## Theories of the fundamental interactions

On the one hand, for well accepted or even established theories a solid understanding of their non-perturbative dynamics remains largely wanting. Undoubtedly, topological and geometrical properties in field space in relation to large gauge symmetries play crucial roles in this regard, to which perturbative gauge fixing procedures remain totally oblivious. A significant component of our research efforts addresses such issues within lower dimensional gauge theories from complementary non-perturbative points of view, also unraveling dualities between apparently disconnected theories.

Parallel to such studies is the pursuit of novel computational techniques and approaches towards multi-loop scattering amplitudes, on a par with studies of the mathematical structures of Feynman integrals and scattering amplitudes, relying on as many new mathematical frameworks as may be garnered and call on, with the aim to design new mathematical tools for precision computations in QFT, especially for LHC motivated precision processes. In particular, as soon as supersymmetries are involved, especially with N=4 supersymmetry in four dimensional space-time, much progress has been made over recent years and much scope for further understanding remains within reach.

On the other hand, present day gauge theories of the fundamental quantum interactions present their own challenges pointing towards new fundamental conceptual paradigms beyond quantum physics and gravity. Some of the exploratory paths being trodden are deformations of quantum mechanics, non-commutative or fuzzy space-time geometries, and topological theories for pure quantum gravity, being applied in a variety of physical circumstances. Approached from other perspectives, attempts are being pursued as well that aim to relate gauge coupling constant sectors and electroweak flavor coupling constant sectors within new unification schemes for all interactions.

Finally, progress in non-perturbative dynamics of gauge theories has often exploited advances made in condensed matter physics. Collective phenomena in lower dimensional fermionic systems display a variety of behaviors, in particular quantum Hall systems and their recently identified generalizations with a topological understanding having been achieved over the recent years of their distinctive physical properties reminding one of holographic-like properties in theories of gravity, which may well prove relevant to non-perturbative gauge dynamics alike. Thus some part of our research activities addresses such issues as well.

### Members

#### Professors

##### Claude Duhr

Jean-Marc Gérard

Jan Govaerts

#### PhD students

##### Robin Marzucca

Bram Verbeek

### Projects

#### Integrable quantum dynamics, Klauder-Daubechies deformations and noncommutative geometric structures.

Combining complementary approaches to quantisation, exploration of integrability issues in quantum dynamics and noncommutative geometric structures

External collaborators: M. Norbert Hounkonnou (ICMPA-UNESCO Chair, UAC, Benin) Calvin Matondo Bwayi (UNIKIN, DRC).

#### Mathematical Structure of Feynman Integrals and Scattering Amplitudes

Analytic and algebraic properties of multi-loop integrals are analysed in the view of devising new mathematical tools for precision computations in QFT.

External collaborators: Samuel Abreu (Universität Freiburg) Ruth Britto (Trinity College Dublin) Einan Gardi (University of Edinburgh).

#### Multi-loop scattering amplitudes in N=4 Super Yang-Mills

Multi-loops scattering amplitudes in N=4 Super Yang-Mills are analysed in the light of the integrability of the theory in the planar limit.

External collaborators: Vittorio Del Duca (ETH Zurich & INFN Frascati) Lance Dixon (SLAC) James Drummond (University of Southampton) Falko Dulat (SLAC) Georgios Papathanasiou (SLAC).

#### Non-commutative quantum dynamics and supersymmetry

Extensions to the supersymmetric context of the Moyal non-commutative plane are being considered from different perspectives.

#### Non-perturbative dynamics of QED in low dimensions

By emphasizing the relevance of topology in nonperturbative gauge dynamics in the presence of nontrivial space(time) topology, develop gauge invariant physical tools to approach the nonperturbative dynamics of such systems in approximation schemes. In an initial study, QED in lower dimensions is considered in detail.

#### Nonperturbative quantisation of gauge theories, noncommutative geometry and unification of the fundamental interactions

Development of nonperturbative quantisation techniques of gauge theories (Yang-Mills, topological, gravity) and their application to particle physics and quantum field theory at finite temperature (in particular, within the context of superconductivity).

Exploration of the consequences of noncommutative geometry in the search for the unification of the fundamental interactions (M-theory and superstrings, quantum gravity).

