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Dirac Decomposition of Wheeler-DeWitt Equation on the Bianchi Class A Models

Hidetomo Yamazaki
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Abstract

The Wheeler-DeWitt equation for the Bianchi Class A cosmological models is expressed generally in terms of the second-order differential equation like the Klein-Gordon equation. To obtain the positive-definite probability density, a new method extending the Dirac-Square-Root formalism, which factorizes the Wheeler-DeWitt equation into the first-order differential equation using the Pauli matrices, is investigated. The solutions to the Dirac type equation thus obtained are expressed in terms of two-component spinor form. The probability density defined by the solution is positive-definite and there is a conserved current. The newly found spin-like degree of freedom causes the universe to go through an early quantum stage of evolution with agitated anisotropy-oscillation like Zitterbewegung.

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Hidetomo Yamazaki. 2001-01-25. Dirac Decomposition of Wheeler-DeWitt Equation on the Bianchi Class A Models. https://arxiv.org/abs/gr-qc/0101066

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