Chu duality theory and coalgebraic representation of quantum symmetries

From Operational Chu Duality to Coalgebraic Quantum Symmetry

We pursue the principles of duality and symmetry building upon Pratt’s idea of the Stone Gamut and Abramsky’s representations of quantum systems. In the first part of the paper, we first observe that the Chu space representation of quantum systems leads us to an operational form of state-observable duality, and then show via the Chu space formalism enriched with a generic concept of closure con...

Coalgebraic Representation Theory of Fractals

Incompleteness of Representation Theory: Hidden symmetries and Quantum Non-Integrability

When regular regions are discovered in the parameter space of a system, where the parameter might be an external field applied to the Hydrogen atom, it usually indicates the existence of new (approximate) integrals of motion, and consequently quantum numbers [1]. In studies of many–body systems, the large number of degrees of freedom generally precludes one from using methods introduced in simp...

Duality Symmetries in String Theory ⋆

We review the status of duality symmetries in superstring theories. These discrete symmetries mark the striking differences between theories of pointlike objects and theories of extended objects. They prove to be very helpful in understanding non-perturbative effects in string theories. We will also briefly discuss the strange role played by open strings and their solitons in the emerging scena...

Interactions between Representation Theory, Quantum Field Theory, Category Theory and Quantum Information Theory Abstracts Representing Physical Systems as Chu Spaces

Representing Physical Systems as Chu Spaces Samson Abramsky Oxford University Computing Laboratory We pursue a model-oriented rather than axiomatic approach to the foundations of Quantum Mechanics, with the idea that new models can often suggest new axioms. This approach has often been fruitful in Logic and Theoretical Computer Science. Rather than seeking to construct a simplified toy model, w...