GEOMETRIA, MECHANICS AND CLASSIC FIELD THEORY

Operation co-funded by EU cohesion policy (European Regional Development Fund (ERDF)) under the programme Multi-regional Spain - ERDF (2014ES16RFOP002), managing authority: Subdirección General de Gestión del FEDER, de la Dirección General de Fondos Europeos del Ministerio de Hacienda.. The source names no beneficiary for this operation. Location: Tenerife (NUTS ES709); Spain. Budget: total eligible expenditure EUR 19,481; EU co-financing EUR 16,558.85 (co-financing rate 85%), as stated by the source. Runs 2019-01-01 to 2021-12-31. Source: Kohesio, EU cohesion policy projects managed by national and regional authorities (not CORDIS); selected because its summary names quantum technology. Summary from Kohesio (English machine translation by the source): 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. 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. 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.

Original source.

Source: Kohesio (EU cohesion policy projects), European Commission, Directorate-General for Regional and Urban Policy (DG REGIO). Retrieved 2026-10-21. Licence: CC0 1.0 (Cohesion Open Data Platform, dataset 2014-2020 Kohesio projects). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: public domain dedication (CC0 1.0).

AI-assisted summary: The project "GEOMETRIA, MECHANICS AND CLASSIC FIELD THEORY" is co-funded by the EU under the Multi-regional Spain programme, with a budget of EUR 19,481. It runs from January 1, 2019, to December 31, 2021, focusing on the intersection of geometry and mechanics. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.