{ "meta": { "api_type": "NWO Projects API", "version": "1.0.2", "licence": { "name": "CC0 1.0 Universal", "url": "https://creativecommons.org/publicdomain/zero/1.0", "description": "To the extent possible under law, all copyright and related or neighbouring rights have been waived worldwide to the data made available through this API." }, "documentation": "https://doi.org/10.5281/zenodo.14918287", "release_date": "2025-08-20T00:00:00", "funder": "https://doi.org/10.13039/501100003246", "ror_id": "https://ror.org/04jsz6e67", "date": "2026-11-05T00:00:00", "count": 1, "per_page": 100, "pages": 1, "page": 1 }, "projects": [ { "project_id": "639.031.827", "title": "Noncommutative geometry of quantum gauge fields", "funding_scheme_id": 417, "funding_scheme": "NWO-Talentprogramma Veni 2008 EW", "department": "Exacte en Natuurwetenschappen", "sub_department": "Exacte Wetenschappen", "start_date": "2009-01-01T00:00:00", "end_date": "2012-09-28T00:00:00", "reporting_year": 2008, "summary_nl": "Noncommutative geometry is a general mathematical framework that so far has been applied to diverse problems in analysis, geometry, number theory, and physics. The goal of the proposed project is to apply this framework to the mathematical formulation of nonabelian quantum gauge field theories. This would be a first step towards a new approach to one of the Millennium Prize Problems of the Clay Mathematical Institute. Gauge fields lie at the basis of modern elementary particle physics: they form the building blocks of the so-called Standard Model of high-energy physics. This model describes three of the four known fundamental interactions in nature, namely the electromagnetic, the weak and the strong interaction. Empirically, the Standard Model is extremely successful, and therefore it is a source of frustration to mathematical physicists that it has not been formulated as a mathematically consistent theory. \n\nThe classical field theory underlying the Standard Model has already been reformulated in terms of Noncommutative geometry by Connes and others. The next step, which I propose to carry out here, is to quantize the theory, i.e. take into account the quantum effects necessary to describe elementary particles. As a first step towards a mathematical construction of the full (nonperturbative) theory, I intend to formulate perturbative quantum gauge theories in noncommutative geometrical terms. On the technical side, a central role will be played by quantum symmetries corresponding to the classical gauge symmetries, as these are crucial in proving finiteness of the renormalized quantum theory. Also, instead of the usual Feynman integrals in quantum field theory, certain traces of operators will play an essential role in the definition of the correlation functions. The evaluation of these 'Feynman traces' requires a novel application of functional analytical techniques such as (holomorphic) functional calculus, trace ideals and spectral theory of unbounded operators.", "summary_en": "Noncommutative geometry is a general mathematical framework that so far has been applied to diverse problems in analysis, geometry, number theory, and physics. The goal of the proposed project is to apply this framework to the mathematical formulation of nonabelian quantum gauge field theories. This would be a first step towards a new approach to one of the Millennium Prize Problems of the Clay Mathematical Institute. Gauge fields lie at the basis of modern elementary particle physics: they form the building blocks of the so-called Standard Model of high-energy physics. This model describes three of the four known fundamental interactions in nature, namely the electromagnetic, the weak and the strong interaction. Empirically, the Standard Model is extremely successful, and therefore it is a source of frustration to mathematical physicists that it has not been formulated as a mathematically consistent theory. \n\nThe classical field theory underlying the Standard Model has already been reformulated in terms of Noncommutative geometry by Connes and others. The next step, which I propose to carry out here, is to quantize the