Objective
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.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences physical sciences quantum physics quantum field theory
- natural sciences mathematics pure mathematics geometry
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
FP6-2002-MOBILITY-11
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Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Coordinator
KRAKOW
Poland
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.