Pub Date : 2021-07-21DOI: 10.1142/9789811237089_0017
{"title":"PATH INTEGRAL QUANTIZATION","authors":"","doi":"10.1142/9789811237089_0017","DOIUrl":"https://doi.org/10.1142/9789811237089_0017","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"374 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132783089","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}
Pub Date : 2021-07-08DOI: 10.1142/9789811237089_0026
R. Bufalo, T. R. Cardoso, B. Pimentel
Noncommutative (NC) quantum field theory is the subject of many analyses on formal and general aspects looking for deviations and, therefore, potential noncommutative spacetime effects. Within of this large class, we may now pay some attention to the quantization of NC field theory on lower dimensions and look closely at the issue of dynamical mass generation to the gauge field. This work encompasses the quantization of the two-dimensional massive quantum electrodynamics and three-dimensional topologically massive quantum electrodynamics. We begin by addressing the problem on a general dimensionality making use of the perturbative Seiberg-Witten map to, thus, construct a general action, to only then specify the problem to two and three dimensions. The quantization takes place through the Källén-Lehmann spectral representation and Yang-Feldman-Källén formulation, where we calculate the respective spectral density function to the gauge field. Furthermore, regarding the photon two-point function, we discuss how its infrared behavior is related to the term generated by quantum corrections in two dimensions, and, moreover, in three dimensions, we study the issue of nontrivial θ -dependent corrections to the dynamical mass generation.
{"title":"QUANTUM ELECTRODYNAMICS","authors":"R. Bufalo, T. R. Cardoso, B. Pimentel","doi":"10.1142/9789811237089_0026","DOIUrl":"https://doi.org/10.1142/9789811237089_0026","url":null,"abstract":"Noncommutative (NC) quantum field theory is the subject of many analyses on formal and general aspects looking for deviations and, therefore, potential noncommutative spacetime effects. Within of this large class, we may now pay some attention to the quantization of NC field theory on lower dimensions and look closely at the issue of dynamical mass generation to the gauge field. This work encompasses the quantization of the two-dimensional massive quantum electrodynamics and three-dimensional topologically massive quantum electrodynamics. We begin by addressing the problem on a general dimensionality making use of the perturbative Seiberg-Witten map to, thus, construct a general action, to only then specify the problem to two and three dimensions. The quantization takes place through the Källén-Lehmann spectral representation and Yang-Feldman-Källén formulation, where we calculate the respective spectral density function to the gauge field. Furthermore, regarding the photon two-point function, we discuss how its infrared behavior is related to the term generated by quantum corrections in two dimensions, and, moreover, in three dimensions, we study the issue of nontrivial θ -dependent corrections to the dynamical mass generation.","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121605181","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}
Pub Date : 2013-07-01DOI: 10.1142/9789814472708_0009
G. Grensing
{"title":"DIFFERENTIAL AND INTEGRAL CALCULUS FOR ANTICOMMUTING VARIABLES","authors":"G. Grensing","doi":"10.1142/9789814472708_0009","DOIUrl":"https://doi.org/10.1142/9789814472708_0009","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127183646","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}
Pub Date : 2013-07-01DOI: 10.1142/9789814472708_0055
G. Grensing
{"title":"QUANTUM GROUPS AND THE NONCOMMUTATIVE TORUS","authors":"G. Grensing","doi":"10.1142/9789814472708_0055","DOIUrl":"https://doi.org/10.1142/9789814472708_0055","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125961898","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}
Pub Date : 2013-07-01DOI: 10.1142/9789814472708_0040
G. Grensing
{"title":"QUANTUM REDUCTION OF CONSTRAINED SYSTEMS","authors":"G. Grensing","doi":"10.1142/9789814472708_0040","DOIUrl":"https://doi.org/10.1142/9789814472708_0040","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128820125","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}
Pub Date : 2013-07-01DOI: 10.1142/9789814472708_0045
G. Grensing
{"title":"WEYL QUANTIZATION OF FERMIONS","authors":"G. Grensing","doi":"10.1142/9789814472708_0045","DOIUrl":"https://doi.org/10.1142/9789814472708_0045","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"47 9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123171664","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}
Pub Date : 2013-07-01DOI: 10.1142/9789814472708_0043
G. Grensing
{"title":"WEYL QUANTIZATION OF BOSONS AND CANONICAL TRANSFORMATIONS","authors":"G. Grensing","doi":"10.1142/9789814472708_0043","DOIUrl":"https://doi.org/10.1142/9789814472708_0043","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"222 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122408370","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}
Pub Date : 2013-07-01DOI: 10.1142/9789814472708_0002
G. Grensing
{"title":"LAGRANGE FORMALISM FOR FIELDS","authors":"G. Grensing","doi":"10.1142/9789814472708_0002","DOIUrl":"https://doi.org/10.1142/9789814472708_0002","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128963129","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}
Pub Date : 2013-07-01DOI: 10.1142/9789814472708_0051
G. Grensing
{"title":"A GLANCE AT NONCOMMUTATIVE QUANTUM FIELD THEORY","authors":"G. Grensing","doi":"10.1142/9789814472708_0051","DOIUrl":"https://doi.org/10.1142/9789814472708_0051","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125913600","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}
Pub Date : 2013-07-01DOI: 10.1142/9789814472708_0033
G. Grensing
{"title":"RELATIVISTIC QUANTUM FIELD THEORY AT NONZERO TEMPERATURE","authors":"G. Grensing","doi":"10.1142/9789814472708_0033","DOIUrl":"https://doi.org/10.1142/9789814472708_0033","url":null,"abstract":"","PeriodicalId":113095,"journal":{"name":"Structural Aspects of Quantum Field Theory and Noncommutative Geometry","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127175398","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}
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