# A length operator for canonical quantum gravity

Thiemann T (1998)

**Publication Status:** Published

**Publication Type:** Journal article

**Publication year:** 1998

### Journal

**Publisher:** AMER INST PHYSICS

**Book Volume:** 39

**Pages Range:** 3372-3392

**Journal Issue:** 6

### Abstract

We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which an SU(2) connection is diagonal and it is therefore surprising that the operator obtained after regularization is densely defined, does not suffer from factor ordering singularities, and does not require any renormalization. We show that the length operator admits self-adjoint extensions and compute part of its spectrum which, like its companions, the volume and area operators already constructed in the literature, is purely discrete and roughly quantized in units of the Planck length. The length operator contains full and direct information about all the components of the metric tensor which facilitates the construction of so-called weave states which approximate a given classical three-geometry. (C) 1998 American Institute of Physics.

### Authors with CRIS profile

### How to cite

**APA:**

Thiemann, T. (1998). A length operator for canonical quantum gravity. *Journal of Mathematical Physics*, *39*(6), 3372-3392.

**MLA:**

Thiemann, Thomas. "A length operator for canonical quantum gravity." *Journal of Mathematical Physics* 39.6 (1998): 3372-3392.

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