# Closed formula for the matrix elements of the volume operator in 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:** 3347-3371

**Journal Issue:** 6

### Abstract

We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four space-time dimensions in the continuum in a spin-network basis. We also display a new technique of regularization which is state dependent but we are forced to it in order to maintain diffeomorphism covariance and in that sense it is natural. We arrive naturally at the expression for the volume operator as defined by Ashtekar and Lewandowski up to a state-independent factor. (C) 1998 American Institute of Physics.

### Authors with CRIS profile

### How to cite

**APA:**

Thiemann, T. (1998). Closed formula for the matrix elements of the volume operator in canonical quantum gravity. *Journal of Mathematical Physics*, *39*(6), 3347-3371.

**MLA:**

Thiemann, Thomas. "Closed formula for the matrix elements of the volume operator in canonical quantum gravity." *Journal of Mathematical Physics* 39.6 (1998): 3347-3371.

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