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arXiv · 2411.19435

Geometrical Quantum Time in the $U(1)^3$ Model of Euclidean Quantum Gravity

Sepideh Bakhoda·Yongge Ma
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Abstract

Loop Quantum Gravity faces challenges in constructing a well-defined Hamiltonian constraint and understanding the quantum notion of time. In this paper these issues are studied by quantizing the $U(1)^3$ model, a simplified system exhibiting features similar to general relativity. By isolating a holonomy component within the Hamiltonian constraint, a discrete relative time evolution equation for quantum states is obtained. Then a Shr\"{o}dinger-like equation is derived in continuous limit. Thus the physical states solving this Shr\"{o}dinger-like equation can be written out. The emergence of the time parameter and its corresponding quantum operator are analyzed. It indicates the notion of a geometrical quantum time for quantum gravity.

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Sepideh Bakhoda, Yongge Ma. 2024-11-29. Geometrical Quantum Time in the $U(1)^3$ Model of Euclidean Quantum Gravity. https://doi.org/10.1088/1572-9494%2Fad972b

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