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

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

2003-10-30

arxiv.org/abs/gr-qc/0310129v3

Classical and Quantum Gravity 21 (2004) 2319-2332

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

14 pages

Scientific paper

10.1088/0264-9381/21/9/008

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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