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The Quantization of Gravity

Part of the Fundamental Theories of Physics Book Series (volume 194)

DOI: 10.1007/978-3-319-77371-1

ISBN: 978-3-319-77370-4

Publisher: Springer International Publishing - Springer Journals

Apr 14, 2018

Available

The Quantization of a Globally Hyperbolic Spacetime

Gerhardt, Claus

Pages: 1 –50

[The quantization of gravity is hampered by the fact that the Einstein–Hilbert Lagrangian is singular. Switching to a Hamiltonian setting requires to impose two constraints, the Hamilton constraint and the diffeomorphism constraint. Though we were able to eliminate the diffeomorphism constraint...
Available

Interaction of Gravity with Yang-Mills and Higgs Fields

Gerhardt, Claus

Pages: 51 –78

[The quantization of gravity interacting with Yang-Mills and Higgs fields poses no additional greater challenges—at least in principle. The number of variables will be increased, the combined Hamiltonian is the sum of several individual Hamiltonians, and, since gravity is involved, we have the...
Available

The Quantum Development of an Asymptotically Euclidean Cauchy Hypersurface

Gerhardt, Claus

Pages: 79 –97

[In the preceding chapters, we obtained as a result of the Canonical quantizationCanonical quantization of gravity a quantized version of the Hamilton constraint which is the wave equation]
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The Quantization of a Schwarzschild-AdS Black Hole

Gerhardt, Claus

Pages: 99 –111

[In the previous chapter, we looked at the quantum model for the interaction of gravity with Yang–Mills and Higgs fields and proved a spectral resolution of the underlying hyperbolic equation provided the Cauchy hypersurface \documentclass[12pt]{minimal} \usepackage{amsmath}...
Available

The Quantization of a Kerr-AdS Black Hole

Gerhardt, Claus

Pages: 113 –131

[In the previous chapter we looked at the quantum development of a Schwarzschild-AdS spacetime and derived a spectral resolution of the underlying wave equation. In the present chapter we want to show that similar arguments can also be used to quantize a Kerr-AdS spacetime with a rotating black...
Available

A Partition Function for Quantized Globally Hyperbolic Spacetimes with a Negative Cosmological Constant

Gerhardt, Claus

Pages: 133 –185

[In this chapter we apply quantum statistics to our quantized versions of Schwarzschild-AdS and Kerr-AdS black holes and also to the quantized globally hyperbolic spacetimes having an asymptotically Euclidean Cauchy hypersurface.]
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Appendix

Gerhardt, Claus

Pages: 187 –190

[We prove that eigendistributions in asymptotically Euclidean Riemannian manifolds are smooth functions with polynomial growth.]
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Erratum to: The Quantization of Gravity

Gerhardt, Claus

Pages: E1 –E1

[The quantization of gravity is hampered by the fact that the Einstein–Hilbert Lagrangian is singular. Switching to a Hamiltonian setting requires to impose two constraints, the Hamilton constraint and the diffeomorphism constraint. Though we were able to eliminate the diffeomorphism constraint...

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