Objective
The development of a mathematical framework for the unified description of all fundamental forces of nature is one of the biggest challenges in mathematical physics and is, therefore, an important objective of European fundamental research.
In order to describe gravity together with the other forces, such a framework will have to unite and generalize the differential geometrical methods of general relativity and the operator algebraic methods of quantum theory. One of the promising candidates for this is non-commutative geometry.
However, its relation to classical gravity and curvature is still an open problem. The project objective is to construct and study non-commutative geometry as induced by curvature on Riemann manifolds, in collaboration with A. Weinstein (Berkeley) and P. Schupp (IU Bremen). Due to the uncertainty principle, a quantum particle in curved spacetime is always subject to tidal forces even if it moves on a geodesic.
Analogous to the motion in a magnetic field, the quantization of the motion in tidal forces yields, in the strong field limit, non-commutative coordinates. The main idea is that, locally, the motion in tidal forces can be reinterpreted as free motion on this non-commutative geometry.
For a mathematically rigorous implementation of this idea, the Hamiltonian formulation of geodesic motion is to be linearized, the local symplectic structure to be quantized, leading to a Lie algebroid description of a bundle of local non-commutative geometries.
The global non-commutative geometry is described in the integrable case by the convolution algebra of the corresponding Lie groupoid, in the non-integrable case by the star product realization of the corresponding Poisson algebra.
These general constructions are to be computed explicitly for the examples of Schwarzschild and Robertson-Walker spacetimes. The representation theory of the resulting algebras will be studied and compared with black hole and cosmological phenomenology.
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 relativistic mechanics
- natural sciences mathematics pure mathematics topology symplectic topology
- natural sciences physical sciences astronomy astrophysics black holes
- natural sciences mathematics pure mathematics algebra
- 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-6
See other projects for this call
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.
OIF - Marie Curie actions-Outgoing International Fellowships
Coordinator
750 561 BREMEN
Germany
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.