External collaborators: Frederik Scholtz (National Institute for Theoretical Physics, NITheP, South Africa); Hendrik Geyer (Stellenbosch Institute for Advanced Study, STIAS; University of Stellenbosch, South Africa); M. Norbert Hounkonnou (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Benin); Calvin Matondo Bwayi (University of Kinshasa, Kinshasa, Democratic Republic of Congo); Habatwa Mweene (University of Zambia, Lusaka, Zambia); John R. Klauder (University of Florida, Gainesville, USA); Peter Jarvis (University of Tasmania, Hobart, Australia).

#### On the unification of gauge coupling constants

In the standard model version of the grand unified theory different gauge couplings intend to, but do not, meet at some higher scale. Here we will look for some better ways for the unification of the gauge coupling constants.

### Past projects

#### Deformation of quantum dynamics in Phase Space

In this project, we study a deformation of the path integral introducing a new time scale. This deformation is inspired by Klauder's path integral construction using a Riemannian metric on phase space. The introduction of this new time scale leads to a complex Landau problem, non commutative geometry and non unitarity effects.

#### Gauge Phase Space Symmetries and Their Interactions

The potential of gauging phase space dynamical symmetries as a principle for generating interactions is explored

#### Superconductivity in extremal regimes and nanoscopic particle detectors

Theoretical and experimental study of superconductivity in extremal regimes (spatial and temporal, and in the presence

of electric fields), aiming towards the development of nanoscopic particle detectors

External collaborators: Vincent Bayot (CERMIN, UCL).

#### The Fuzzy Ball

We are beginning to investigate the possibility of using finite sized matrices to describe a non-commutative three dimensional ball.

#### The Laplace and Dirac operators on the Fuzzy Grassmanians

This project is concerned with the construction the polarization tensors for (some of) the Fuzzy Grassmanians. We will then consider the Dirac operator and spinors for these spaces in the compact formalism recently introduced for the complex projective spaces. We will also consider structures.

#### Weak and strong CP violations

Weak interaction contributions to the strong

### Publications

#### 2018

*Claude Duhr, Zhengwen Liu*

[Abstract] [PDF]

Refereed paper. 2nd November.

*Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi*

Refereed paper. 25th September.

*Zhengwen Liu and Xiaoran Zhao*

[Abstract] [PDF]

Refereed paper. 19th September.

*Del Duca, Vittorio and Druc, Stefan and Drummond, James and Duhr, Claude and Dulat, Falko and Marzucca, Robin and Papathanasiou, Georgios and Verbeek, Bram*

[Abstract] [PDF]

Contribution to proceedings. 13th July.

*Samuel Abreu, Ruth Britto, Claude Duhr, Einan Gardi, James Matthew*

Contribution to proceedings. 12th July.

*Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi*

Contribution to proceedings. 12th July.

*Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi*

To appear in "Elliptic integrals, elliptic functions and modular forms in quantum field theory"

Contribution to proceedings. 2nd July.

*Bertrand, Bruno and Govaerts, Jan*

[Abstract] [PDF] Submitted to the Journal of Physics A: Mathematical and Theoretical

Refereed paper. 27th June.

*Jan Govaerts*

[Abstract] [PDF] To appear in "Mathematical Structures and Applications", Proceedings of the International Workshop on Contemporary Problems in Mathematical Physics (COPROMAPH), October 2016 (Cotonou, Republic of Benin), eds. T. Diagana and B. Toni (Springer, 2018)

Refereed paper. Contribution to proceedings. 27th June.

*Johannes Broedel, Claude Duhr, Falko Dulat, Brenda Penante, Lorenzo Tancredi*

Refereed paper. 23rd March.

#### 2017

*Broedel, Johannes and Duhr, Claude and Dulat, Falko and Tancredi, Lorenzo*

[Abstract] [PDF] [Journal] Submitted to PRD.

Refereed paper. 18th December.

*Broedel, Johannes and Duhr, Claude and Dulat, Falko and Tancredi, Lorenzo*

[Abstract] [PDF] [Journal] Submitted to JHEP

Refereed paper. 18th December.

*Almelid, Øyvind and Duhr, Claude and Gardi, Einan and McLeod, Andrew and White, Chris D.*

[Abstract] [PDF] [Journal]

Refereed paper. 26th June.

