Related papers: Localized type I algebras and their entropy in qua…
The general boundary formulation of quantum field theory is applied to a massive scalar field in two dimensional Rindler space. The field is quantized according to both the Schr\"odinger-Feynman quantization prescription and the holomorphic…
Within the frame of a Group Approach to Quantization anomalies arise in a quite natural way. We present in this talk an analysis of the basic obstructions that can be found when we try to translate symmetries of the Newton equations to the…
We present solutions to a set of problems that arise in quantum entanglement theory, whose common trait is the use of algebraic methods. The backbone of the thesis consists of two general theorems, pertaining to specific convex sets of…
The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is…
This paper develops a concept of 2-categorical algebraic quantum field theories (2AQFTs) that assign locally presentable linear categories to spacetimes. It is proven that ordinary AQFTs embed as a coreflective full 2-subcategory into the…
The recent construction of integrable quantum field theories on two-dimensional Minkowski space by operator-algebraic methods is extended to models with a richer particle spectrum, including finitely many massive particle species…
Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q=1, the algebra reduces to the one proposed by Uglov-Ivanov. In the general case and $q\neq 1$, an explicit algebra homomorphism…
To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two dimensional string…
In analogy to the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study…
The study of entanglement in quantum field theories provides insight into universal properties which are typically challenging to extract by means of local observables. However, calculations of quantities related to entanglement in gauge…
Quantum duality principle is applied to study classical limits of quantum algebras and groups. For a certain type of Hopf algebras the explicit procedure to construct both classical limits is presented. The canonical forms of quantized…
We study atom canonicity for several varieties of cylindric like algebras that contain properly the variety of representable algebras. The algebras in such varieties have relativized representations, and we thereby obtain many omitting…
By fully exploiting the existence of the unitarily inequivalent representations of quantum fields, we exhibit the entanglement between inner and outer particles, with respect to the event horizon of a black hole. We compute the entanglement…
In Einstein's gravity, the entropy of horizons is proportional to their area. Several arguments given in the literature suggest that, in this context, both area and entropy should be quantized with an equally spaced spectrum for large…
We define a generalized form of $L_\infty$-algebras called $E_2L_\infty$-algebras. As we show, these provide the natural algebraic framework for generalized geometry and the symmetries of double field theory as well as the gauge algebras…
We study entanglement entropies of simply connected surfaces in field theories dual to Lovelock gravities. We consider Gauss-Bonnet and cubic Lovelock gravities in detail. In the conformal case the logarithmic terms in the entanglement…
Let L be a Lie superalgebra over a fled of characteristic p\neq 2 with enveloping algebra U(L) or let L be a restricted Lie superalgebra over a field of characteristic p > 2 with restricted enveloping algebra u(L). In this note, we…
We study the local quantization principle (after Sorin Popa~\cite{popa 94} and \cite{popa 95}) of inclusions of tracial von Neumann algebras. Let $(\mathcal{M},\tau)$ be a type ${\rm II}_1$ von Neumann algebra and let $\mathcal{N}\subseteq…
We study the entropy bound for local quantum field theory (LQFT) with generalized uncertainty principle. The generalized uncertainty principle provides naturally a UV cutoff to the LQFT as gravity effects. Imposing the non-gravitational…
In this paper we seek to understand what current knowledge of entanglement entropies suggests about the appropriate way to interpret the covariant entropy bound. We first begin by arguing that just as in the classical case, a universal…