Pub Date : 2023-10-11DOI: 10.1142/s0129055x23500320
Alessio Marrani, Daniele Corradetti, David Chester, Raymond Aschheim, Klee Irwin
In his study on the geometry of Lie groups, Rosenfeld postulated a strict relation between all real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces over the (rank-2) tensor product of Hurwitz algebras taken with appropriate conjugations. Unfortunately, the procedure carried out by Rosenfeld was not rigorous, since many of the theorems he had been using do not actually hold true in the case of algebras that are not alternative nor power-associative. A more rigorous approach to the definition of all the planes presented more than thirty years ago by Rosenfeld in terms of their isometry group, can be considered within the theory of coset manifolds, which we exploit in this work, by making use of all real forms of Magic Squares of order three and two over Hurwitz normed division algebras and their split versions. Within our analysis, we find seven pseudo-Riemannian symmetric coset manifolds which seemingly cannot have any interpretation within Rosenfeld’s framework. We carry out a similar analysis for Rosenfeld lines, obtaining that there are a number of pseudo-Riemannian symmetric cosets which do not have any interpretation á la Rosenfeld.
{"title":"A “magic” approach to octonionic Rosenfeld spaces","authors":"Alessio Marrani, Daniele Corradetti, David Chester, Raymond Aschheim, Klee Irwin","doi":"10.1142/s0129055x23500320","DOIUrl":"https://doi.org/10.1142/s0129055x23500320","url":null,"abstract":"In his study on the geometry of Lie groups, Rosenfeld postulated a strict relation between all real forms of exceptional Lie groups and the isometries of projective and hyperbolic spaces over the (rank-2) tensor product of Hurwitz algebras taken with appropriate conjugations. Unfortunately, the procedure carried out by Rosenfeld was not rigorous, since many of the theorems he had been using do not actually hold true in the case of algebras that are not alternative nor power-associative. A more rigorous approach to the definition of all the planes presented more than thirty years ago by Rosenfeld in terms of their isometry group, can be considered within the theory of coset manifolds, which we exploit in this work, by making use of all real forms of Magic Squares of order three and two over Hurwitz normed division algebras and their split versions. Within our analysis, we find seven pseudo-Riemannian symmetric coset manifolds which seemingly cannot have any interpretation within Rosenfeld’s framework. We carry out a similar analysis for Rosenfeld lines, obtaining that there are a number of pseudo-Riemannian symmetric cosets which do not have any interpretation á la Rosenfeld.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136057608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1142/s0129055x23500356
Alexander D. Popov
We consider Yang-Mills theory with a compact structure group $G$ on a Lorentzian 4-manifold $M={mathbb R}timesSigma$ such that gauge transformations become identity on a submanifold $S$ of $Sigma$ (framing over $SsubsetSigma$). The space $S$ is not necessarily a boundary of $Sigma$ and can have dimension $kle 3$. Framing of gauge bundles over $SsubsetSigma$ demands introduction of a $G$-valued function $phi_S$ with support on $S$ and modification of Yang-Mills equations along ${mathbb R}times Ssubset M$. The fields $phi_S$ parametrize nonequivalent flat connections mapped into each other by a dynamical group ${mathcal G}_S$ changing gauge frames over $S$. It is shown that the charged condensate $phi_S$ is the Stueckelberg field generating an effective mass of gluons in the domain $S$ of space $Sigma$ and keeping them massless outside $S$. We argue that the local Stueckelberg field $phi_S$ can be responsible for color confinement. We also briefly discuss local breaking of symmetries in gravity. It is shown that framing of the tangent bundle over a subspace of space-time makes gravitons massive in this subspace.
{"title":"Yang-Mills-Stueckelberg Theories, Framing and Local Breaking of Symmetries","authors":"Alexander D. Popov","doi":"10.1142/s0129055x23500356","DOIUrl":"https://doi.org/10.1142/s0129055x23500356","url":null,"abstract":"We consider Yang-Mills theory with a compact structure group $G$ on a Lorentzian 4-manifold $M={mathbb R}timesSigma$ such that gauge transformations become identity on a submanifold $S$ of $Sigma$ (framing over $SsubsetSigma$). The space $S$ is not necessarily a boundary of $Sigma$ and can have dimension $kle 3$. Framing of gauge bundles over $SsubsetSigma$ demands introduction of a $G$-valued function $phi_S$ with support on $S$ and modification of Yang-Mills equations along ${mathbb R}times Ssubset M$. The fields $phi_S$ parametrize nonequivalent flat connections mapped into each other by a dynamical group ${mathcal G}_S$ changing gauge frames over $S$. It is shown that the charged condensate $phi_S$ is the Stueckelberg field generating an effective mass of gluons in the domain $S$ of space $Sigma$ and keeping them massless outside $S$. We argue that the local Stueckelberg field $phi_S$ can be responsible for color confinement. We also briefly discuss local breaking of symmetries in gravity. It is shown that framing of the tangent bundle over a subspace of space-time makes gravitons massive in this subspace.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135131563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1142/s0129055x2350037x
Qi Han, Shuai Wang, Lijie Gou, Rong Zhang
{"title":"Quantum conditional entropy based on local quantum Bernoulli noises","authors":"Qi Han, Shuai Wang, Lijie Gou, Rong Zhang","doi":"10.1142/s0129055x2350037x","DOIUrl":"https://doi.org/10.1142/s0129055x2350037x","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135247448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1142/s0129055x23500344
U.A. Rozikov
Kittel's 1D model represents a natural DNA with two strands as a (molecular) zipper, which may separated as the temperature is varied. We define multidimensional version of this model on a Cayley tree and study the set of Gibbs measures. We reduce description of Gibbs measures to solving of a non-linear functional equation, with unknown functions (called boundary laws) defined on vertices of the Cayley tree. Each boundary law defines a Gibbs measure. We give general formula of free energy depending on the boundary law. Moreover, we find some concrete boundary laws and corresponding Gibbs measures. Explicit critical temperature for occurrence a phase transition (non-uniqueness of Gibbs measures) is obtained.
