The Variational Problem and Background Field in the Renormalization Group Method for Nonlinear Sigma Models
We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in d = 3 , 4 and adapt it to a class of nonlinear sigma models in d = 2 . The result of the variational problem is a minimal configuration, which can serve as a classical background f...
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| Published in: | Annales Henri Poincaré Vol. 25; no. 3; pp. 2065 - 2085 |
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| Abstract | We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in
d
=
3
,
4
and adapt it to a class of nonlinear sigma models in
d
=
2
. The result of the variational problem is a minimal configuration, which can serve as a classical background field in the renormalization group analysis. |
|---|---|
| AbstractList | We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in
d
=
3
,
4
and adapt it to a class of nonlinear sigma models in
d
=
2
. The result of the variational problem is a minimal configuration, which can serve as a classical background field in the renormalization group analysis. We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in $$d = 3, 4$$ d = 3 , 4 and adapt it to a class of nonlinear sigma models in $$d=2$$ d = 2 . The result of the variational problem is a minimal configuration, which can serve as a classical background field in the renormalization group analysis. We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in d=3,4 and adapt it to a class of nonlinear sigma models in d=2. The result of the variational problem is a minimal configuration, which can serve as a classical background field in the renormalization group analysis. |
| Author | Goswami, Abhishek |
| Author_xml | – sequence: 1 givenname: Abhishek orcidid: 0000-0001-6868-8815 surname: Goswami fullname: Goswami, Abhishek email: goswami.abhishek33@gmail.com organization: Faculty of Mathematics and Computer Science, Adam Mickiewicz University |
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| References | Balaban (CR3) 1985; 98 Jaffe, Witten, Carlson, Jaffe, Wiles (CR13) 2006 Balaban (CR9) 1988; 116 Balaban (CR4) 1985; 99 Balaban (CR6) 1985; 99 Balaban (CR7) 1985; 102 Balaban (CR11) 1989; 122 Balban, Jaffe, Velo, Wightman (CR18) 1986 Balaban (CR5) 1985; 102 Abbott (CR15) 1982; 13 Balaban (CR10) 1988; 119 Howe, Papadopoulos, Stelle (CR16) 1988; 296 Balaban (CR1) 1984; 95 Balaban (CR2) 1984; 96 Balaban (CR8) 1987; 109 Magnen, Rivasseau, Sénéor (CR14) 1993; 155 Dimock (CR17) 2013; 25 Balaban (CR12) 1989; 122 T Balban (1353_CR18) 1986 T Balaban (1353_CR11) 1989; 122 T Balaban (1353_CR1) 1984; 95 LF Abbott (1353_CR15) 1982; 13 PS Howe (1353_CR16) 1988; 296 T Balaban (1353_CR2) 1984; 96 T Balaban (1353_CR4) 1985; 99 T Balaban (1353_CR5) 1985; 102 J Dimock (1353_CR17) 2013; 25 A Jaffe (1353_CR13) 2006 J Magnen (1353_CR14) 1993; 155 T Balaban (1353_CR3) 1985; 98 T Balaban (1353_CR7) 1985; 102 T Balaban (1353_CR8) 1987; 109 T Balaban (1353_CR10) 1988; 119 T Balaban (1353_CR12) 1989; 122 T Balaban (1353_CR6) 1985; 99 T Balaban (1353_CR9) 1988; 116 |
| References_xml | – volume: 102 start-page: 277 year: 1985 end-page: 309 ident: CR7 article-title: The variational problem and background fields in renormalization group method for lattice gauge theories publication-title: Commun. Math. Phys. doi: 10.1007/BF01229381 – volume: 119 start-page: 243 year: 1988 end-page: 285 ident: CR10 article-title: Convergent renormalization expansions for lattice gauge field theories publication-title: Commun. Math. Phys. doi: 10.1007/BF01217741 – volume: 296 start-page: 26 year: 1988 end-page: 48 ident: CR16 article-title: The background field method and the non-linear Model publication-title: Nucl. Phys. 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| Snippet | We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in
d
=
3
,
4
and adapt it to a class of... We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in $$d = 3, 4$$ d = 3 , 4 and adapt it to... We study the variational problem as described by Balaban in his renormalization group method for Yang–Mills theories in d=3,4 and adapt it to a class of... |
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| SubjectTerms | Classical and Quantum Gravitation Dynamical Systems and Ergodic Theory Elementary Particles Mathematical and Computational Physics Mathematical Methods in Physics Original Paper Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Theoretical |
| Title | The Variational Problem and Background Field in the Renormalization Group Method for Nonlinear Sigma Models |
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