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On the metric operator for quantum cylindrical waves

Madhavan Varadarajan
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Abstract

Every (1 polarization) cylindrical wave solution of vacuum general relativity is completely determined by a corresponding axisymmetric solution to the free scalar wave equation on an auxilliary 2+1 dimensional flat spacetime. The physical metric at radius R is determined by the energy, $γ(R)$, of the scalar field in a box (in the flat spacetime) of radius R. In a recent work, among other important results, Ashtekar and Pierri have introduced a strategy to study the quantum geometry in this system, through a regularized quantum counterpart of $γ(R)$. We show that this regularized object is a densely defined symmetric operator, thereby correcting an error in their proof of this result. We argue that it admits a self adjoint extension and show that the operator, unlike its classical counterpart, is not positive.

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Madhavan Varadarajan. 1999-10-12. On the metric operator for quantum cylindrical waves. https://doi.org/10.1088/0264-9381%2F17%2F1%2F313

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