Titlebook: Quantum Cosmology; A Fundamental Descri Martin Bojowald Book 2011 Springer Science+Business Media, LLC 2011 big bang physics.bouncing cosmo

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Difference Equations, as usual for a dynamical equation for wave functions. But their coefficients are in general non-constant and depend on the discrete variables, which implies several subtleties in the analysis and solution of such equations. Moreover, in models less symmetric than isotropic ones or with matter fiel

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Physical Hilbert Spacesint that states have to satisfy, analogous to the Friedmann equation which is a constraint in canonical relativity. Zero eigenvalues of the constraint operator are thus to be found. For the difference equation (.) encountered for isotropic models there is in fact a kinematically normalizable eigenst

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Difference Equationsise. Several examples for such classes of difference equations have been derived in the models seen in preceding chapters. In this chapter, some mathematical properties related to questions of physical interest are discussed. Finally, we will sketch how non-linear difference equations may arise as a result of inhomogeneity.

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Anisotropynature which makes operators such as that for volume quite involved. Such issues have to be faced before one even tries to describe and solve the dynamics, and so already a kinematical reduction must be undertaken with care.

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