Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number
This work studies two physical effects derived from considering topological solutions to gauge theories. In particular, for the case of euclidean solutions (instantons), we analyze the singlet chiral anomaly, while for the solutions in Minkowski space (solitons), we clarify the link between kinks an...
- Autores:
-
Morales Castellanos, Juan Sebastián
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2022
- Institución:
- Universidad de los Andes
- Repositorio:
- Séneca: repositorio Uniandes
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.uniandes.edu.co:1992/54586
- Acceso en línea:
- http://hdl.handle.net/1992/54586
- Palabra clave:
- Quantum field theory
Gauge theory
Instanton
Soliton
Differential geometry
Fermiones
Quiralidad
Física
Matemáticas
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
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| dc.title.none.fl_str_mv |
Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number |
| dc.title.alternative.none.fl_str_mv |
Aspectos topológicos en teorías Gauge: Anomalía quiral singlete y número fermiónico fraccionario |
| title |
Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number |
| spellingShingle |
Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number Quantum field theory Gauge theory Instanton Soliton Differential geometry Fermiones Quiralidad Física Matemáticas |
| title_short |
Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number |
| title_full |
Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number |
| title_fullStr |
Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number |
| title_full_unstemmed |
Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number |
| title_sort |
Some topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion number |
| dc.creator.fl_str_mv |
Morales Castellanos, Juan Sebastián |
| dc.contributor.advisor.none.fl_str_mv |
Reyes Lega, Andrés Fernando |
| dc.contributor.author.none.fl_str_mv |
Morales Castellanos, Juan Sebastián |
| dc.contributor.jury.none.fl_str_mv |
Cardona Guio, Alexander |
| dc.contributor.researchgroup.es_CO.fl_str_mv |
Quantum Field Theory and Mathematical Physics |
| dc.subject.keyword.none.fl_str_mv |
Quantum field theory Gauge theory Instanton Soliton Differential geometry |
| topic |
Quantum field theory Gauge theory Instanton Soliton Differential geometry Fermiones Quiralidad Física Matemáticas |
| dc.subject.armarc.none.fl_str_mv |
Fermiones Quiralidad |
| dc.subject.themes.es_CO.fl_str_mv |
Física Matemáticas |
| description |
This work studies two physical effects derived from considering topological solutions to gauge theories. In particular, for the case of euclidean solutions (instantons), we analyze the singlet chiral anomaly, while for the solutions in Minkowski space (solitons), we clarify the link between kinks and fractional fermion number. Additionally, we present a review on the geometry of gauge theories, a discussion on the Fujikawa method for anomalies in the light of the Atiyah-Singer index theorem, and an investigation of the QCD vacua structure. |
| publishDate |
2022 |
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2022-02-08T20:27:39Z |
| dc.date.available.none.fl_str_mv |
2022-02-08T20:27:39Z |
| dc.date.issued.none.fl_str_mv |
2022-02-21 |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Pregrado |
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http://purl.org/coar/version/c_970fb48d4fbd8a85 |
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info:eu-repo/semantics/bachelorThesis |
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Text |
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http://hdl.handle.net/1992/54586 |
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instname:Universidad de los Andes |
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reponame:Repositorio Institucional Séneca |
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eng |
| language |
eng |
| dc.relation.references.es_CO.fl_str_mv |
