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 natural sciencesphysical sciencesquantum physicsquantum field theory Programme(s) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Call for proposal ERC-2010-StG_20091028 See other projects for this call Funding Scheme ERC-SG - ERC Starting Grant Host institution UNIVERSITAET LEIPZIG EU contribution € 537 226,49 Address RITTERSTRASSE 26 04109 Leipzig Germany See on map Region Sachsen Leipzig Leipzig Activity type Higher or Secondary Education Establishments Principal investigator Stefan Hollands (Dr.) Administrative Contact Gerhard Fuchs (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data Beneficiaries (2) Sort alphabetically Sort by EU Contribution Expand all Collapse all UNIVERSITAET LEIPZIG Germany EU contribution € 537 226,49 Address RITTERSTRASSE 26 04109 Leipzig See on map Region Sachsen Leipzig Leipzig Activity type Higher or Secondary Education Establishments Principal investigator Stefan Hollands (Dr.) Administrative Contact Gerhard Fuchs (Mr.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data CARDIFF UNIVERSITY United Kingdom EU contribution € 280 872,11 Address NEWPORT ROAD 30 36 CF24 0DE Cardiff See on map Region Wales East Wales Cardiff and Vale of Glamorgan Activity type Higher or Secondary Education Establishments Administrative Contact Eevi Laukkanen (Ms.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
