Publications

Below you find my list of publications, sorted by theme. At the bottom you find books and more popularizing articles.

Preprints

  • Factorization of Dirac operators on almost-regular fibrations of spin$^c$ manifolds (with Jens Kaad)  
  • Quantization commutes with singular reduction: cotangent bundles of compact Lie groups (with Jord Boeijink and Klaas Landsman)  

Publications

Noncommutative geometry and particle-physics

  • Grand Unification in the Spectral Pati-Salam Model (with Ali Chamseddine and Alain Connes). JHEP11(2015)011  
  • Beyond the Spectral Standard Model: Emergence of Pati-Salam Unification (with Ali Chamseddine and Alain Connes). JHEP 11 (2013) 132  
  • Gauge networks in noncommutative geometry (with Matilde Marcolli). J. Geom. Phys. 75 (2014) 71-91  
  • Inner Fluctuations in Noncommutative Geometry without the first order condition (with Ali Chamseddine and Alain Connes). J. Geom. Phys. 73 (2013) 222-234  
  • Going beyond the Standard Model with noncommutative geometry (with Thijs van den Broek). JHEP 3 (2013) 112  
  • Particle Physics from Almost Commutative Spacetimes (with Koen van den Dungen). Rev. Math. Phys. 24 (2012) 1230004  
  • Supersymmetric QCD from noncommutative geometry (with Thijs van den Broek). Phys. Lett. B. 699 (2011) 119-122  
  • Electrodynamics from Noncommutative Geometry (with Koen van den Dungen). J. Noncomm. Geom. 7 (2013) 433-456  
  • The noncommutative geometry of Yang-Mills fields (with Jord Boeijink). J. Geom. Phys. 61 (2011) 1122-1134  
  • Supersymmetric QCD and noncommutative geometry (with Thijs van den Broek). Commun. Math. Phys. 303 (2011) 149-173  

Noncommutative geometry and applications

  • Factorization of Dirac operators on toric noncommutative manifolds (with Jens Kaad). J. Geom. Phys. 132 (2018) 282-300.  
  • Reflection positivity in higher derivative scalar theories (with Francesca Arici, Daniel Becker, Chris Ripken, Frank Saueressig). To appear in J. Math. Phys.  
  • On a theorem of Kucerovsky for half-closed chains (with Jens Kaad). To appear in J. Operator Theory  
  • Reduction of quantum systems and the local Gauss law (with Ruben Stienstra). Lett. Math. Phys. (online first).  
  • Quantum lattice gauge fields and groupoid C*-algebras (with Francesca Arici and Ruben Stienstra). Annales Henri Poincare (online first).  
  • Noncommutative geometry and the BV formalism: application to a matrix model (with Roberta Iseppi). J. Geom. Phys 120 (2017) 129-141.  
  • Riemannian submersions and factorization of Dirac operators (with Jens Kaad). To appear in J. Noncommut. Geom.  
  • Localizing gauge theories from noncommutative geometry. Adv. Math. 290 (2016) 682-708.  
  • Perturbation semigroup of matrix algebras (with Niels Neumann). J. Noncomm. Geom 10 (2016) 245-264  
  • Gauge Theory for Spectral Triples and the Unbounded Kasparov Product (with Simon Brain and Bram Mesland). J. Noncomm. Geom. 10 (2016) 135-206  
  • Perturbations and operator trace functions. Journ. Funct. Anal. 260 (2011) 2483-2496  
  • Holomorphic structures on the quantum projective line (with G. Landi and M. Khalkhali). Int. Math. Res. Not. IMRN (2010) doi 10.1093/imrn/rnq097  
  • Noncommutative tori and the Riemann-Hilbert correspondence (with S. Mahanta). J. Noncomm. Geom. 3 (2009) 261-287  
  • The Dirac operator on SUq(2) (with L. Dabrowski, G. Landi, A. Sitarz and J. Varilly). Commun. Math. Phys. 259 (2005), 729-759  
  • The local index formula for SUq(2) (with L. Dabrowski, G. Landi, A. Sitarz and J. Varilly). K-Theory 35 (2005) 375-394  
  • The noncommutative Lorentzian cylinder as an isospectral deformation. J. Math. Phys. 30 (2004), 537-556  

Noncommutative geometry and renormalization

  • Renormalizability conditions for almost-commutative manifolds. Annales Henri Poincare 15 (2014), 985-1011  
  • Renormalizability conditions for almost-commutative geometries. Phys. Lett. B711 (2012) 434-438  
  • Renormalization of the asymptotically expanded Yang-Mills spectral action. Commun. Math. Phys. 312 (2012) 883-912  
  • Renormalization of the spectral action for the Yang-Mills system. JHEP 3 (2011) 146  

