DISCRETENESS OF AREA AND VOLUME IN QUANTUM-GRAVITY

被引:849
作者
ROVELLI, C [1 ]
SMOLIN, L [1 ]
机构
[1] PENN STATE UNIV,CTR GRAVITAT PHYS & GEOMETRY,DEPT PHYS,UNIVERSITY PK,PA 16802
基金
美国国家科学基金会;
关键词
D O I
10.1016/0550-3213(95)00150-Q
中图分类号
O412 [相对论、场论]; O572.2 [粒子物理学];
学科分类号
摘要
We study the operator that corresponds to the measurement of volume, in non-perturbative quantum gravity, and we compute its spectrum, The operator is constructed in the loop representation, via a regularization procedure; it is finite, background independent, and diffeomorphism-invariant, and therefore well. defined on the space of diffeomorphism invariant states (knot states). We find that the spectrum of the volume of any physical region is discrete. A family of eigenstates are in one to one correspondence with the spin networks, which were introduced by Penrose in a different context. We compute the corresponding component of the spectrum, and exhibit the eignvalues explicitly, The other eigenstates are related to a generalization of the spin networks, and their eigenvalues can be computed by diagonalizing finite dimensional matrices. Furthermore, we show that the eigenstates of the volume diagonalize also the area operator. We argue that the spectra of volume and area determined here can be considered as predictions of the loop-representation formulation of quantum gravity on the outcomes of (hypothetical) Planck-scale sensitive measurements of the geometry of space.
引用
收藏
页码:593 / 619
页数:27
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