The canonical approach to quantum gravity has been put on a firm mathematical foundation
in the recent decades. Even the quantum dynamics can be rigorously defined, however, due …

We provide a rigorous lattice approximation of conformal field theories given in terms of
lattice fermions in 1+ 1-dimensions, focussing on free fermion models and Wess–Zumino …

We analyze the renormalization group fixed point of the two-dimensional Ising model at
criticality. In contrast with expectations from tensor network renormalization (TNR), we show …

Many features of physical systems, both qualitative and quantitative, become sharply
defined or tractable only in some limiting situation. Examples are phase transitions in the …

If two parties share sufficient entanglement, they are able to implement any channel on a
shared bipartite state via non-local quantum computation--a protocol consisting of local …

We present a rigorous renormalization group scheme for lattice quantum field theories in
terms of operator algebras. The renormalization group is considered as an inductive system …

Vaughan Jones discovered unexpected connections between Richard Thompson's group
and subfactor theory while attempting to construct conformal field theories (in short CFT) …

In the quest in constructing conformal field theories (CFTs), Jones has discovered a beautiful
and deep connection between CFT, Richard Thompson's groups, and knot theory. This led …

We report on a rigorous operator-algebraic renormalization group scheme and construct the
free field with a continuous action of translations as the scaling limit of Hamiltonian lattice …

In this second article, we continue to study classes of groups constructed from a functorial
method due to Vaughan Jones. A key observation of the author shows that these groups …