Abstract
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under D-dimensional finite Möbius transformations. The invariance of the cocycle condition under finite Möbius transformations implies that space is compact. Additionally, it implies energy quantisation and the undefinability of quantum trajectories. I argue that the decompactification limit coincides with the classical limit. Evidence for the compactness of the universe may exist in the Cosmic Microwave Background Radiation.
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Acknowledgements
I thank Marco Matone for discussions and Subir Sarkar and Theoretical Physics Department at the University of Oxford for hospitality. This work is supported in part by the STFC (PP/D000416/1).
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Faraggi, A.E. (2014). The Quantum Closet. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_41
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DOI: https://doi.org/10.1007/978-4-431-55285-7_41
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