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We review the definition of hypergroups by Sunder, and we associate a hypergroup to a type III subfactor $Nsubset M$ of finite index, whose canonical endomorphism $gammainmathrm{End}(M)$ is multiplicity-free. It is realized by positive maps of $M$ that have $N$ as fixed points. If the depth is $>2$, this hypergroup is different from the hypergroup associated with the fusion algebra of $M$-$M$ bimodules that was Sunders original motivation to introduce hypergroups. We explain how the present hypergroup, associated with a suitable subfactor, controls the composition of transparent boundary conditions between two isomorphic quantum field theories, and that this generalizes to a hypergroupoid of boundary conditions between different quantum field theories sharing a common subtheory.
In this work we study the Casimir effect for massless scalar fields propagating in a piston geometry of the type $Itimes N$ where $I$ is an interval of the real line and $N$ is a smooth compact Riemannian manifold. Our analysis represents a generaliz
We study the self adjoint extensions of a class of non maximal multiplication operators with boundary conditions. We show that these extensions correspond to singular rank one perturbations (in the sense of cite{AK}) of the Laplace operator, namely t
We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras $B_N$, $C_N$, $D_N$ to the case of supersymmetric ${rm gl}(m|n)$ Gaudin model
In this contribution we discuss the role which incoherent boundary conditions can play in the study of phase transitions. This is a question of particular relevance for the analysis of disordered systems, and in particular of spin glasses. For the mo
Linking numbers appear in local quantum field theory in the presence of tensor fields, which are closed two-forms on Minkowski space. Given any pair of such fields, it is shown that the commutator of the corresponding intrinsic (gauge invariant) vect