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Register a new userQuantum mechanics and gravity as preclusion principles of four dimensional geometries
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Authors
Roman Sverdlov
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The goal of this paper is to employ a preclusion principle originally suggested by Rafael Sorkin in order to come up with a relativistically covariant model of quantum mechanics and gravity. Space-time is viewed as geometry as opposed to dynamics, and unwanted histories in that geometry are precluded.
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Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure General Relativity with cosmological constant, $Lambda$, is reexpressed as an affine algebra with the commutator of the imaginary part of the Chern-Simons functional, $Q$, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant; and it facilitates the construction of solutions to all of the constraints. Unitary, irreducible representations of the affine group exhibit a natural Hilbert space structure, and coherent states and other physical states can be generated from a fiducial state. It is also intriguing that formulation of the Hamiltonian constraint or Wheeler-DeWitt equation as an affine algebra requires a non-vanishing cosmological constant; and a fundamental uncertainty relation of the form $frac{Delta{V}}{<{V}>}Delta {Q}geq 2pi Lambda L^2_{Planck}$ (wherein $V$ is the total volume) may apply to all physical states of quantum gravity.
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