Factorisation of generalised theta functions. I.
Among (conformal) quantum field theories, the rational conformal field theories are singled out by the fact that their correlators can be constructed from a modular tensor category 𝓒 with a distinguished object, a symmetric special Frobenius algebra A in 𝓒, via the so-called TFT-construction. These correlators satisfy in particular all factorization constraints, which involve gluing homomorphisms relating correlators of world sheets of different topology. We review the action...
A method to study the embedded point spectrum of self-adjoint operators is described. The method combines the Mourre theory and the Limiting Absorption Principle with the Feshbach Projection Method. A more complete description of this method is contained in a joint paper with V. Jakić, where it is applied to a study of embedded point spectrum of Pauli-Fierz Hamiltonians.
For correlations of the form (0.2) we consider a critical case and prove power decay upper bounds in terms of the fundamental solution of a certain elliptic operator. This is achieved by improving the use of a maximum principle. We also formulate a general maximum principle and give two applications.
We present quantum stochastic calculus in terms of diagrams taking weights in the algebra of observables of some quantum system. In particular, we note the absence of non-time-consecutive Goldstone diagrams. We review recent results in Markovian limits in these terms.