Transition probability spaces in loop quantum gravity

doi:10.1063/1.5022662

	Transition probability spaces in loop quantum gravity
	Guoa, Xiao-Kan 1,2
刊名	JOURNAL OF MATHEMATICAL PHYSICS
	2018-03-01
卷号	59 期号:3
ISSN号	0022-2488
DOI	10.1063/1.5022662
文献子类	Article
英文摘要	We study the (generalized) transition probability spaces, in the sense of Mielnik and Cantoni, for spacetime quantum states in loop quantum gravity. First, we show that loop quantum gravity admits the structures of transition probability spaces. This is exemplified by first checking such structures in covariant quantum mechanics and then identifying the transition probability spaces in spin foam models via a simplified version of general boundary formulation. The transition probability space thus defined gives a simple way to reconstruct the discrete analog of the Hilbert space of the canonical theory and the relevant quantum logical structures. Second, we show that the transition probability space and in particular the spin foam model are 2-ategories. Then we discuss how to realize in spin foam models two proposals by Crane about the mathematical structures of quantum gravity, namely, the quantum topos and causal sites. We conclude that transition probability spaces provide us with an alternative framework to understand various foundational questions of loop quantum gravity. Published by AIP Publishing.
WOS关键词	AMPLITUDE SPACES ; SPIN NETWORKS ; MECHANICS ; LOGIC ; STATES ; FORMULATION ; MIELNIK ; TIME
WOS研究方向	Physics
语种	英语
出版者	AMER INST PHYSICS
WOS记录号	WOS:000428902300019
资助机构	National Natural Science Foundation of China(11725524 ; National Natural Science Foundation of China(11725524 ; 61471356 ; 61471356 ; 11674089) ; 11674089) ; National Natural Science Foundation of China(11725524 ; National Natural Science Foundation of China(11725524 ; 61471356 ; 61471356 ; 11674089) ; 11674089) ; National Natural Science Foundation of China(11725524 ; National Natural Science Foundation of China(11725524 ; 61471356 ; 61471356 ; 11674089) ; 11674089) ; National Natural Science Foundation of China(11725524 ; National Natural Science Foundation of China(11725524 ; 61471356 ; 61471356 ; 11674089) ; 11674089)
内容类型	期刊论文
源URL	[http://ir.wipm.ac.cn/handle/112942/12984]
专题	中国科学院武汉物理与数学研究所
通讯作者	Guoa, Xiao-Kan
作者单位	1.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Guoa, Xiao-Kan. Transition probability spaces in loop quantum gravity[J]. JOURNAL OF MATHEMATICAL PHYSICS,2018,59(3).
APA	Guoa, Xiao-Kan.(2018).Transition probability spaces in loop quantum gravity.JOURNAL OF MATHEMATICAL PHYSICS,59(3).
MLA	Guoa, Xiao-Kan."Transition probability spaces in loop quantum gravity".JOURNAL OF MATHEMATICAL PHYSICS 59.3(2018).