Below you find my list of publications, sorted by theme. At the bottom you find books and more popularizing articles.
- Reflection positivity in higher derivative scalar theories (with Francesca Arici, Daniel Becker, Chris Ripken, Frank Saueressig)
- Factorization of Dirac operators on almost-regular fibrations of spin$^c$ manifolds (with Jens Kaad)
- On a theorem of Kucerovsky for half-closed chains (with Jens Kaad)
- Quantization commutes with singular reduction: cotangent bundles of compact Lie groups (with Jord Boeijink and Klaas Landsman)
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.
- 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). To appear in Annales Henri Poincare.
- 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
- 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.
- 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).
- 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
- 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