Quantizing de Sitter Spacetime in Heisenberg Picture

Details Quantizing de Sitter Spacetime in Heisenberg Picture Quantizing de Sitter Spacetime in Heisenberg Picture

Jun 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996pthph..95.1199d&link_type=abstract

Progress of Theoretical Physics, Vol. 95, No. 6, pp. 1199-1210

Physics

Scientific paper

We consider the spatially flat Friedman-Robertson-Walker Universe with positive cosmological constant. By a suitable redefinition of the essential dynamical variable, the metric function f, we perform a non-perturbative canonical quantization within the framework of the Heisenberg picture. Our approach is different from the usual ones in that it imposes the Wheeler-DeWitt equation as a constraint at the end of the quantization procedure. It turns out that there are no operator-ordering problems, and all the Heisenberg dynamical operators can be expressed in terms of two (time-independent) lowering and raising operators that generate and act on a Fock space spanned by the eigenstates of an associated harmonic oscillator. As expected, the Wheeler-DeWitt equation generalizing the G44-Einstein equation for the classical de Sitter spacetime selects the physical states of the quantum de Sitter Universe. We show that there exist two orthogonal solutions (to the derived Wheeler-DeWitte equation) which are explicitly worked out as mixed quantum states. As a result of the exponential universal expansion, the usual Fock states (defined as the eigenstates of the number-operator) are no longer invariant under the derived Hamiltonian. They exhibit energy and metric quantum fluctuations which lead to a (geometrical) volume quantization.

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