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arXiv 1602.08688gr-qc
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圈量子引力的新体积和逆体积算符

New volume and inverse volume operators for loop quantum gravity

Jinsong Yang, Yongge Ma

备注：
14 pages, 1 figure; version published in PRD
发表信息：
Phys. Rev. D 94, 044003 (2016)
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摘要：

利用所谓的余三阶算符作为积木，构造了圈量子引力的一个新的替代体积算符。结果表明，新的体积算子与标准体积算子具有相同的定性性质。此外，根据替代体积算子的构造方法，构造了一种新的替代逆体积算子，它具有与替代体积算子相同的性质.新的反体积算符可以用来构造物质场的哈密顿算符，从而可以得到一个无反常的在壳量子约束代数，而对引力与物质场耦合的正则化过程没有任何特殊的限制.

英文摘要：

A new alternative volume operator is constructed for loop quantum gravity by using the so-called cotriad operators as building blocks. It is shown that the new volume operator shares the same qualitative properties with the standard volume operator. Moreover, a new alternative inverse volume operator is also constructed in the light of the construction of the alternative volume operator, which is possessed of the same qualitative properties as those of the alternative volume operator. The new inverse volume operator can be employed to construct the Hamiltonian operator of matter fields, which may lead to an anomaly-free on-shell quantum constraint algebra without any special restriction on the regularization procedure for gravity coupled to matter fields.

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