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      On the Wheeler-DeWitt equation for Kasner-like Cosmologies

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          Abstract

          The Wheeler-DeWitt equation is obtained for Kasner-like cosmologies. Some solutions to this equation are presented for empty space, space filled with a cosmological constant and in the presence of a scalar field. We also briefly discuss a non-commutative extension of these results.

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          Quantum Theory of Gravity. I. The Canonical Theory

          Bryce S. DeWitt (1967)
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            Noncommutative Quantum Cosmology

            O Obregón, C. Ramírez, H García-Compeán (2001)
            We propose a model for noncommutative quantum cosmology by means of a deformation of minisuperspace. For the Kantowski-Sachs metric we are able to find the exact wave function. We construct wave packets and show that new quantum states that ``compete'' to be the most probable state appear, in clear contrast with the commutative case. A tunneling process could be possible among these states.
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              Moyal Quantum Mechanics: The Semiclassical Heisenberg Dynamics

              T. A. Osborn, F. Molzahn (1994)
              The Moyal--Weyl description of quantum mechanics provides a comprehensive phase space representation of dynamics. The Weyl symbol image of the Heisenberg picture evolution operator is regular in \(\hbar\). Its semiclassical expansion `coefficients,' acting on symbols that represent observables, are simple, globally defined differential operators constructed in terms of the classical flow. Two methods of constructing this expansion are discussed. The first introduces a cluster-graph expansion for the symbol of an exponentiated operator, which extends Groenewold's formula for the Weyl product of symbols. This Poisson bracket based cluster expansion determines the Jacobi equations for the semiclassical expansion of `quantum trajectories.' Their Green function solutions construct the regular \(\hbar\downarrow0\) asymptotic series for the Heisenberg--Weyl evolution map. The second method directly substitutes such a series into the Moyal equation of motion and determines the \(\hbar\) coefficients recursively. The Heisenberg--Weyl description of evolution involves no essential singularity in \(\hbar\), no Hamilton--Jacobi equation to solve for the action, and no multiple trajectories, caustics or Maslov indices.
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                Publication date Created: 31 August 2004
                Article
                ArXiV ID: hep-th/0408239
                SO-VID: 911b0c73-9018-4ce2-a093-13f93ee09c71
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                Comments 12 pages
                Categories hep-th

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