M. Nakahara, Geometry, Topology and Physics, Taylor and Francis Group (2003). F. Atiyah. Geometry of Yang-Mills fields, pages 216¿221. Springer Berlin Heidel berg, Berlin, Heidelberg, (1978). E. Kanso, J. Marsden, C. Rowley, and J. Melli-Huber, Locomotion of Articulated Bodies in a Perfect Fluid, J. Nonlinear Sci. 15 (2005). Tazerenix. Wikimedia Commons: Images by Tazerenix, (2021). R. A. Bertlmann, Anomalies in Quantum Field Theory, Oxford Science Publications (1996). R. Feynman, A. Hibbs, and D. Styer, Quantum Mechanics and Path Integrals, Dover Publications (2010). V. P. Nair, Quantum Field Theory: A Modern Perspective, Springer Science (2005). R. Feynman, R. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. II: The New Millennium Edition: Mainly Electromagnetism and Matter, Basic Books (2011). P. Bracken, Quantum mechanics in terms of an action principle, Canadian Journal of Physics 75, 261¿271 (2011). A. Belavin, A. Polyakov, A. Schwartz, and Y. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Physics Letters B 59, 85¿87 (1975). E. J. Weinberg, Classical Solutions in Quantum Field Theory: Solitons and In stantons in High Energy Physics, Cambridge University Press (2012). S. L. Adler, Axial-Vector Vertex in Spinor Electrodynamics, Phys. Rev. 177, 2426¿2438 (1969). K. Fujikawa and H. Suzuki, Path integrals and quantum anomalies (2004). K. Fujikawa, Path-Integral Measure for Gauge-Invariant Fermion Theories, Phys. Rev. Lett. 42, 1195¿1198 (1979). G. Rudolph and M. Schmidt, Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields, Springer Netherlands (2017). E. Z. Hisham Sati, Silviu-Marian Udrescu, GJM 3, 60¿93 (2018). H. Lawson and M. Michelsohn, Spin Geometry (PMS-38), Volume 38, Princeton University Press (1989). P. Shanahan, The Atiyah-Singer Index Theorem: An Introduction, Springer (1978). N. Berline, E. Getzler, and M. Vergne, Heat Kernels and Dirac Operators, Springer Berlin Heidelberg (2003). S. Coleman, Aspects of Symmetry: Selected Erice Lectures, Cambridge University Press (1988). M. Shifman, Instantons in Gauge Theories, World Scientific (1994). R. Rajaraman, Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory, North-Holland Publishing Company (1982). D. Spitz. Solitons with fractional fermion number, (2016). R. Jackiw and C. Rebbi, Solitons with fermion number ½, Phys. Rev. D 13, 3398¿3409 (1976). A. J. Niemi and G. W. Semenoff, Fermion Number Fractionization in Quantum Field Theory, Phys. Rept. 135, 99 (1986). L. Alvarez-Gaume and M. A. Vazquez-Mozo, An Invitation to Quantum Field Theory (2012). K. Rao, N. Sahu, and P. K. Panigrahi. Fermion Number Fractionization, (2007). |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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info:eu-repo/semantics/openAccess |
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100 páginas |
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Física |
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Facultad de Ciencias |
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Departamento de Física |
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Universidad de los Andes |
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Al consultar y hacer uso de este recurso, está aceptando las condiciones de uso establecidas por los autores.http://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Reyes Lega, Andrés Fernandovirtual::9238-1Morales Castellanos, Juan Sebastián4d97c638-c04c-4cda-b8fa-e7003c49e23d600Cardona Guio, AlexanderQuantum Field Theory and Mathematical Physics2022-02-08T20:27:39Z2022-02-08T20:27:39Z2022-02-21http://hdl.handle.net/1992/54586instname:Universidad de los Andesreponame:Repositorio Institucional Sénecarepourl:https://repositorio.uniandes.edu.co/This work studies two physical effects derived from considering topological solutions to gauge theories. In particular, for the case of euclidean solutions (instantons), we analyze the singlet chiral anomaly, while for the solutions in Minkowski space (solitons), we clarify the link between kinks and fractional fermion number. Additionally, we present a review on the geometry of gauge theories, a discussion on the Fujikawa method for anomalies in the light of the Atiyah-Singer index theorem, and an investigation of the QCD vacua structure.En este trabajo estudiamos dos efectos físicos que se derivan de considerar soluciones topológicas a teorías gauge. En particular, para las soluciones en el espacio euclido (instantones) analizamos la anomalía quiral singlete, y para las soluciones en el espacio de Minkowski (solitones) esclarecemos el vínculo entre kinks y la fraccionalización del número fermiónico. Adicionalmente, presentamos una revisión de la geometría intrínseca de las teorías gauge, discutimos el método de Fujikawa para anomalías a la luz del teorema de Atiyah-Singer e investigamos la estructura del vacío en QCD.FísicoPregrado100 páginasengUniversidad de los AndesFísicaFacultad de CienciasDepartamento de FísicaSome topological aspects in Gauge theories: Singlet chiral anomaly and fractional fermion numberAspectos topológicos en teorías Gauge: Anomalía