Abstract
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 in a recent paper [16], the Hamilton constraint is a serious obstacle. Quantization of a Hamiltonian setting requires a model in which the quantized variables, which turn into operators, act, and, in case of constraints, preferably given as an equation, to quantize this equation.
The original version of this chapter was revised: Belated corrections have been updated. The erratum to this chapter is available at https://doi.org/10.1007/978-3-319-77371-1_8
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Note that the left-hand side of this equation is a variant of the evolution equation of the mean curvature of the foliation hypersurfaces, cf. (1.6.16) on page 42, i.e., the implementation of the Hamilton constraint is very similar for these two models.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Gerhardt, C. (2018). The Quantization of a Globally Hyperbolic Spacetime. In: The Quantization of Gravity. Fundamental Theories of Physics, vol 194. Springer, Cham. https://doi.org/10.1007/978-3-319-77371-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-77371-1_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-77370-4
Online ISBN: 978-3-319-77371-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)