Abstract
We review the canonical quantisation of minisuperspace models by promoting to operators the constraints as well as the additional symmetries of the metric of the configuration space of variables. We describe the classical and quantum formulation of the theory and give an application of this approach to the FLRW spacetime coupled to a massless scalar field.
Prepared for the proceedings of the 1st Domoschool, Domodossola.
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Notes
- 1.
The line element has been turned to a simplified form without the shift vectors since it is always possible to make a choice of the three out of the four gauge functions of the independent variable x such that N i = 0 at the expense of a more complicated spatial metric components.
- 2.
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Acknowledgements
I would like to thank the organisers of the 1st Domoschool for their kind hospitality and the high level of lectures they provided during the school. This work was supported by the grant GAČR 14-37086G.
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Zampeli, A. (2019). Minisuperspace Quantisation via Conditional Symmetries. In: Cacciatori, S., Güneysu, B., Pigola, S. (eds) Einstein Equations: Physical and Mathematical Aspects of General Relativity. DOMOSCHOOL 2018. Tutorials, Schools, and Workshops in the Mathematical Sciences . Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-18061-4_13
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