Objective
It was realized already from the beginning that the theory of quantized fields (QFT) does not easily fit into known mathematical structures, and the quest for a satisfactory mathematical foundation continues to-day. Parts of this theory have already been tremendously successful, e.g. in the quantitative description of elementary particles, and ideas from QFT have revolutionized entire fields of mathematics. But the non-perturbative construction of the most important QFT s, namely renormalizable theories in 4d, remains unsolved. The aim of this project is to make a substantial contribution to this quest for the mathematical construction of such QFT s (on curved manifolds), and the exploration of their mathematical structure. We want to pursue a novel ansatz to achieve this goal. The essence of our novel approach is to focus attention on the algebraic backbone of the theory, which manifests itself in the so-called operator-product-expansion. The study of such algebraic structures related to operator products has already been tremendously useful in the study of conformal field theories in low dimensions, but we here propose that a suitable version of it also has great potential to be used as a constructive tool for the much more complicated quantum gauge theories in four dimensions. It is not expected that an explicit solution can be obtained for such models-especially so in curved space-but the idea is instead to analyze powerful consistency conditions on the quantum field theory arising from the OPE ( associativity conditions ) and to use them to prove that the theory exists in a mathematically rigorous sense. Our approach will be complemented by other powerful and deep mathematical tools that have been developed over the past decades, such as the sophisticated non-perturbative expansions uncovered in the school of constructive quantum fields theory , Hochschild cohomology, RG-flow equation techniques, microlocal analysis, curvature expansions, and many more.
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: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: https://op.europa.eu/en/web/eu-vocabularies/euroscivoc.
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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.
ERC-2010-StG_20091028
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.
Host institution
04109 Leipzig
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.