{"title":"Consequences of Gödel theorems on third quantized theories like string field theory and group field theory","authors":"Mir Faizal , Arshid Shabir , Aatif Kaisar Khan","doi":"10.1016/j.nuclphysb.2024.116774","DOIUrl":null,"url":null,"abstract":"<div><div>The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a theory is described on the configuration space of fields rather than spacetime, which is a third quantized theory. So, both string theory and group field theory are third-quantized theories. Thus, using axioms of string field theory, we motivate similar axioms for group field theory. Then, using the structure of these axioms for string field theory and group field theory, we identify general features of axioms for any such third quantized theory of quantum gravity. Thus, we show that such third-quantized theories of quantum gravity can be formulated as formal axiomatic systems. We then analyze the consequences of Gödel theorems on such third quantized theories. We thus address problems of consistency and completeness of any third quantized theories of quantum gravity.</div></div>","PeriodicalId":54712,"journal":{"name":"Nuclear Physics B","volume":"1010 ","pages":"Article 116774"},"PeriodicalIF":2.5000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nuclear Physics B","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0550321324003407","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 0
Abstract
The observation that spacetime and quantum fields on it have to be dynamically produced in any theory of quantum gravity implies that quantum gravity should be defined on the configuration space of fields rather than spacetime. Such a theory is described on the configuration space of fields rather than spacetime, which is a third quantized theory. So, both string theory and group field theory are third-quantized theories. Thus, using axioms of string field theory, we motivate similar axioms for group field theory. Then, using the structure of these axioms for string field theory and group field theory, we identify general features of axioms for any such third quantized theory of quantum gravity. Thus, we show that such third-quantized theories of quantum gravity can be formulated as formal axiomatic systems. We then analyze the consequences of Gödel theorems on such third quantized theories. We thus address problems of consistency and completeness of any third quantized theories of quantum gravity.
期刊介绍:
Nuclear Physics B focuses on the domain of high energy physics, quantum field theory, statistical systems, and mathematical physics, and includes four main sections: high energy physics - phenomenology, high energy physics - theory, high energy physics - experiment, and quantum field theory, statistical systems, and mathematical physics. The emphasis is on original research papers (Frontiers Articles or Full Length Articles), but Review Articles are also welcome.