{"title":"Quantization of Measure in Gravitation","authors":"V. Dzhunushaliev, V. Folomeev","doi":"10.1134/S0202289323040072","DOIUrl":null,"url":null,"abstract":"<p>Using the Radon–Nikodym theorem concerning the relation between any two measures, as well as the methods employed in loop quantum gravity, it is shown that in gravitation one can quantize any measure which is not even associated with metric. We have considered the simplest case where the proportionality coefficient between two operators of measure (the Radon–Nikodym derivative) is some function. The result is that in the right-hand side of the commutation relations for the measure the fundamental length becomes a variable quantity, and this can lead to smoothing the singularity. The case where the Radon–Nikodym derivative is an operator is also under discussion. Classical and quantum theories in the background of space endowed with quantum measure are under consideration.</p>","PeriodicalId":583,"journal":{"name":"Gravitation and Cosmology","volume":"29 4","pages":"367 - 373"},"PeriodicalIF":1.2000,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Gravitation and Cosmology","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1134/S0202289323040072","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 1
Abstract
Using the Radon–Nikodym theorem concerning the relation between any two measures, as well as the methods employed in loop quantum gravity, it is shown that in gravitation one can quantize any measure which is not even associated with metric. We have considered the simplest case where the proportionality coefficient between two operators of measure (the Radon–Nikodym derivative) is some function. The result is that in the right-hand side of the commutation relations for the measure the fundamental length becomes a variable quantity, and this can lead to smoothing the singularity. The case where the Radon–Nikodym derivative is an operator is also under discussion. Classical and quantum theories in the background of space endowed with quantum measure are under consideration.
期刊介绍：
Gravitation and Cosmology is a peer-reviewed periodical, dealing with the full range of topics of gravitational physics and relativistic cosmology and published under the auspices of the Russian Gravitation Society and Peoples’ Friendship University of Russia. The journal publishes research papers, review articles and brief communications on the following fields: theoretical (classical and quantum) gravitation; relativistic astrophysics and cosmology, exact solutions and modern mathematical methods in gravitation and cosmology, including Lie groups, geometry and topology; unification theories including gravitation; fundamental physical constants and their possible variations; fundamental gravity experiments on Earth and in space; related topics. It also publishes selected old papers which have not lost their topicality but were previously published only in Russian and were not available to the worldwide research community
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