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Quantum Spin Dynamics (QSD) II

T. Thiemann
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Abstract

We continue here the analysis of the previous paper of the Wheeler-DeWitt constraint operator for four-dimensional, Lorentzian, non-perturbative, canonical vacuum quantum gravity in the continuum. In this paper we derive the complete kernel, as well as a physical inner product on it, for a non-symmetric version of the Wheeler-DeWitt operator. We then define a symmetric version of the Wheeler-DeWitt operator. For the Euclidean Wheeler-DeWitt operator as well as for the generator of the Wick transform from the Euclidean to the Lorentzian regime we prove existence of self-adjoint extensions and based on these we present a method of proof of self-adjoint extensions for the Lorentzian operator. Finally we comment on the status of the Wick rotation transform in the light of the present results.

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T. Thiemann. 1996-06-29. Quantum Spin Dynamics (QSD) II. https://doi.org/10.1088/0264-9381%2F15%2F4%2F012

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