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首页> 外文期刊>American Journal of Space Science >SPACE TIME COVARIANCE OF CANONICAL QUANTIZATION OF GRAVITY: A (FORMAL) GENERAL RESULT AND THE (RIGOROUS) EXPLICIT CASE OF 2+1 QUANTUM COSMOLOGY
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SPACE TIME COVARIANCE OF CANONICAL QUANTIZATION OF GRAVITY: A (FORMAL) GENERAL RESULT AND THE (RIGOROUS) EXPLICIT CASE OF 2+1 QUANTUM COSMOLOGY

机译：重力规范化的时空协方差：（正式）一般结果和（严格）2 + 1量子宇宙学的显式情况

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摘要

A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), be-come weakly vanishing functions of the Quadratic and Linear Constraints. The implication of this result is that (formal) Dirac consistency of the Quantum Operator Constraints (annihilating the wave Function) suffices to guarantee space time covariance of the ensuing quantum theory: An ordering for each invariant relation will always exist such that the emanating operator has an eigenvalue identical to the classical value. The example of 2+1 Quantum Cosmology is explicitly considered: The four possible "Cosmological Solutions" -two for pure Einstein's equations plus two more when a A term is present- are exhibited and the corresponding models are quantized. The invariant relations describing the geometries are explicitly calculated and promoted to operators whose eigenvalues are their corresponding classical values.
机译：提出了一个一般的经典定理，根据该定理，当将时空标量标量之间的所有不变关系转换为全纯引力的相空间上的函数（使用经典的运动方程式）时，将变成二次函数和二次函数的弱消失函数。线性约束。该结果的含义是，量子算子约束的（形式）狄拉克一致性（消除波函数）足以保证随后的量子理论的时空协方差：每个不变关系的排序将始终存在，以使发散的算子具有与经典值相同的特征值。明确考虑了2 + 1量子宇宙学的示例：展示了四个可能的“宇宙学解”-两个用于纯爱因斯坦方程式，另外两个在存在A项时（如果存在A项），并且对相应的模型进行了量化。明确计算描述几何的不变关系，并将其推广给特征值为其对应经典值的算子。

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