QC&C
Quantum fields and Curvature--Novel Constructive Approach via Operator Product Expansion
| Coordinatore | UNIVERSITAET LEIPZIG
Spiacenti, non ci sono informazioni su questo coordinatore. Contattare Fabio per maggiori infomrazioni, grazie. |
| Nazionalità Coordinatore | Germany [DE] |
| Totale costo | 818˙098 € |
| EC contributo | 818˙098 € |
| Programma | 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) |
| Code Call | ERC-2010-StG_20091028 |
| Funding Scheme | ERC-SG |
| Anno di inizio | 2011 |
| Periodo (anno-mese-giorno) | 2011-04-01 - 2016-03-31 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
CARDIFF UNIVERSITY
Organization address
address: Newport Road 30-36 contact info |
UK (CARDIFF) | beneficiary | 280˙872.12 |
| 2 |
UNIVERSITAET LEIPZIG
Organization address
address: RITTERSTRASSE 26 contact info |
DE (LEIPZIG) | hostInstitution | 537˙226.50 |
| 3 |
UNIVERSITAET LEIPZIG
Organization address
address: RITTERSTRASSE 26 contact info |
DE (LEIPZIG) | hostInstitution | 537˙226.50 |
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Obiettivo del progetto (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.'