GPSAFT · Geometry of pseudoriemannian spaces and its application in field theory
6РП — Действия „Мария Кюри“
- Период
- 2004-05-01 → 2005-04-30
- Финансиране от ЕС
- 37 938 €
- Участници
- 1
- Схема
- EIF
Линиите свързват координатора с партньорите.
Накратко на български
Геометрията на специални математически пространства, като квантовите сфери и торои, се анализира чрез нови структури и изчисления. Тези разработки помагат за по-доброто разбиране на моделите в теорията на полето и Римановата геометрия.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Final Activity Report Summary - GPSAFT (Geometry of pseudoriemannian spaces and its application in field theory)
The main results of the project included: 1. the construction of spectral triples on a large family of non-commutative objects, including the quantum three-sphere 2. the construction of different spin structures on non-commutative tori 3. the construction of indefinite-type metrics of quantum three-sphere 4. the calculation of Hochschild and cyclic homologies on quantum hyperplanes. These were the fundamental steps, as was the main objective of the first year of the long-term project. The future research steps would be the analysis of field-theory models and Riemannian geometry, and were under investigation by the time of the project completion.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
The success of no commutative geometry as an algebraic tool, which enables the geometrical unification of fundamental interactions with gravity and opens new possibilities in our understanding of the mathematical structure of the geometry of space-time and quantum field theory, is limited by its restriction to Euclidean signatures. The aim of the proposed project is the construction of the fundaments of the no commutative theory of pseudoriemannian no commutative spaces, based on the Euclidean formulation and on conjectured easy examples (constructed like, for instance, the Cartesian product of a Euclidean manifold with the real line) but not restricting oneself to such cases only). The main problem and the main task are the construction of the Direct operator and the analysis of its spectral properties, and the proposition of the general definition (like in Cones Euclidean framework). It is rather evident that in the no commutative description of pseudoriemannian spin manifolds one should use the formalism of Rein spaces and Krein-selfadjoint operators (that is selfadjoint with respect to the Rein product). The analysis of their spectral properties and the definition of a class of such operators, which generalise the Direct operator, is the first objective of the project. The final task of the proposed research is the test of construction and its mathematical justification, which is the formulation and verification (on examples) of the local index formula of Connes-Moscovici adapted to the pseudoriemannian case, generalising their Euclidean result. The construction of physically motivated examples, in particular the no commutative analysis of singularities (in the Schawarzschild-type geometries in no commutative geometries) shall follow.
Оригинален текст от CORDIS (на английски).
Участници
- UNIWERSYTET JAGIELLONSKI · KRAKOWКоординаторПолша
Връзки
Данни: CORDIS, © Европейски съюз