*Vittorio Del Duca, Claude Duhr, Robin Marzucca, Bram Verbeek*

[Abstract] [PDF] [Journal]

Refereed paper. 19th May.

*Abreu, Samuel and Britto, Ruth and Duhr, Claude and Gardi, Einan*

[Abstract] [PDF] [Journal]

Refereed paper. 21st April.

#### 2016

*Song He and Zhengwen Liu*

[Abstract] [PDF] [Journal] Published in JHEP 1612 (2016) 006

Refereed paper. 15th August.

*Song He, Zhengwen Liu and Jun-Bao Wu*

[Abstract] [PDF] [Journal] [Full text] Published in JHEP 1607 (2016) 060

Refereed paper. 1st July.

*Del Duca, Vittorio and Druc, Stefan and Drummond, James and Duhr, Claude and Dulat, Falko and Marzucca, Robin and Papathanasiou, Georgios and Verbeek, Bram*

[Abstract] [PDF] [Journal] Published in JHEP.

Refereed paper. 16th June.

#### 2014

*Fanuel, Michaël and Govaerts, Jan*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/017/2014, published in J. Phys. A: Math. Theor. 47 (2014) 405401 (39 pages)

Refereed paper. 26th May.

*Fanuel, Michaël and Govaerts, Jan and Avossevou, Gabriel Y. H. and Dossa, Anselme F.*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/018/2014, published in J. Phys. A: Math. Theor. 47 (2014) 465401 (10 pages)

Refereed paper. 21st May.

#### 2013

*Simone Zonetti and Jan Govaerts*

[Full text] Journal of Physics: Conference Series 410 (2013) 012134 (4 pages);

Proceedings IC-MSQUARE 2012, International Conference on Mathematical Modelling in Physical Sciences, September 3-7, 2012, Budapest (Hungary)

Refereed paper. Contribution to proceedings. 10th February.

#### 2012

*Jan Govaerts and Simone Zonetti*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/040/2012, published in Phys. Rev. D87 (2013) 084016 (10 pages)

Refereed paper. 20th December.

*Jose Beltran Jimenez, Enea Di Dio and Ruth Durrer*

[Abstract] [PDF] [Journal] Published in JHEP 1304 (2013) 030

Refereed paper. 12th December.

*Grumiller, Daniel and McNees, Robert and Zonetti, Simone*

[Abstract] [PDF] [Journal] 51 pages, 7 figures, published in Phys.Rev.D

Refereed paper. 26th October.

*Daddy Balondo Iyela, Jan Govaerts and M. Norbert Hounkonnou*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/026/2012, Published in J. Math. Phys. 54 (2013) 093502 (18 pages)

Refereed paper. 10th August.

#### 2011

*Zonetti, Simone and Govaerts, Jan*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/014/2011; Published in J. Phys. A: Math. Theor. 45 (2012) 042001 (7 pages)

Refereed paper. 8th November.

*Fanuel Michael, Govaerts Jan*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/013/2011; Published in J. Phys. A: Math. Theor. 45 (2012) 035401 (26 pages)

Selected for inclusion in IOP Select, http://Select.iop.org, Included in the highlights 2012 (excellent papers published in 2012)

Refereed paper. 25th August.

#### 2010

#### 2009

*Jan Govaerts and Seán Murray*

[Abstract] [PDF] [Journal] Published as JHEP 01 (2010) 008 (8 pages)

Refereed paper. 22nd October.

*Jan Govaerts, M. Nobert Hounkonnou and Habatwa V. Mweene*

[Abstract] [PDF] [Journal] Published in J. Phys. A: Math. Theor. 42 (2009) 485209 (19 pages)

Highlighted on IoP Select: http://www.iop.org/Select/toc/-group=subject/500

Refereed paper. 23rd August.

*Bruno Bertrand and Jan Govaerts*

23rd August.

*Joseph Ben Geloun, Jan Govaerts and Frederik G. Scholtz*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/2007/19, published in J. Phys. A: Math. Theor. 42 (2009) 495203 (18 pages)

Refereed paper. 14th August.

