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
Problemi ellittici nonlineari nella teoria di gauge di Chern-Simons
Properties of non-hermitian quantum field theories
In this paper I discuss quantum systems whose Hamiltonians are non-Hermitian but whose energy levels are all real and positive. Such theories are required to be symmetric under , but not symmetric under and separately. Recently, quantum mechanical systems having such properties have been investigated in detail. In this paper I extend the results to quantum field theories. Among the systems that I discuss are and theories. These theories all have unexpected and remarkable properties. I discuss...
Pseudo algebras and pseudo double categories.