Zobrazeno 1 - 10
of 216
pro vyhledávání: '"Giorgetti, Luca"'
We introduce and study the crossing map, a closed linear map acting on operators on the tensor square of a given Hilbert space that is inspired by the crossing property of quantum field theory. This map turns out to be closely connected to Tomita--Ta
Externí odkaz:
http://arxiv.org/abs/2402.15763
Publikováno v:
AIMS Mathematics 9 (2024) 11320-11334. Special Issue Operator Theory: Advances and Applications
Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building on this result,
Externí odkaz:
http://arxiv.org/abs/2312.12019
Autor:
Giorgetti, Luca
Publikováno v:
Note Mat. 43 (2023) 41-56
Conformal Quantum Field Theories (CFT) in 1 or 1+1 spacetime dimensions (respectively called chiral and full CFTs) admit several "axiomatic" (mathematically rigorous and model-independent) formulations. In this note, we deal with the von Neumann alge
Externí odkaz:
http://arxiv.org/abs/2303.15171
Two-dimensional full conformal field theories have been studied in various mathematical frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our attention on theories with chiral components having pointed braided tens
Externí odkaz:
http://arxiv.org/abs/2301.12310
Publikováno v:
Commun. Math. Phys. 402 (2023) 169-212
We prove that a haploid associative algebra in a $C^*$-tensor category $\mathcal{C}$ is equivalent to a Q-system (a special $C^*$-Frobenius algebra) in $\mathcal{C}$ if and only if it is rigid. This allows us to prove the unitarity of all the 70 stro
Externí odkaz:
http://arxiv.org/abs/2211.12790
Publikováno v:
Rev. Math. Phys. 35 (2023) 2350007
On a conformal net $\mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $\mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call \emph{quantum o
Externí odkaz:
http://arxiv.org/abs/2204.14105
Publikováno v:
Quart. J. Math. 74 (2023) 975-1014
We show that conditional expectations, optimal hypotheses, disintegrations, and adjoints of unital completely positive maps, are all instances of Bayesian inverses. We study the existence of the latter by means of the Tomita-Takesaki modular group an
Externí odkaz:
http://arxiv.org/abs/2112.03129
Autor:
Giorgetti, Luca
Publikováno v:
Internat. J. Math. 33 (2022) 2250037
Let $\mathcal{N}\subset\mathcal{M}$ be a unital inclusion of arbitrary von Neumann algebras. We give a 2-{$C^*$}-categorical/planar algebraic description of normal faithful conditional expectations $E:\mathcal{M}\to\mathcal{N}\subset\mathcal{M}$ with
Externí odkaz:
http://arxiv.org/abs/2111.04488
Publikováno v:
Commun. Math. Phys. 395, 269-298 (2022)
A simple model for the localization of the category $\mathbf{CLoc}_2$ of oriented and time-oriented globally hyperbolic conformal Lorentzian $2$-manifolds at all Cauchy morphisms is constructed. This provides an equivalent description of $2$-dimensio
Externí odkaz:
http://arxiv.org/abs/2111.01837
Publikováno v:
Ann. Henri Poincar\'e 23 (2022) 2979-3020
Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of Quantum Fi
Externí odkaz:
http://arxiv.org/abs/2107.09345