*Jan Govaerts, Calvin Matondo Bwayi and Olivier Mattelaer*

[Abstract] [PDF] [Journal] Published in J. Phys. A: Math. Theor. 42 (2009) 445304 (20 pages)

Highlighted on IoP Select: http://www.iop.org/Select/toc/-group=subject/500

Refereed paper. 6th August.

#### 2008

*Jan Govaerts and Olivier Mattelaer*

[Abstract] [PDF] [Full text] Proc. Fifth International Workshop on Contemporary Problems in Mathematical Physics, October 27th-November 2nd, 2007, Cotonou, Republic of Benin, Eds. J. Govaerts and M. N. Hounkonnou (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Cotonou, Republic of Benin, 2008), pp. 170-186, refereed contribution.

Contribution to proceedings. 2nd December.

*Laure Gouba, Jan Govaerts and M. Norbert Hounkonnou*

[Abstract] [PDF] [Full text] Proc. Fifth International Workshop on Contemporary Problems in Mathematical Physics, October 27th-November 2nd, 2007, Cotonou, Republic of Benin, Eds. J. Govaerts and M. N. Hounkonnou (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Cotonou, Republic of Benin, 2008), pp. 164-169, refereed contribution.

Contribution to proceedings. 2nd December.

*Laure Gouba and Jan Govaerts*

[Abstract] [PDF] [Full text] Proc. Fifth International Workshop on Contemporary Problems in Mathematical Physics, October 27th-November 2nd, 2007, Cotonou, Republic of Benin, Eds. J. Govaerts and M. N. Hounkonnou (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Cotonou, Republic of Benin, 2008), pp. 159-163, refereed contribution.

Contribution to proceedings. 2nd December.

*Joseph Ben Geloun, Jan Govaerts and M. Norbert Hounkonnou*

[Abstract] [PDF] [Full text] Proc. Fifth International Workshop on Contemporary Problems in Mathematical Physics, October 27th-November 2nd, 2007, Cotonou, Republic of Benin, Eds. J. Govaerts and M. N. Hounkonnou (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Cotonou, Republic of Benin, 2008), pp. 124-129, refereed contribution.

Contribution to proceedings. 2nd December.

*Jan Govaerts*

[Abstract] [PDF] [Full text] Proc. Fifth International Workshop on Contemporary Problems in Mathematical Physics, October 27th-November 2nd, 2007, Cotonou, Republic of Benin, Eds. J. Govaerts and M. N. Hounkonnou (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Cotonou, Republic of Benin, 2008), pp. 36-114, refereed contribution.

Contribution to proceedings. 2nd December.

*Jan Govaerts and M. Norbert Hounkonnou, eds.*

[Full text] October 27th-November 2nd, 2007, Cotonou, Republic of Benin (International Chair in Mathematical Physics and Applications, ICMPA-UNESCO Chair, Cotonou, Republic of Benin, 2008), 327 pages, refereed contributions.

Contribution to proceedings. 2nd December.

#### 2007

*Florian Payen*

[Abstract] [PDF] [Journal] Physics Letters B654 (2007) 121 - 126

Refereed paper. 6th August.

*F. G. Scholtz, B. Chakraborty, J. Govaerts and S. Vaidya*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/2007/19, IISc/CHEP/14/07, published in J. Phys. A40 (2007) 14581-14592

Refereed paper. 31st July.

*Hendrik B. Geyer, Laure Gouba, Jan Govaerts and Frederik G. Scholtz*

In preparation, Preprint ICMPA-MPA/2007/18

18th June.

*Joseph Ben Geloun, Jan Govaerts and M. Norbert Hounkonnou*

In preparation, Preprint ICMPA-MPA/2006/40

18th June.

*Jan Govaerts and Frederik G. Scholtz*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/2007/17, published in J. Phys. A40 (2007) 12415-12438

Refereed paper. 7th June.

*J. Govaerts, P. D. Jarvis, S. O. Morgan and S. G. Low*

[Abstract] [PDF] [Journal] Preprint ICMPA-MAP/2007/16, UTAS-PHYS-2007-07, published in J. Phys. A40 (2007) 12095-12111

Refereed paper. 17th May.

