We give a proof of a formula for the trace of self-braidings (in an arbitrary channel) in UMTCs which first appeared in the context of rational conformal field theories (CFTs) 2. The trace is another ...invariant for UMTCs which depends only on modular data, and contains the expression of the Frobenius–Schur indicator 21 as a special case. Furthermore, we discuss some applications of the trace formula to the realizability problem of modular data and to the classification of UMTCs.
In a recent paper we studied general properties of super-KMS functionals on graded quantum dynamical systems coming from graded translation-covariant quantum field nets over
R
, and we carried out a ...detailed analysis of these objects on certain models of superconformal nets. In the present article, we show that these locally bounded functionals give rise to local-entire cyclic cocycles (generalized JLO cocycles) which are homotopy-invariant for a suitable class of perturbations of the dynamical system. Thus we can associate meaningful noncommutative geometric invariants to those graded quantum dynamical systems.
We consider conformal nets on S1 of von Neumann algebras, acting on the full Fock space, arising in Free Probability. These models are twisted local, but non-local. We extend to the non-local case ...the general analysis of the modular structure. The local algebras turn out to be III1-factors associated with free groups. We use our setup to show examples exhibiting arbitrarily large maximal temperatures, but failing to satisfy the split property, then clarifying the relation between the latter property and the trace class conditions on e–βL, where L is the conformal Hamiltonian.
Gibbs Random Fields Koralov, Leonid; Sinai, Yakov G.
Theory of Probability and Random Processes
Book Chapter
The notion of Gibbs random fields was formalized by mathematicians relatively recently. Before that, these fields were known in physics, particularly in statistical physics and quantum field theory. ...Later, it was understood that Gibbs fields play an important role in many applications of probability theory. In this section we define the Gibbs fields and discuss some of their properties.
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