Frank Witte's page

Welcome to my personal webpage. I have only recently joined UCL and so this is all still very much under construction. So please return here every now and then to spot the updates.

Email: f.witte@ucl.ac.uk

Facebook: http://www.facebook.com/profile.php?id=539293045

Brief C.V.

**2010 - now: London. **

- Departmental tutor at the department of Economics of University College London;

- Academic visitor at the Quantum Optics & Laser Science group at Imperial College (fall 2009);

**1997- 2010: Utrecht.**

- Senior lecturer in theoretical physics at Utrecht University in the Netherlands;

- Fellow for Physics & Mathematics at University College Utrecht (January 2005 - August 2010);

- Projectleader: Utrecht Summerschools in Science (2002-2010);

- Visiting fellow of St. John's College, Cambridge (Lent & Easter terms 2001)

**1992-1997: Heidelberg.**

- Birth of my daughter Leonie;

- PhD in Theoretical Physics (1995) at the University of Heidelberg, Germany;

- Birth of my daughter Juliane (1993)

**1987-1992: Utrecht.**

- MSc in Theoretical Astrophysics at Utrecht University in the Netherlands;

- 1987: University entrance.

Research interests

I have a variety of research interests, some which I actively pursue and others where I am happy to passively follow current developments as much as possible.

**1] Econophysics / Econometrics / Financial Mathematics**

I am interested in the stochastic processes driving pricechanges in markets, in the appearance of bubbles in markets as well as in society and in the dynamics of these processes lying behing the randomness. As a result I am puzzling on the connection between decision-making as well as pricing processes and measurement-theory on the other. Whether recreationally or potentially useful, I enjoy studying the possibillities of generalizing game theory in a meaningful way into quantum game theory. Last but not least I am interested in the geometries of spanning trees of correlations between pricechanges of assets or commodities and questions regarding the embedding of those geometries in 2 or higher-dimensional manifolds. Technically speaking I am interested in finding out which random geometries could be made usefull in the (risk-)analysis of portfolios of stocks , options and/or assets.

**2] Gravitational physics & the Standard Model: or "What is Spin?"**

In the recent past I worked on gravitational physics in several ways. In 2007 with my student Ivo Sturm & I computed the boundstate energies and decay-rates of fermions around rotating blackholes (Kerr blackholes). Considering the bound state of a spin 1/2 fermion with a blackhole as a model system in which tweaking of parameters allows a smooth transition between the regime where non-relativistic QM applies down to a regime where full quantum gravity wouldbe required. Our approximation methods only allowed us to infer the (till that moment unknown) existence of those boundstates for relativistic systems in which particle-creation plays no substantial role.

Spin plays the role of a fundamental angular momentum in quantum mechanics, yet in gravitational systems it can also act as a source of torsion, which is a second deformation of spacetime geometry next to curvature. Einsteins theory of General Relativity describes torsion-free but curved spacetime interacting with matter. With several students (Thomas Rot, Wilke vd Schee, Jelle Aalbers Rutger-Jan Lange, 2007-2009) I investigated whether the Newman-Janis algorithm (that "mysteriously" relates rotating and non-rotating blackhole geometries) can be seen to induce torsion in intermediate stages of the algorithm.

In the theory of the weak interactions spin takes on yet another role as it non-trivially enters the way in which leptons interact and the way charges are assigned to these particles. The keyword here is chirality. With Inge Kielen (2009) I studied an earlier idea on using geometric algebras (or Clifford algebras with an added interpretation) to possibly clarify the spacetime-geometric role of these charge-assignments.

Particles with half-integer spin are described by variants of the Dirac equation. Using geometric algebra this Dirac equation in spacetime can be closely associated to classical equations of motion of spinning, massive, particles in the eigen-rotor form. With Misha Spelt & Selma Koghee (2009) I formulated an eigen-rotor formulation of the dynamics of relativistic strings in (ordinary) spacetime that provides and even closer association of the Dirac equation with relativistic classical dynamics.

**3] Non-equilibrium quantum field theory**

I am interested in the non-equilibrium formulation of quantum field theory as in such a context many of the familiar notions of particle physics lose their immediate physical interpretation. Non-equilibrium dynamics requires us to completely rethink what a particle is, how it's properties are co-determined by the surrounding medium and how the lack of isolation (or the persistance of interactions) changes our view of the identity of particles. Our intuitive understanding of reality largely rests on non-relativistic classical physics whereas the extreme conditions in high-energy phenomena such as quark-gluon plasma's, or close to blackholes, or near the origin of the universe itself, require the language of relativistic quantum field theory involving a high density of excitations. In 1995 (as part of my PhD thesis) is found a infinite family of (Ward-like) identities satisfied by non-equilibrium qft's, unfortunately without proper application so far. In 1997 I showed for a simple model system that non-relativistic limit and classical limit do not neccesarilly commute.