Quantum Spin Dynamics (QSD) II

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.

27 pages, Latex, preceded by a companion paper before this one

References in corpus (10)

• Quantum Spin Dynamics (QSD)
• Spin Networks and Quantum Gravity
• QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
• Geometry Eigenvalues and Scalar Product from Recoupling Theory in Loop Quantum Gravity
• QSD III : Quantum Constraint Algebra and Physical Scalar Product in Quantum General Relativity
• Reality conditions inducing transforms for quantum gauge field theory and quantum gravity
• QSD VI : Quantum Poincaré Algebra and a Quantum Positivity of Energy Theorem for Canonical Quantum Gravity
• A real alternative to quantum gravity in loop space
• Perturbation study on the spin and charge susceptibilities of the two-dimensional Hubbard model
• Functional Integration on Spaces of Connections

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