https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=95.146.224.76formulasearchengine - User contributions [en]2026-08-15T09:22:56ZUser contributionsMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Devil%27s_curve&diff=17550Devil's curve2013-06-09T22:57:20Z<p>95.146.224.76: </p>
<hr />
<div><br />
A [[quantum field theory]] of [[General Relativity]] provides [[Operator (mathematics)|operators]] that measure the [[geometry]] of [[space time]]. The volume operator <math>V(R)</math> of a region <math>R</math> is defined as the operator that yields the expectation value of a volume measurement of the region <math>R</math>, given a state <math>\psi</math> of quantum General Relativity. I.e.<math>\lang \psi, V(R) \psi \rang</math> is the expectation value for the volume of <math>R</math>. [[Loop Quantum Gravity]], for example, provides volume operators, area operators and length operators for regions, surfaces and path respectively. <br />
<br />
==Sources==<br />
*[[Carlo Rovelli]] and [[Lee Smolin]], [http://arxiv.org/abs/gr-qc/9411005 "Discreteness of Area and Volume in Quantum Gravity", Nuclear Physics B 442, 593 (1995)].<br />
<br />
*[[Abhay Ashtekar]] and [[Jerzy Lewandowski]], [http://www.arxiv.org/abs/gr-qc/9711031 ''Quantum Theory of Geometry II: Volume operators''] <br />
<br />
[[Category:Quantum field theory]]</div>95.146.224.76