On the use of modular groups in quantum field theory
On vector-valued modular forms and their Fourier coefficients
On Yetter's invariant and an extension of the Dijkgraaf-Witten invariant to categorical groups.
One-loop calculations and detailed analysis of the localized non-commutative gauge model.
Open/Closed string topology and moduli space actions via open/closed Hochschild actions.
Optimal Holomorphic Hypercontractivity for CAR Algebras
We present a new proof of Janson’s strong hypercontractivity inequality for the Ornstein-Uhlenbeck semigroup in holomorphic algebras associated with CAR (canonical anticommutation relations) algebras. In the one generator case we calculate optimal bounds for t such that is a contraction as a map for arbitrary p ≥ 2. We also prove a logarithmic Sobolev inequality.
Optique Géométrique et invariance de jauge : Solutions oscillantes d’amplitude critique pour les équations de Yang-Mills
Orthogonal Forms and Probability in von Neumann Algebras.
Perturbative quantum gravity and its relation to gauge theory.
Phase field model for mode III crack growth in two dimensional elasticity
A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regularization parameter and we approximate the Francfort–Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as a gradient flow of this regularized energy. We show several numerical examples of the crack growth computed with an adaptive mesh finite element method.
Phase space properties of local observables and structure of scaling limits
Physique quantique et formules de localisation
Poisson geometry of flat connections for SU(2)-bundles on surfaces.
Poisson structures on certain moduli spaces for bundles on a surface
Let be a closed surface, a compact Lie group, with Lie algebra , and a principal -bundle. In earlier work we have shown that the moduli space of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from onto a certain representation space , in fact a diffeomorphism, with reference to suitable smooth structures and , where denotes the universal central extension of...
Poisson-Lie groups and complete integrability. I. Drinfeld bigebras, dual extensions and their canonical representations
Positive energy quantization of linear dynamics
The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into three stages: the description of a classical system, the algebraic quantization and the Hilbert space quantization. Four kinds of systems are distinguished: neutral bosonic, neutral bosonic, charged bosonic and charged fermionic. The formalism that is described follows closely the usual constructions employed in quantum physics to introduce noninteracting quantum...
Positivity Properties of Measures in Euclidean Quantum Field Theory
Precise study of some number fields and Galois actions occurring in conformal field theory
Preon model and family replicated unification.
Problèmes mathématiques de la théorie quantique des champs