Operators for quantized directions

Details Operators for quantized directions Operators for quantized directions

1999-05-06

arxiv.org/abs/gr-qc/9905019v2

Class.Quant.Grav. 16 (1999) 3859-3877

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

v1: 20 pages, 23 figures v2: changes in presentation and regularization (final results unchanged). This is an expanded version

Scientific paper

10.1088/0264-9381/16/12/307

Inspired by the spin geometry theorem, two operators are defined which measure angles in the quantum theory of geometry. One operator assigns a discrete angle to every pair of surfaces passing through a single vertex of a spin network. This operator, which is effectively the cosine of an angle, is defined via a scalar product density operator and the area operator. The second operator assigns an angle to two ``bundles'' of edges incident to a single vertex. While somewhat more complicated than the earlier geometric operators, there are a number of properties that are investigated including the full spectrum of several operators and, using results of the spin geometry theorem, conditions to ensure that semiclassical geometry states replicate classical angles.

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