Geometrical Quantum Time in the Model of Euclidean Quantum Gravity
arXiv:2411.19435 · doi:10.1088/1572-9494/ad972b
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 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 Shrödinger-like equation is derived in continuous limit. Thus the physical states solving this Shrödinger-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.
arXiv comment21 pages, accepted for publication in Communications in Theoretical Physics
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