theory, i.e. take into account the quantum effects necessary to describe elementary particles. As a first step towards a mathematical construction of the full (nonperturbative) theory, I intend to formulate perturbative quantum gauge theories in noncommutative geometrical terms. On the technical side, a central role will be played by quantum symmetries corresponding to the classical gauge symmetries, as these are crucial in proving finiteness of the renormalized quantum theory. Also, instead of the usual Feynman integrals in quantum field theory, certain traces of operators will play an essential role in the definition of the correlation functions. The evaluation of these 'Feynman traces' requires a novel application of functional analytical techniques such as (holomorphic) functional calculus, trace ideals and spectral theory of unbounded operators.", "project_members": [ { "role": "Project leader", "member_id": 130274, "last_name": "Suijlekom", "degree_pre_nominal": "prof. dr.", "initials": "W.D.", "first_name": "Walter", "prefix": "van", "organisation": "Radboud Universiteit Nijmegen||Faculteit der Natuurwetenschappen, Wiskunde en Informatica||Subfaculteit Wiskunde", "organisation_id": 77719, "ror": "https://ror.org/016xsfp80", "active": false }, { "role": "Researcher", "member_id": 130274, "last_name": "Suijlekom", "degree_pre_nominal": "prof. dr.", "initials": "W.D.", "first_name": "Walter", "prefix": "van", "organisation": "Radboud Universiteit Nijmegen||Faculteit der Natuurwetenschappen, Wiskunde en Informatica||Subfaculteit Wiskunde", "organisation_id": 77719, "ror": "https://ror.org/016xsfp80", "active": false }, { "role": "Main Applicant", "member_id": 130274, "last_name": "Suijlekom", "degree_pre_nominal": "prof. dr.", "initials": "W.D.", "first_name": "Walter", "prefix": "van", "organisation": "Radboud Universiteit Nijmegen||Faculteit der Natuurwetenschappen, Wiskunde en Informatica||Institute for Mathematics, Astrophysics and Particle Physics (IMAPP)", "organisation_id": 73889, "ror": "https://ror.org/016xsfp80", "active": true } ], "products": [ { "title": "Recursive relations in the core Hopf algebra", "year": 2009, "edition": "820", "start": 682, "end": 693, "type": "Wetenschappelijk artikel", "journal_title": "Nucl. Phys.", "authors": [ { "last_name": "Suijlekom", "initials": "W.D.", "prefix": "van", "role": "Auteur", "index_number": 1 }, { "last_name": "Kreimer", "initials": "D", "role": "Auteur", "index_number": 2 } ] }, { "title": "The noncommutative geometry of Yang-Mills fields", "year": 2011, "edition": "61", "start": 1122, "end": 1134, "type": "Wetenschappelijk artikel", "journal_title": "J. Geom. Phys.", "authors": [ { "last_name": "Suijlekom", "initials": "W.D.", "prefix": "van", "role": "Auteur", "index_number": 1 }, { "last_name": "Boeijink", "initials": "J", "role": "Auteur", "index_number": 2 } ] }, { "title": "Perturbations and operator trace functions.", "year": 2011, "edition": "260", "start": 2483, "end": 2496, "type": "Wetenschappelijk artikel", "journal_title": "Journ. Funct. Anal.", "authors": [ { "last_name": "Suijlekom", "initials": "W.D.", "prefix": "van", "role": "Auteur", "index_number": 1 } ] }, { "title": "Renormalization of the spectral action for the Yang-Mills system.", "year": 2011, "edition": "3", "start": 146, "type": "Wetenschappelijk artikel", "url_open_access": "http://www.springerlink.com/content/f4x526254517m245/fulltext.pdf", "journal_title": "JHEP", "authors": [ { "last_name": "Suijlekom", "initials": "W.D.", "prefix": "van", "role": "Auteur", "index_number": 1 } ] }, { "title": "Interview Alain Connes. The flashes of insight never came for free", "year": 2010, "edition": "5", "start": 250, "end": 256, "type": "Publicatie", "url_open_access": "http://www.nieuwarchief.nl/serie5/deel011/dec2010/nawdec250.pdf", "journal_title": "Archief voor Wiskunde", "authors": [ { "last_name": "Suijlekom", "initials": "W.D.", "prefix": "van", "role": "Maker", "index_number": 1 }, { "last_name": "Landsman", "initials": "N.P.", "role": "Maker", "index_number": 2 }, { "last_name": "Cornelissen", "initials": "G.L.M.", "role": "Maker", "index_number": 3 } ] } ] } ] }