The Use of Quantum Algebras in Quantum Gravity

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

Use of Quantum Algebras in Quantum Gravity

After brief survey of appearance of quantum algebras in diverse contexts of quantum gravity, we demonstrate that the particular deformed algebras, which arise within the approach of J. Nelson and T. Regge to (2 + 1) anti-de Sitter quantum gravity (for space surface of genus g) and which should generate algebras of independent quantum observables, are in fact isomorphic to nonstandard q-deformed...

The witness set of coexistence of quantum effects and its preservers

One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...

فرمولبندی هندسی کوانتش تغییرشکل برزین

  In this paper we try to formulate the Berezin quantization on projective Hilbert space P(H) and use its geometric structure to construct a correspondence between a given classical theory and a given quantum theory. It wil be shown that the star product in berezin quantization is equivalent to the Posson bracket on coherent states manifold M, embodded in P(H), and the Berezin method is used to...

Fock representations from U(1) holonomy algebras

We revisit the quantization of U(1) holonomy algebras using the abelian C algebra based techniques which form the mathematical underpinnings of current efforts to construct loop quantum gravity. In particular, we clarify the role of “smeared loops” and of Poincare invariance in the construction of Fock representations of these algebras. This enables us to critically re-examine early pioneering ...