Renormalization of gauge theories using Hopf algebras

  • Quantization of gauge fields, graph polynomials and graph cohomology (with Dirk Kreimer and Matthias Sars). Annals of Physics 336 (2013) 180-222  
  • The structure of renormalization Hopf algebras for gauge theories I: Representing Feynman graphs on BV-algebras. Commun. Math. Phys. 290 (2009) 291-319  
  • Recursive relations in the core Hopf algebra (with D. Kreimer). Nucl. Phys. B820 (2009) 682-693  
  • Renormalization of gauge fields: A Hopf algebra approach. Commun. Math. Phys. 276 (2007) 773-798  
  • The Hopf algebra of Feynman graphs in QED. Lett. Math. Phys. 77 (2006) 265-281  

Instantons on toric noncommutative manifolds

  • Moduli Spaces of Instantons on Toric Noncommutative Manifolds (with Simon Brain, Giovanni Landi). Adv. Theor. Math. Phys. 17 (2013) 1129 – 1193.  
  • The ADHM Construction of Instantons on Noncommutative Spaces (with Simon Brain). Rev. Math. Phys. 23 (2011) 1-47  
  • Noncommutative families of instantons (with G. Landi, C. Pagani and C. Reina). Int. Math. Res. Not. IMRN 12 Art. ID rnn038 (2008)  
  • Noncommutative instantons from twisted conformal symmetries (with G. Landi). Commun. Math. Phys. 271 (2007) 591-634  
  • Principal fibrations from noncommutative spheres (with G. Landi). Commun. Math. Phys. 260 (2005), 203-225  

Conference proceedings

  • Higher-derivative gauge theories from noncommutative geometry. PoS Corfu 2011  
  • The Hopf algebraic structure of perturbative quantum gauge theories. In Noncommutative Geometry, Arithmetic, and Related Topics, Eds. C. Consani and A. Connes. Johns Hopkins University Press, 2011  
  • Combinatorics and Feynman graphs for gauge theories. In Combinatorics and Physics. Eds. K. Ebrahimi-Fard, M. Marcolli and W. van Suijlekom. Cont. Math. 539 (2011) 417-442  
  • In Motives, QFT and PsiDOs conference, Eds. A. Carey, D. Ellwood, S. Paycha and S. Rosenberg. Clay Mathematics Proceedings 12, 2011.  
  • Renormalization Hopf algebras for gauge symmetries and BRST-symmetries. In Motives, QFT and PsiDOs conference, Eds. A. Carey, D. Ellwood, S. Paycha and S. Rosenberg. Clay Mathematics Proceedings 12, 2011  
  • Renormalization of gauge fields using Hopf algebras. In Quantum Field Theory, Eds. B. Fauser, J. Tolksdorf and E. Zeidler, Birkhauser Verlag, Basel, 2008  
  • Multiplicative renormalization and Hopf algebras. In Arithmetic and geometry around quantization. Eds. O. Ceyhan, Yu.-I. Manin and M. Marcolli. Progress in Mathematics 279, Birkhauser Verlag, Basel, 2010  
  • Noncommutative Bundles and Instantons in Tehran (with G. Landi). In An Invitation to Noncommutative Geometry, Eds. M. Khalkhali and M. Marcolli, World Scientific Publishing, Hackensack, 2008  
  • The noncommutative spin geometry of quantum SU(2), Comptes-Rendus des Rencontres Mathematiques de Glanon, 2005.  

Theses

  • Geometry of Noncommutative Spheres and their Symmetries, Ph.D. Thesis, SISSA, 2005  
  • Noncommutative geometry, deformation quantization and string theory, M.Sc. Thesis, UvA, 2001  

Books

  • Symmetrie in de deeltjesfysica. Epsilon Uitgaven, 2016.   
  • Supersymmetry and Noncommutative Geometry (with Wim Beenakker and Thijs van den Broek). SpringerBrief in Mathematical Physics 9, Springer, 2016.  
  • Noncommutative Geometry and Particle Physics, Mathematical Physics Studies, Springer 2015. List of Errata draft version (Book review by Matilde Marcolli in Bulletin of the AMS   
  • Combinatorics and Physics. Eds. K. Ebrahimi-Fard, M. Marcolli and W. van Suijlekom. Cont. Math. 539 (2011).  

Popular

  • The spectral model of particle physics. Nieuw Archief voor Wiskunde 5/15 nr.4 (december 2014) 240-250   
  • Ricci-stroming in 2D (met E. van Dongen en J. Vervoort), Nieuw Archief voor Wiskunde 5/12 (september 2011) 212-216   
  • Interview Alain Connes. The flashes of insight never came for free (with G. Cornelissen and N.P. Landsman), Nieuw Archief voor Wiskunde 5/11 (december 2010) 250-256  
  • Niet-commutatieve meetkunde niet-communicabel? (in dutch), Nieuw Archief voor Wiskunde 5/7 (maart 2006) 27-31  

Other

  • Book review Alain Connes, Matilde Marcolli: "Noncommutative geometry, quantum fields and motives". Mathematical Reviews, AMS.  
  • Book review Frederic Paugam: “Towards the Mathematics of Quantum Field Theory” To appear in Jahresber Dtsch Math-Ver.   
  • Combinatorics and Feynman graphs for gauge theories, lecture notes  
  • Noncommutative Geometry and Particle Physics, short survey