The algebraic formulation of the axioms quantum field theory
The based SU(n)-instanton moduli spaces.
The Bisognano-Wichmann theorem for charged states and the conformal boundary of a black hole.
The boundary value problem for Dirac-harmonic maps
Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We...
The canonical structure of generalized non-linear sigma models in constrained hamiltonian formalism
The canonical structure of the supersymmetric non-linear σ model in the constrained hamiltonian formalism
The Cauchy problem for coupled Yang-Mills and scalar fields in the Lorentz gauge
The Cauchy-Riemann equations in anticomuting variables
The classification of modular invariants revisited
The classifying space of the 1 + 1 dimensional cobordism category.
The configuration space of gauge theory on open manifolds of bounded geometry
We define suitable Sobolev topologies on the space of connections of bounded geometry and finite Yang-Mills action and the gauge group and show that the corresponding configuration space is a stratified space. The underlying open manifold is assumed to have bounded geometry.
The evolution of the Dirac field in cuved space-times.
The form factor program: a review and new results - the nested off-shell Bethe ansatz.
The Gap Phenomena of Yang-Mills Fields over the Complete Manifold.
The generalized Lichnerowicz formula and analysis of Dirac operators.
The geometry of Brownian surfaces.
The global Yang-Mills equations depending on an arbitrary metric
The Group of Large Diffeomorphisms in General Relativity
We investigate the mapping class groups of diffeomorphisms fixing a frame at a point for general classes of 3-manifolds. These groups form the equivalent to the groups of large gauge transformations in Yang-Mills theories. They are also isomorphic to the fundamental groups of the spaces of 3-metrics modulo diffeomorphisms, which are the analogues in General Relativity to gauge-orbit spaces in gauge theories.
The Hawking effect
The initial value problem of the Poincaré gauge theory in vacuum. II. First order formalism