Volume operator

Operator whose expectation value gives the volume

A quantum field theory of general relativity provides operators that measure the geometry of spacetime. The volume operator V ( R ) {\displaystyle V(R)} of a region R {\displaystyle R} is defined as the operator that yields the expectation value of a volume measurement of the region R {\displaystyle R} , given a state ψ {\displaystyle \psi } of quantum General Relativity. I.e. ⟨ ψ , V ( R ) ψ ⟩ {\displaystyle \langle \psi ,V(R)\psi \rangle } is the expectation value for the volume of R {\displaystyle R} . Loop Quantum Gravity, for example, provides volume operators, area operators and length operators for regions, surfaces and path respectively.

Sources

  • Carlo Rovelli and Lee Smolin, "Discreteness of Area and Volume in Quantum Gravity", Nuclear Physics B 442, 593 (1995).
  • Abhay Ashtekar and Jerzy Lewandowski, Quantum Theory of Geometry II: Volume operators


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