Related papers: Using Weyl operators to study Mermin's inequalitie…
The theme of this work is that the theory of charged particles in a uniform magnetic field can be generalized to a large class of operators if one uses an extended a class of Weyl operators which we call "Landau--Weyl pseudodifferential…
Lecture notes prepared for the EMS--IAMP Spring School ``Symmetries and Measurement in Quantum Field Theory''. This set of lecture notes covers four lectures: 1. Operator Algebras and Quantum Field Theory, 2. Tomita-Takesaki Modular Theory…
The relationship between the noncommutativity of operators and the violation of the Bell inequality is exhibited in the light of the n-particle Bell-type inequality discovered by Mermin [PRL 65, 1838 (1990)]. It is shown, in particular,…
We briefly review the main methods for the description of massive Weyl fields in vacuum. On the classical level we discuss Weyl fields expressed through Grassmann variables as well as having spinors with commuting components. In both…
The construction of the known interacting quantum field theory models is mostly based on euclidean techniques. The expectation values of interesting quantities are usually given in terms of euclidean correlation functions from which one…
We provide an explicit expression for the modular hamiltonian of the von Neumann algebras associated to the unit double cone for the (fermionic) quantum field theories of the 2-component Weyl (helicity 1/2) field, and of the 4-component…
Unitary transformations are employed to enhance the violations of the Bell-CHSH inequality in relativistic Quantum Field Theory. The case of the scalar field in $1+1$ Minkowski space-time is scrutinized by relying on the Tomita-Takesaki…
We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl…
We numerically investigate the Araki-Uhlmann relative entropy in Quantum Field Theory, focusing on a free massive scalar field in 1+1-dimensional Minkowski spacetime. Using Tomita-Takesaki modular theory, we analyze the relative entropy…
In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We…
Based on the relationship of symmetric operators with Hermitian symmetric spaces, we introduce the notion of \emph{Weyl curve} for a symmetric operator $T$, which is the geometric abstraction and generalization of the well-known Weyl…
One of the key conceptual challenges in quantum gravity is to understand how quantum theory should modify the very notion of spacetime. One way to investigate this question is to study the alternatives to Schr\"odinger quantum mechanics.…
The quantum vacuum (Casimir) energy arising from noninteracting massless quanta is known to induce a long-range force, while decays exponentially for massive fields and separations larger than the inverse mass of the quanta involved. Here,…
Bell-inequality violations reveal the presence of quantum correlations between two particles that have interacted and then separated. Their generalisation to quantum fields is necessary to study a number of field-theoretic setups, such as…
In this article we review our recent work on the causal structure of symmetric spaces and related geometric aspects of Algebraic Quantum Field Theory. Motivated by some general results on modular groups related to nets of von Neumann…
We consider the entanglement of orthogonal generalized Bernoulli states in two separate single-mode high-$Q$ cavities. The expectation values and the correlations of the electric field in the cavities are obtained. We then define, in each…
A concise and self-contained introduction to the Bell inequality in relativistic Quantum Field Theory is presented. Taking the example of a real scalar massive field, the violation of the Bell inequality in the vacuum state and for causal…
The massive Majorana field in $1+1$ dimension is employed to investigate the violation of the Bell-CHSH inequality in relativistic Quantum Field Theory. We give an explicit rapidity-space realization of the Summers-Werner…
We present a model unifying general relativity and quantum mechanics. The model is based on the (noncommutative) algebra \mbox{{\cal A}} on the groupoid \Gamma = E \times G where E is the total space of the frame bundle over spacetime, and…
Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…