Beyond semiclassical time

被引:4
作者
Chataignier, Leonardo [1 ,2 ]
机构
[1] Univ Bologna, Dipartimento Fis & Astron, Via Irnerio 46, I-40126 Bologna, Italy
[2] Ist Nazl Fis Nucl, Sez Bologna, IS FLAG, Viale B Pichat 6-2, I-40127 Bologna, Italy
来源
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 2022年 / 77卷 / 08期
关键词
Born-Oppenheimer approach; problem of time; quantum gravity; semiclassical approximation; WKB time; QUANTUM-GRAVITATIONAL CORRECTIONS; GAUGE-INVARIANT SCALAR; TENSOR PERTURBATIONS; COMPLETE OBSERVABLES; GRAVITY; INFLATION; QUANTIZATION; PERSPECTIVE; UNITARITY; ORIGIN;
D O I
10.1515/zna-2022-0106
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
We show that the usual Born-Oppenheimer type of approximation used in quantum gravity, in which a semiclassical time parameter emerges from a weak-coupling expansion of the Wheeler-DeWitt constraint, leads to a unitary theory at least up to the next-to-leading order in minisuperspace models. As there are no unitarity-violating terms, this settles the issue of unitarity at this order, which has been much debated in the literature. Furthermore, we also show that the conserved inner product is gauge-fixed in the sense that the measure is related to the Faddeev-Popov determinant associated with the choice of semiclassical time as a reparametrization gauge. This implies that the Born-Oppenheimer approach to the problem of time is, in fact, an instance of a relational quantum theory, in which transition amplitudes can be related to conditional probabilities.
引用
收藏
页码:805 / 812
页数:8
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