>}Δ{Q}\geq 2πΛL^2_{Planck}$形式的基本不确定关系（其中$V$是总体积）可以适用于量子引力的所有物理状态。

英文摘要：

Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $Λ$, is reexpressed as an affine algebra with the commutator of the imaginary part of the Chern-Simons functional, $Q$, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant; and it facilitates the construction of solutions to all of the constraints. Unitary, irreducible representations of the affine group exhibit a natural Hilbert space structure, and coherent states and other physical states can be generated from a fiducial state. It is also intriguing that formulation of the Hamiltonian constraint or Wheeler-DeWitt equation as an affine algebra requires a non-vanishing cosmological constant; and a fundamental uncertainty relation of the form $\frac{Δ{V}}{<{V}>}Δ{Q}\geq 2πΛL^2_{Planck}$ (wherein $V$ is the total volume) may apply to all physical states of quantum gravity.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文