GEOMETRIA, MECHANICS AND CLASSIC FIELD THEORY (Q3145225): Difference between revisions
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GÉOMETRIE, MÉCANIQUE ET THÉORIE DES CHAMPS CLASSIQUES | |||
Revision as of 15:30, 2 December 2021
Project Q3145225 in Spain
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | GEOMETRIA, MECHANICS AND CLASSIC FIELD THEORY |
Project Q3145225 in Spain |
Statements
16,558.85 Euro
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19,481.0 Euro
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85.0 percent
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1 January 2019
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31 December 2021
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UNIVERSIDAD DE LA LAGUNA
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28°29'8.77"N, 16°18'57.38"W
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38023
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ESTE PROYECTO SE BASA EN LA INTERRELACION ENTRE LA GEOMETRIA, LA MECANICA Y LA TEORIA CLASICA DE CAMPOS. POR UN LADO, LA MECANICA GEOMETRICA SE BASA EN EL USO DE HERRAMIENTAS DE LA GEOMETRIA DIFERENCIAL EN DISTINTOS PROBLEMAS PROCEDENTES DE LA MECANICA CLASICA. EN ESTA DIRECCION, UN OBJETIVO ES ESTUDIAR DIVERSOS ASPECTOS RELACIONADOS CON LA INTEGRABILIDAD DE LAS ECUACIONES DE HAMILTON, COMO SON LA TEORIA DE HAMILTON JACOBI O LA RELACION CON LOS GRUPOS DE LIE POISSON. EN PRESENCIA DE LIGADURAS NO-HOLONOMAS, UNA HERRAMIENTA QUE CONSIDERAREMOS SERA LA HAMILTONIZACION DEL CORRESPONDIENTE SISTEMA NO-HOLONOMO. POR OTRA PARTE, CUANDO NO SABEMOS COMO INTEGRAR LAS ECUACIONES DE MOVIMIENTO, EL DESARROLLO DE INTEGRADORES GEOMETRICOS ES UNA HERRAMIENTA POTENTE PARA APROXIMAR LA DINAMICA DEL SISTEMA. _x000D_ _x000D_ NO SOLO LA MECANICA CLASICA SE NUTRE DE SU RELACION CON LA GEOMETRIA. DE HECHO, PRETENDEMOS DAR UNA NUEVA FORMULACION GEOMETRICA CANONICA DE LA TEORIA CLASICA DE CAMPOS UTILIZANDO LA GEOMETRIA AFIN._x000D_ _x000D_ RECIPROCAMENTE, DIVERSAS GEOMETRIAS HAN SIDO INTRODUCIDAS POR SU PAPEL COMO HERRAMIENTA NO SOLO DE LA MECANICA CLASICA, SINO TAMBIEN DE LA CUANTICA, TERMODINAMICA, GEOMETRIA DE LA INFORMACION.... ESTE ES EL CASO DE LA GEOMETRIA SIMPLECTICA, DE POISSON, DE CONTACTO, KAHLER¿ UNO DE NUESTROS OBJETIVOS ES INVESTIGAR SOBRE UNA ADECUADA COMBINACION DE LA GEOMETRIA KAHLER Y DE POISSON QUE NOS DEBERIA CONDUCIR A LA NOCION Y EL ESTUDIO DE LOS ESPACIOS POISSON-KAHLER. OTRO OBJETO GEOMETRICO, RELACIONADO EN ESTE CASO CON LOS SISTEMAS COMPLETAMENTE INTEGRABLES, SON LAS FIBRACIONES LAGRANGIANAS. ESTUDIAREMOS LAS ACCIONES SIMPLECTICAS FIBRADAS SOBRE ESTE TIPO DE OBJETOS. FINALMENTE, DEBIDO A SU RELACION CON LA TERMODINAMICA E INCLUSO CON AREAS MAS NOVEDOSAS, COMO LA GEOMETRIA DE LA INFORMACION Y LA NEUROGEOMETRIA, QUEREMOS ESTUDIAR LA RELACION EXISTENTE ENTRE ESTOS TEMAS Y LA GEOMETRIA DE CONTACTO. ESTOS ULTIMOS ASPECTOS CONSTITUYEN UNA LINEA EXPLORATORIA QUE ESPERAMOS SE CONSOLIDE EN FUTUROS PROYECTOS. (Spanish)
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THIS PROJECT IS BASED ON THE INTERTWINING BETWEEN GEOMETRY, MECHANICS AND CLASSICAL FIELD THEORIES. ON ONE HAND, GEOMETRIC MECHANICS IS GROUNDED IN THE USE OF TOOLS FROM DIFFERENTIAL GEOMETRY IN DIFFERENT PROBLEMS COMING FROM CLASSICAL MECHANICS. IN THIS DIRECTION, AN OBJECTIVE IS TO STUDY SEVERAL ASPECTS RELATED TO THE INTEGRABILITY OF HAMILTON EQUATIONS, SUCH AS HAMILTON-JACOBI THEORY OR THE RELATION WITH LIE POISSON GROUPS. IN THE PRESENCE OF NONHOLONOMIC CONSTRAINTS, A TOOL TO BE CONSIDERED IS THE HAMILTONIZATION OF THE CORRESPONDING NONHOLONOMIC SYSTEM. ON THE OTHER HAND, WHEN IT IS NOT KNOWN HOW TO INTEGRATE THE EQUATIONS OF MOVEMENT, THE DEVELOPMENT OF GEOMETRIC INTEGRATORS IS A POWERFUL TOOL TO APPROXIMATE THE DYNAMICS OF THE SYSTEM._x000D_ _x000D_ NOT ONLY CLASSICAL MECHANICS IS NOURISHED FROM ITS RELATION WITH GEOMETRY. INDEED, WE PRETEND TO GIVE A NEW CANONICAL GEOMETRIC FORMULATION OF THE CLASSICAL FIELD THEORY USING AFFINE GEOMETRY. _x000D_ _x000D_ CONVERSELY, SEVERAL GEOMETRIES HAVE BEEN INTRODUCED DUE TO ITS ROLE AS A TOOL, NOT ONLY IN CLASSICAL MECHANICS, BUT ALSO QUANTUM MECHANICS, THERMODYNAMICS, INFORMATION GEOMETRY... THIS IS THE CASE OF SYMPLECTIC GEOMETRY, POISSON GEOMETRY, CONTACT GEOMETRY, KAHLER... ONE OF OUR PURPOSES IS TO INVESTIGATE ABOUT A POSSIBLE COMBINATION OF KAHLER AND POISSON GEOMETRY WHICH SHOULD LEAD US TO THE NOTION AND STUDY OF POISSON-KAHLER SPACES. ANOTHER GEOMETRIC OBJECT, RELATED IN THIS CASE WITH COMPLETELY INTEGRABLE SYSTEMS, ARE LAGRANGIAN FIBRATIONS. WE WILL STUDY FIBERED SYMPLECTIC ACTIONS ON THIS TYPE OF OBJECTS. FINALLY, DUE TO ITS RELATION WITH THERMODYNAMICS AND OTHER MORE INNOVATIVE AREAS, SUCH AS INFORMATION GEOMETRY AND NEUROGEOMETRY, WE WOULD LIKE TO STUDY THE EXISTING RELATION BETWEEN THESE TOPICS AND CONTACT GEOMETRY. THESE LAST ASPECTS CONSTITUTE AN EXPLORATORY LINE WHICH WE HOPE WILL BE CONSOLIDATED IN FUTURE PROJECTS. (English)
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San Cristóbal de La Laguna
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Identifiers
PGC2018-098265-B-C32
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