quiral singlete y número fermiónico fraccionarioTrabajo de grado - Pregradoinfo:eu-repo/semantics/bachelorThesishttp://purl.org/coar/resource_type/c_7a1fhttp://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/TPQuantum field theoryGauge theoryInstantonSolitonDifferential geometryFermionesQuiralidadFísicaMatemáticasM. Nakahara, Geometry, Topology and Physics, Taylor and Francis Group (2003).F. Atiyah. Geometry of Yang-Mills fields, pages 216¿221. Springer Berlin Heidel berg, Berlin, Heidelberg, (1978).E. Kanso, J. Marsden, C. Rowley, and J. Melli-Huber, Locomotion of Articulated Bodies in a Perfect Fluid, J. Nonlinear Sci. 15 (2005).Tazerenix. Wikimedia Commons: Images by Tazerenix, (2021).R. A. Bertlmann, Anomalies in Quantum Field Theory, Oxford Science Publications (1996).R. Feynman, A. Hibbs, and D. Styer, Quantum Mechanics and Path Integrals, Dover Publications (2010).V. P. Nair, Quantum Field Theory: A Modern Perspective, Springer Science (2005).R. Feynman, R. Leighton, and M. Sands, The Feynman Lectures on Physics, Vol. II: The New Millennium Edition: Mainly Electromagnetism and Matter, Basic Books (2011).P. Bracken, Quantum mechanics in terms of an action principle, Canadian Journal of Physics 75, 261¿271 (2011).A. Belavin, A. Polyakov, A. Schwartz, and Y. Tyupkin, Pseudoparticle solutions of the Yang-Mills equations, Physics Letters B 59, 85¿87 (1975).E. J. Weinberg, Classical Solutions in Quantum Field Theory: Solitons and In stantons in High Energy Physics, Cambridge University Press (2012).S. L. Adler, Axial-Vector Vertex in Spinor Electrodynamics, Phys. Rev. 177, 2426¿2438 (1969).K. Fujikawa and H. Suzuki, Path integrals and quantum anomalies (2004).K. Fujikawa, Path-Integral Measure for Gauge-Invariant Fermion Theories, Phys. Rev. Lett. 42, 1195¿1198 (1979).G. Rudolph and M. Schmidt, Differential Geometry and Mathematical Physics: Part II. Fibre Bundles, Topology and Gauge Fields, Springer Netherlands (2017).E. Z. Hisham Sati, Silviu-Marian Udrescu, GJM 3, 60¿93 (2018).H. Lawson and M. Michelsohn, Spin Geometry (PMS-38), Volume 38, Princeton University Press (1989).P. Shanahan, The Atiyah-Singer Index Theorem: An Introduction, Springer (1978).N. Berline, E. Getzler, and M. Vergne, Heat Kernels and Dirac Operators, Springer Berlin Heidelberg (2003).S. Coleman, Aspects of Symmetry: Selected Erice Lectures, Cambridge University Press (1988).M. Shifman, Instantons in Gauge Theories, World Scientific (1994).R. Rajaraman, Solitons and Instantons: An Introduction to Solitons and Instantons in Quantum Field Theory, North-Holland Publishing Company (1982).D. Spitz. Solitons with fractional fermion number, (2016).R. Jackiw and C. Rebbi, Solitons with fermion number ½, Phys. Rev. D 13, 3398¿3409 (1976).A. J. Niemi and G. W. Semenoff, Fermion Number Fractionization in Quantum Field Theory, Phys. Rept. 135, 99 (1986).L. Alvarez-Gaume and M. A. Vazquez-Mozo, An Invitation to Quantum Field Theory (2012).K. Rao, N. Sahu, and P. K. Panigrahi. Fermion Number Fractionization, (2007).201615855Publicationhttps://scholar.google.es/citations?user=04V0g64AAAAJvirtual::9238-1https://scienti.minciencias.gov.co/cvlac/visualizador/generarCurriculoCv.do?cod_rh=0000055174virtual::9238-19cfe3fb3-ca67-4abc-bf3f-6ceb7f9f4adfvirtual::9238-19cfe3fb3-ca67-4abc-bf3f-6ceb7f9f4adfvirtual::9238-1ORIGINALSome topological aspects in Gauge theories.pdfSome topological aspects in Gauge theories.pdfTrabajo de gradoapplication/pdf1313290https://repositorio.uniandes.edu.co/bitstreams/e0aa35f3-2793-4393-8186-532a80fe6097/download3cd0441f126fb560d79b355a4f07d9aeMD52TEXTSome topological aspects in Gauge theories.pdf.txtSome topological aspects in Gauge theories.pdf.txtExtracted texttext/plain160410https://repositorio.uniandes.edu.co/bitstreams/b00710fb-d455-4f3a-a509-aab2d89066b1/download088f7e8954b1ae5ff5f531c58ea5e091MD53THUMBNAILSome topological aspects in Gauge theories.pdf.jpgSome topological aspects in Gauge theories.pdf.jpgIM Thumbnailimage/jpeg9637https://repositorio.uniandes.edu.co/bitstreams/832988ac-96f9-4881-a058-263e2ad9d127/download5be403cae5510fb3f6bc2487098ee33aMD54LICENSElicense.txtlicense.txttext/plain; charset=utf-81810https://repositorio.uniandes.edu.co/bitstreams/fc63cbe9-fc0b-49c9-b330-072028bd18e8/download5aa5c691a1ffe97abd12c2966efcb8d6MD511992/54586oai:repositorio.uniandes.edu.co:1992/545862024-03-13 13:52:59.958http://creativecommons.org/licenses/by-nc-sa/4.0/open.accesshttps://repositorio.uniandes.edu.coRepositorio institucional Sénecaadminrepositorio@uniandes.edu.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 |