{"title":"Notation and Conventions","authors":"","doi":"10.1017/9781316227596.014","DOIUrl":"https://doi.org/10.1017/9781316227596.014","url":null,"abstract":"• Rn denotes the Euclidean space of dimension n. Subsets of Rn are viewed as metric spaces using the standard Euclidean distance on Rn. • Mn(R) denotes the real vector space of n× n real matrices with the Euclidean metric, and I denotes the identity matrix in Mn(R). • All rings are associative, with a multiplicative identity. • For any prime number p, Fp denotes the finite field with p elements. • If A and B are sets, then A−B refers to {x ∈ A | x 6∈ B}. • For a ring R, R[x] denotes the polynomial ring in one variable over R, and R[x, y] denotes the polynomial ring in two variables over R.","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"237 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121631468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Functional Renormalization Group for Gravity","authors":"M. Reuter, F. Saueressig","doi":"10.1017/9781316227596.005","DOIUrl":"https://doi.org/10.1017/9781316227596.005","url":null,"abstract":"","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127637954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Truncations of Single-Metric Type","authors":"M. Reuter, F. Saueressig","doi":"10.1017/9781316227596.006","DOIUrl":"https://doi.org/10.1017/9781316227596.006","url":null,"abstract":"","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116777845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Functional Renormalization Group","authors":"M. Reuter, F. Saueressig","doi":"10.1017/9781316227596.003","DOIUrl":"https://doi.org/10.1017/9781316227596.003","url":null,"abstract":"","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"147 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134498050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Organizing the Derivative Expansion","authors":"","doi":"10.1017/9781316227596.015","DOIUrl":"https://doi.org/10.1017/9781316227596.015","url":null,"abstract":"","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116045198","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Metric Variations","authors":"","doi":"10.1017/9781316227596.016","DOIUrl":"https://doi.org/10.1017/9781316227596.016","url":null,"abstract":"","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122033360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Alternative Field Variables","authors":"M. Reuter, F. Saueressig","doi":"10.1017/9781316227596.010","DOIUrl":"https://doi.org/10.1017/9781316227596.010","url":null,"abstract":"","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127162171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Field Decompositions","authors":"","doi":"10.1017/9781316227596.019","DOIUrl":"https://doi.org/10.1017/9781316227596.019","url":null,"abstract":"","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122471442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Matter Coupled to Quantum Gravity","authors":"M. Reuter, F. Saueressig","doi":"10.1017/9781316227596.011","DOIUrl":"https://doi.org/10.1017/9781316227596.011","url":null,"abstract":"","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117140970","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Reconstruction Problem","authors":"","doi":"10.1017/9781316227596.009","DOIUrl":"https://doi.org/10.1017/9781316227596.009","url":null,"abstract":"Both intrinsic and extr insic parameters are known: we can solv e the reconstruction problem unambiguously by triangulation. Only the intrinsic parameters are known: we can solv e the reconstruction problem but only up to an unkno wn scaling f actor. Neither the extr insic nor the intrinsic parameters are available: we can solv e the reconstruction problem b ut only up to an unkno wn, global projecti ve transformation. Reconstruction by triangulation Assumptions and problem statement Both the extrinsic and intrinsic camera parameters are kno wn. Compute the location of the 3D points from their projections pl and pr","PeriodicalId":185321,"journal":{"name":"Quantum Gravity and the Functional Renormalization Group","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129749256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}