--- title: "Causality and Dispersion Relations and the Role of the S-matrix in the Ongoing Research • CBPF Index" description: "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." canonical_url: "https://index.cbpf.br/en/publicacoes/6ad2a767639f62b11adbb33e" locale: en meta: "og:description": "CBPF INDEX is the system that tracks the scientific and technological output of CBPF. It lists the articles, books, technical reports and other publications of the whole CBPF community." "og:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Causality%2Band%2BDispersion%2BRelations%2Band%2Bthe%2BRole%2Bof%2Bthe%2BS-matrix%2Bin%2Bthe%2BOngoing%2BResearch%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_Bert%2BSchroer%2Cdetalhe_~MjgvMDIvMjAxMQ%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIzM2Ui%2Cs_NsSas-ZYOWQXivq2.png" "og:image:height": "600" "og:image:type": image/png "og:image:width": "1200" "og:title": "Causality and Dispersion Relations and the Role of the S-matrix in the Ongoing Research • CBPF Index" "twitter:image": "https://index.cbpf.br/_og/d/c_Item%2Ctitulo_Causality%2Band%2BDispersion%2BRelations%2Band%2Bthe%2BRole%2Bof%2Bthe%2BS-matrix%2Bin%2Bthe%2BOngoing%2BResearch%2Ctipo_Physics%2BNote%2Ccor_~I2E4MmMwMA%2Cautores_Bert%2BSchroer%2Cdetalhe_~MjgvMDIvMjAxMQ%2Csecao_Publications%2Cp_Ii9lbi9wdWJsaWNhY29lcy82YWQyYTc2NzYzOWY2MmIxMWFkYmIzM2Ui%2Cs_NsSas-ZYOWQXivq2.png" --- > Index of every page on this site: [llms.txt](https://index.cbpf.br/llms.txt) **Physics Note****Published** # **Causality and Dispersion Relations and the Role of the S-matrix in the Ongoing Research** **Bert Schroer** 02/28/2011 [**Download PDF **0.2 MB](https://index.cbpf.br/files/publicacao/6ad2a767639f62b11adbb33e/pdf) [**Contact owner**](mailto:apub@cbpf.br?subject=Causality%20and%20Dispersion%20Relations%20and%20the%20Role%20of%20the%20S-matrix%20in%20the%20Ongoing%20Research) ## **Publication details**
Authors
Bert Schroer
Type
Physics Note
Status
Published
Publication date
28/02/2011
Description
The adaptation of the Kramers-Kronig dispersion relations to the causal localization structure of QFT led to an important project in particle physics, the only one with a successful closure. The same cannot be said about the subsequent attempts to formulate particle physics as a pure S-matrix project. The feasibility of a pure S-matrix approach are critically analyzed and their serious shortcomings are highlighted. Whereas the conceptual/mathematical demands of renormalized perturbation theory are modest and misunderstandings could easily be corrected, the correct understanding about the origin of the crossing property demands the use of the mathematical theory of modular localization and its relation to the thermal KMS condition. These concepts which combine localization, vacuum polarization and thermal properties under the roof of modular theory will be explained and their use in a new constructive (nonperturbative) approach to QFT will be indicated. The S-matrix still plays a predominant role, but different from Heisenberg's and Mandelstam's proposals the new project is not a pure S-matrix approach.
Year
2011
Number
CBPF-NF-004/11
Linked to a thesis
No
Linked to a grant
No
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