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An action principle for the quantization of parametric theories and nonlinear quantum cosmology

Charles H-T Wang·Smaragda Kessari·Edward R Irvine
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Abstract

By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to nonlinear quantum mechanics. This generalization enables a unitary description of the quantum evolution for a broad class of constrained Hamiltonian systems with a nonlinear kinematic structure. In particular, the new theory is applicable to the quantization of cosmological models where a chosen gravitational degree of freedom acts as geometric time. This is demonstrated explicitly using three cosmological models: the Friedmann universe with a massless scalar field and Bianchi type I and IX models. Based on these investigations, the prospect of further developing the proposed quantization scheme in the context of quantum gravity is discussed.

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Charles H-T Wang, Smaragda Kessari, Edward R Irvine. 2004-04-05. An action principle for the quantization of parametric theories and nonlinear quantum cosmology. https://doi.org/10.1088/0264-9381%2F21%2F9%2F008

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