{"title":"Kittel's molecular zipper model on cayley trees","authors":"U.A. Rozikov","doi":"10.1142/s0129055x23500344","DOIUrl":"https://doi.org/10.1142/s0129055x23500344","url":null,"abstract":"Kittel's 1D model represents a natural DNA with two strands as a (molecular) zipper, which may separated as the temperature is varied. We define multidimensional version of this model on a Cayley tree and study the set of Gibbs measures. We reduce description of Gibbs measures to solving of a non-linear functional equation, with unknown functions (called boundary laws) defined on vertices of the Cayley tree. Each boundary law defines a Gibbs measure. We give general formula of free energy depending on the boundary law. Moreover, we find some concrete boundary laws and corresponding Gibbs measures. Explicit critical temperature for occurrence a phase transition (non-uniqueness of Gibbs measures) is obtained.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135247620","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1142/s0129055x23500332
Fangcheng Fan, Weikang Xie
{"title":"A generalized integrable lattice hierarchy related to the Ablowitz-Ladik lattice: conservation law, Darboux transformation and exact solution","authors":"Fangcheng Fan, Weikang Xie","doi":"10.1142/s0129055x23500332","DOIUrl":"https://doi.org/10.1142/s0129055x23500332","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135247624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-13DOI: 10.1142/s0129055x23300078
Meenal Singhal, Kavita Goyal, Rohit K. Singla
{"title":"A review of regularization strategies and solution techniques for ill-posed inverse problems, with application to inverse heat transfer problems","authors":"Meenal Singhal, Kavita Goyal, Rohit K. Singla","doi":"10.1142/s0129055x23300078","DOIUrl":"https://doi.org/10.1142/s0129055x23300078","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135781276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-04DOI: 10.1142/s0129055x23500319
M. Sababheh, S. Furuichi, H. Moradi
{"title":"Sharpening Celebrated Convex Inequalities with Applications to Operators and Entropies","authors":"M. Sababheh, S. Furuichi, H. Moradi","doi":"10.1142/s0129055x23500319","DOIUrl":"https://doi.org/10.1142/s0129055x23500319","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49599398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-13DOI: 10.1142/s0129055x23300066
Andreas Kraft, Jonas Schnitzer
{"title":"An Introduction to L∞-Algebras and their Homotopy Theory for the working Mathematician","authors":"Andreas Kraft, Jonas Schnitzer","doi":"10.1142/s0129055x23300066","DOIUrl":"https://doi.org/10.1142/s0129055x23300066","url":null,"abstract":"","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42343036","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-13DOI: 10.1142/s0129055x23600024
G. Androulakis, Tiju Cherian John
The main result in this article shows that the quantum $f$-divergence of two states is equal to the classical $f$-divergence of the corresponding Nussbaum-Szko{l}a distributions. This provides a general framework for studying certain properties of quantum entropic quantities using the corresponding classical entities. The usefulness of the main result is illustrated by obtaining several quantum $f$-divergence inequalities from their classical counterparts. All results presented here are valid in both finite and infinite dimensions and hence can be applied to continuous variable systems as well. A comprehensive review of the instances in the literature where Nussbaum-Szko{l}a distributions are used, is also provided in this article.
{"title":"Quantum f-divergences via Nussbaum-Szkola Distributions and Applications to f-divergence Inequalities","authors":"G. Androulakis, Tiju Cherian John","doi":"10.1142/s0129055x23600024","DOIUrl":"https://doi.org/10.1142/s0129055x23600024","url":null,"abstract":"The main result in this article shows that the quantum $f$-divergence of two states is equal to the classical $f$-divergence of the corresponding Nussbaum-Szko{l}a distributions. This provides a general framework for studying certain properties of quantum entropic quantities using the corresponding classical entities. The usefulness of the main result is illustrated by obtaining several quantum $f$-divergence inequalities from their classical counterparts. All results presented here are valid in both finite and infinite dimensions and hence can be applied to continuous variable systems as well. A comprehensive review of the instances in the literature where Nussbaum-Szko{l}a distributions are used, is also provided in this article.","PeriodicalId":54483,"journal":{"name":"Reviews in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.8,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42368778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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