Hadamard states from null infinity

Free field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic approach. It consists of a two-step procedure: In the first part one identifies the observables of the underlying physical system collecting them in a *-algebra which encodes their relational and structural properties. In the second step one must identify a quantum state, that is a positive, normalized linear functional on the *-algebra out of which one recovers the interpretation proper of quantum mechanical theories via the so-called Gelfand-Naimark-Segal theorem. In between the plethora of possible states, only few of them are considered physically acceptable and they are all characterized by the so-called Hadamard condition, a constraint on the singular structure of the associated two-point function. Goal of this paper is to outline a construction scheme for these states which can be applied whenever the underlying background possesses a null (conformal) boundary. We discuss in particular the examples of a real, massless conformally coupled scalar field and of linearized gravity on a globally hyperbolic and asymptotically flat spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum Mathematical Physics", held in Regensburg from the 29th of September to the 02nd of October 201

Real-Word Effectiveness and Safety of Dimethyl Fumarate in a Multiple Sclerosis Portuguese Population

Objectives: The aim of this study was to evaluate postmarketing dimethyl fumarate (DMF) safety and effectiveness in a real-world population with relapsing-remitting multiple sclerosis (RRMS). Methods: This was a retrospective, single-center study with RRMS patients treated with DMF. Demographic, clinical, and imagiological characteristics were analyzed, including annualized relapse rate (ARR), Expanded Disability Status Scale, "No Evidence of Disease Activity 3," previous treatment, adverse events, treatment duration, and reason for discontinuation. We investigated which baseline variables were associated with clinical and radiological outcomes. Results: We included 176 patients (70.4% females) with a median on-treatment follow-up time of 25.5 months. In total, 139 patients received prior disease-modifying therapies, and 37 were treatment-naive. Annualized relapse rate decreased by 77.1% in the total population (P < 0.001) and also decreased in the naive, tolerability switch, and efficacy switch groups by 95.8%, 56.7%, and 76.6% (P < 0.001). No Evidence of Disease Activity 3 status after 12 months of DMF treatment was maintained in 69.2% patients. Thirty patients (17%) discontinued treatment because of adverse drug reactions, and 21 (11.9%) because of lack of effectiveness. The occurrence of first relapse during follow-up was associated with higher ARR in the year before DMF start (hazard ratio, 4.833; P < 0.001) and prior exposure to multiple sclerosis treatments (tolerability and efficacy switchers). Conclusions: In this real-world audit, DMF appeared to be effective and safe for RRMS. Additionally, the study suggested that naive patients strongly benefit from DMF, and DMF also improves ARR in patients who switched from injectable therapies due to tolerability and efficacy issues.info:eu-repo/semantics/publishedVersio