Emergence of kinematic space from quantum modular geometric tensor

From Quantum Groups to Unitary Modular Tensor Categories

Modular tensor categories are generalizations of the representation theory of quantum groups at roots of unity axiomatizing the properties necessary to produce 3-dimensional TQFT and invariants of 3-manifolds. Although other constructions have since been found, quantum groups remain the most prolific source. Recently proposed applications to quantum computing have provided an impetus to underst...

On Endomorphisms of Quantum Tensor Space

We give a presentation of the endomorphism algebra EndUq(sl2)(V ), where V is the 3-dimensional irreducible module for quantum sl2 over the function field C(q 1 2 ). This will be as a quotient of the Birman-Wenzl-Murakami algebra BMWr(q) := BMWr(q , q2− q) by an ideal generated by a single idempotent Φq. Our presentation is in analogy with the case where V is replaced by the 2dimensional irredu...

A not on modular hyperconvex space

A note on modular hyperconvex space

Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory

A summary of some lines of ideas leading to model-independent frameworks of relativistic quantum field theory is given. It is followed by a discussion of the ReehSchlieder theorem and geometric modular action of Tomita-Takesaki modular objects associated with the quantum field vacuum state and certain algebras of observables. The distillability concept, which is significant in specifying useful...