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Contenido archivado el 2024-06-16

Geometry of pseudoriemannian spaces and its application in field theory

Objetivo

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.

Ámbito científico (EuroSciVoc)

Palabras clave

Tema(s)

Convocatoria de propuestas

FP6-2002-MOBILITY-11
Consulte otros proyectos de esta convocatoria

Régimen de financiación

EIF - Marie Curie actions-Intra-European Fellowships

Coordinador

UNIWERSYTET JAGIELLONSKI
Aportación de la UE
Sin datos
Dirección
Ul. Golebia 24
KRAKOW
Polonia
Coste total
Sin datos