Operators for quantized directions

Type of Work

Article

Date

12-1999

Journal Title

Classical and Quantum Gravity

Journal ISSN

0264-9381

Journal Volume

16

Journal Issue

12

First Page

3859

Last Page

3877

DOI

10.1088/0264-9381/16/12/307

Abstract

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.

Hamilton Areas of Study

Physics

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