Scaling limit for subsystems and Doplicher-Roberts reconstruction

Given an inclusion $B \subset F$ of (graded) local nets, we analyse the structure of the corresponding inclusion of scaling limit nets $B_0 \subset F_0$, giving conditions, fulfilled in free field theory, under which the unicity of the scaling limit of $F$ implies that of the scaling limit of $B$. As a byproduct, we compute explicitly the (unique) scaling limit of the fixpoint nets of scalar free field theories. In the particular case of an inclusion $A \subset B$ of local nets with the same canonical field net $F$, we find sufficient conditions which entail the equality of the canonical field nets of $A_0$ and $B_0$.Comment: 31 page

Asymptotic morphisms and superselection theory in the scaling limit II: analysis of some models

We introduced in a previous paper a general notion of asymptotic morphism of a given local net of observables, which allows to describe the sectors of a corresponding scaling limit net. Here, as an application, we illustrate the general framework by analyzing the Schwinger model, which features confined charges. In particular, we explicitly construct asymptotic morphisms for these sectors in restriction to the subnet generated by the derivatives of the field and momentum at time zero. As a consequence, the confined charges of the Schwinger model are in principle accessible to observation. We also study the obstructions, that can be traced back to the infrared singular nature of the massless free field in d=2, to perform the same construction for the complete Schwinger model net. Finally, we exhibit asymptotic morphisms for the net generated by the massive free charged scalar field in four dimensions, where no infrared problems appear in the scaling limit.Comment: 36 pages; no figure

On Quantum Spacetime and the horizon problem

In the special case of a spherically symmetric solution of Einstein equations coupled to a scalar massless field, we examine the consequences on the exact solution imposed by a semiclassical treatment of gravitational interaction when the scalar field is quantized. In agreement with the work of Doplicher, Fredenhagen and Roberts (DFR), imposing the principle of gravitational stability against localization of events, we find that the region where an event is localized, or where initial conditions can be assigned, has a minimal extension, of the order of the Planck length. This conclusion, though limited to the case of spherical symmetry, is more general than that of DFR, since it does not require the use of the notion of energy through the Heisenberg Principle, nor of any approximation as the linearized Einstein equations. We shall then describe the influence of this minimal length scale in a cosmological model, namely a simple universe filled with radiation, which is effectively described by a conformally coupled scalar field in a conformal KMS state. Solving the backreaction, a power law inflation scenario appears close to the initial singularity. Furthermore, the initial singularity becomes light like and thus the standard horizon problem is avoided in this simple model. This indication goes in the same direction as those drawn at a heuristic level from a full use of the principle of gravitational stability against localization of events, which point to a background dependence of the effective Planck length, through which a-causal effects may be transmitted.Comment: 26 pages. v3: several discussions and clarifications added, misprints correcte

Scaling algebras for charged fields and short-distance analysis for localizable and topological charges

The method of scaling algebras, which has been introduced earlier as a means for analyzing the short-distance behaviour of quantum field theories in the setting of the model-independent, operator-algebraic approach, is extended to the case of fields carrying superselection charges. In doing so, consideration will be given to strictly localizable charges ("DHR-type" superselection charges) as well as to charges which can only be localized in regions extending to spacelike infinity ("BF-type" superselection charges). A criterion for the preservance of superselection charges in the short-distance scaling limit is proposed. Consequences of this preservance of superselection charges are studied. The conjugate charge of a preserved charge is also preserved, and for charges of DHR-type, the preservance of all charges of a quantum field theory in the scaling limit leads to equivalence of local and global intertwiners between superselection sectors.Comment: Latex 2e, 57 pages. Supersedes hep-th/030114

Pale Glares of Dark Matter in Quantum Spacetime

A U(1) gauge theory turns, on physically motivated models of Quantum Spacetime, into a U($\infty$) gauge theory, hence free classical electrodynamics is no longer free and neutral fields may have electromagnetic interactions. We discuss the last point for scalar fields, possibly describing dark matter; we have in mind the gravitational collapse of binary systems or future applications to self gravitating Bose-Einstein condensates as possible sources of evidence of quantum gravitational phenomena. The effects so far considered, however, seem too faint to be detectable at present.Comment: 14 page

Quantum Spacetime and Algebraic Quantum Field Theory

We review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and General Relativity. We also discuss the different approaches to (perturbative) Quantum Field Theory on Quantum Spacetime, and some of the possible cosmological consequences.Comment: 49 pages, 2 figure

The difference between conscious and unconscious brain circuits

Theoretical frameworks in which consciousness is an inherent property of the neuron must account for the contrast between conscious and unconscious processes in the brain and address how neural events can ever be unconscious if consciousness is a property of all neurons. Other approaches have sought answers regarding consciousness by contrasting conscious and unconscious processes and through investigating the complex interactions between the two kinds of processes, as occurs most notably in human voluntary action. In voluntary action, consciousness is associated most, not with motor control or low-level perceptual processing, but with the stage of processing known as action selection

The difference between conscious and unconscious brain circuits

Theoretical frameworks in which consciousness is an inherent property of the neuron must account for the contrast between conscious and unconscious processes in the brain and address how neural events can ever be unconscious if consciousness is a property of all neurons. Other approaches have sought answers regarding consciousness by contrasting conscious and unconscious processes and through investigating the complex interactions between the two kinds of processes, as occurs most notably in human voluntary action. In voluntary action, consciousness is associated most, not with motor control or low-level perceptual processing, but with the stage of processing known as action selection

The massive modular Hamiltonian

We compute the vacuum local modular Hamiltonian associated with a space ball region in the free scalar massive Quantum Field Theory. We give an explicit expression on the one particle Hilbert space in terms of the massive Legendre differential operator and the Green integral for the Helmholtz operator. The quadratic form of the massive modular Hamiltonian is expressed in terms of an integral of the energy density with parabolic distribution and of a Yukawa potential, that here appears intrinsically. We then get the formula for the local entropy of a Klein-Gordon wave packet. This gives the vacuum relative entropy of a coherent state on the double cone von Neumann algebras associated with the free scalar QFT. Among other points, we provide the passivity characterisation of the modular Hamiltonian within the standard subspace set up.Comment: The essential change concerns the final part of proof of the main result, that is now more direct, and the result is valid in arbitrary spacetime dimension d + 1, d > 1. There are also minor style improvements. The structure of the paper, and the main results, remain unchanged. 36 pages, 1 figur