#### 2006

*J. Govaerts and D. Bertrand*

[Abstract] [PDF] Proceedings of the Fourth International Workshop on Contemporary Problems in Mathematical Physics,

Cotonou (International Chair in Mathematical Physics and Applications, University of Abomey-Calavi,

Republic of Benin), November 5 -- 11, 2005, 2006, eds. J. Govaerts, M. N. Hounkonnou and A. Z. Msezane,

World Scientific, Singapore, 237 - 254

Contribution to proceedings. 3rd August.

*L. Gouba, J. Govaerts and M.N. Hounkonnou*

[Abstract] [PDF] Proceedings of the Fourth International Workshop on Contemporary Problems in Mathematical Physics,

Cotonou (International Chair in Mathematical Physics and Applications, University of Abomey-Calavi,

Republic of Benin), November 5 -- 11, 2005, 2006, eds. J. Govaerts, M. N. Hounkonnou and A. Z. Msezane,

World Scientific, Singapore, 230 - 236

Contribution to proceedings. 3rd August.

*J. Govaerts*

2006, eds. Jan Govaerts, M. Norbert Hounkonnou and Alfred Z. Msezane, Singapore, World Scientific, 453 pages

Contribution to proceedings. 3rd August.

*J. Ben Geloun, J. Govaerts and M.N. Hounkonnou*

[Abstract] [PDF] Published in the Proceedings of the Fourth International Workshop on Contemporary Problems in Mathematical Physics, Cotonou (International Chair in Mathematical Physics and Applications, University of Abomey-Calavi, Republic of Benin), November 5-11,2005, eds. J. Govaerts, M.N. Hounkonnou and A.Z. Msezane, World Scientific, Singapore, 2006, 173-180

Contribution to proceedings. 3rd August.

*Gerard, Jean-Marc an Smith, Christopher and Trine, Stephanie*

[Abstract] [PDF] Talk given at 41st Rencontres de Moriond on Electroweak Interactions and Unified Theories, La Thuile, Aosta Valley, Italy, 11-18 Mar 2006

Contribution to proceedings. 14th May.

*Joseph Ben Geloun, Jan Govaerts and M. Norbert Hounkonnou*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/2006/20; published in J. Math. Phys. 48 (2007) 032107 (23 pages)

Refereed paper. 8th September.

*Joseph Ben Geloun, Jan Govaerts and M. Norbert Hounkonnou*

[Abstract] [PDF] [Journal] Preprint ICMPA-MPA/2006/22, published in Europhysics Letters 80 (2007) 30001 (6 pages)

Refereed paper. 8th September.

*Jan Govaerts and Damien Bertrand*

[Abstract] [PDF] Proc. Fourth International Workshop on Contemporary Problems in Mathematical Physics, November 5th-11th, 2005, Cotonou, Republic of Benin, Eds. J. Govaerts, M. N. Hounkonnou and A. Z. Msezane (World Scientific, Singapore, 2006), pp. 237 - 254, Preprint ICMPA-MPA/2006/28

Contribution to proceedings. 27th July.

*Laure Gouba, Jan Govaerts and M. Norbert Hounkonnou*

[Abstract] [PDF] Proc. Fourth International Workshop on Contemporary Problems in Mathematical Physics, November 5th-11th, 2005, Cotonou, Republic of Benin, Eds. J. Govaerts, M. N. Hounkonnou and A. Z. Msezane (World Scientific, Singapore, 2006), pp. 230 - 236, Preprint ICMPA-MPA/2006/27

Contribution to proceedings. 27th July.

*Joseph Ben Geloun, Jan Govaerts and M. Norbert Hounkonnou*

[Abstract] [PDF] Proc. Fourth International Workshop on Contemporary Problems in Mathematical Physics, November 5th-11th, 2005, Cotonou, Republic of Benin, Eds. J. Govaerts, M. N. Hounkonnou and A. Z. Msezane (World Scientific, Singapore, 2006), pp. 173 - 180, Preprint ICMPA-MPA/2006/26

Contribution to proceedings. 27th July.

*Jan Govaerts, M. Norbert Hounkonnou and Alfred Z. Msezane, eds.*

[Full text] November 5th-11th, 2005, Cotonou, Republic of Benin (World Scientific, Singapore, 2006), 450 pages, Preprint ICMPA-MPA/2006/25. ISBN 981-256-853-0.

Contribution to proceedings. 27th July.