Related papers: Localized type I algebras and their entropy in qua…
In all local realistic theories worked out till now, locality is considered as a basic assumption. Most people in the field consider the inconsistency between local realistic theories and quantum mechanics to be a result of non-local nature…
Over the last three decades entanglement entropy has been obtained for quantum fields propagating in genus zero topologies (Spheres). For scalar fields propagating in these topologies, it has been shown that the entanglement entropy scales…
Calculations of the entanglement entropy of a spatial region in continuum quantum field theory require boundary conditions on the fields at the fictitious boundary of the region. These boundary conditions impact the treatment of the zero…
The paper investigates relations between the phase space structure of a quantum field theory ("nuclearity") and the concept of pointlike localized fields. Given a net of local observable algebras, a phase space condition is introduced that…
Certain criteria are demonstrated for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms of that algebra. These are then used to establish a converse to recent results of Borchers and of…
The main new notions are the notions of tangent-like spaces and local monoids. The main result is the pasage from a local monoid to its tangent-like space which is a local Leibniz algebra.
The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very…
We compute the entanglement entropy, in real space, of the ground state of the integer Quantum Hall states for three different domains embedded in the torus, the disk and the sphere. We establish the validity of the area law with a…
We develop basic homological machinery for Z-algebras in order to prove a version of local duality for Ext-finite connected Z-algebras. As an application, we compare two notions of regularity for such algebras.
In this note we develop some properties of those algebras (called here locally simple) which can be generated by a single element after, if need be, a faithfully flat extension. For finite algebras, this is shown to be in fact a property of…
Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy…
We introduce the algebraic entropy for continuous endomorphisms of locally linearly compact vector spaces over a discrete field, as the natural extension of the algebraic entropy for endomorphisms of discrete vector spaces. We show that the…
Field Theories in Physics can be formulated giving a local Lagrangian density. Locality is imposed using the infinite jet bundle. That bundle is viewed as a pro-finite dimensional smooth manifold and that point of view has been compared to…
An early result of algebraic quantum field theory is that the algebra of any subregion in a QFT is a von Neumann factor of type III$_1$, in which entropy cannot be well-defined because such algebras do not admit a trace or density states.…
If A is a C*-algebra, G a locally compact group, K{\subset}G a compact subgroup and {\alpha}:G{\to}Aut(A) a continuous homomorphism, let Ax_{{\alpha}}G denote the crossed product. In this paper we prove that Ax_{{\alpha}}G is nuclear…
We present a general approach to quantum entanglement and entropy that is based on algebras of observables and states thereon. In contrast to more standard treatments, Hilbert space is an emergent concept, appearing as a representation…
In an earlier paper of the author, locally compact quantum torsors were defined for locally compact quantum groups, putting into the analytic framework the theory of Galois objects for Hopf algebras. Such quantum torsors allow to deform the…
Linking numbers appear in local quantum field theory in the presence of tensor fields, which are closed two-forms on Minkowski space. Given any pair of such fields, it is shown that the commutator of the corresponding intrinsic (gauge…
We consider the problem of defining localized subsystems in gauge theory and gravity. Such systems are associated to spacelike hypersurfaces with boundaries and provide the natural setting for studying entanglement entropy of regions of…
We consider various aspects of Kitaev's toric code model on a plane in the C^*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground state can be described by localized…