Hadamard States From Light-like Hypersurfaces

This book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary. The first two sections focus on explaining a few introductory aspects of this topic and on providing the relevant geometric background material. The notions of asymptotically flat spacetimes and of expanding universes with a cosmological horizon are analysed in detail, devoting special attention to the characterization of asymptotic symmetries. In the central part of the book, the quantization of a real scalar field theory on such class of backgrounds is discussed within the framework of algebraic quantum field theory. Subsequently it is explained how it is possible to encode the information of the observables of the theory in a second, ancillary counterpart, which is built directly on the conformal (null) boundary. This procedure, dubbed bulk-to-boundary correspondence, has the net advantage of allowing the identification of a distinguished state for the theory on the boundary, which admits a counterpart in the bulk spacetime which is automatically of Hadamard form. In the last part of the book, some applications of these states are discussed, in particular the construction of the algebra of Wick polynomials. This book is aimed mainly, but not exclusively, at a readership with interest in the mathematical formulation of quantum field theory on curved backgrounds.Comment: 106 pages, 2 figures, to appear in SpringerBriefs in Mathematical Physics, references adde

Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime

The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hormander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime.Comment: 63 pages, 3 figure

Phenomenology of minimal Z' models: from the LHC to the GUT scale

We consider a class of minimal abelian extensions of the Standard Model with an extra neutral gauge boson $Z'$ at the TeV scale. In these scenarios an extended scalar sector and heavy right-handed neutrinos are naturally envisaged. We present some of their striking signatures at the Large Hadron Collider, the most interesting arising from a $Z'$ decaying to heavy neutrino pairs as well as a heavy scalar decaying to two Standard Model Higgses. Using renormalisation group methods, we characterise the high energy behaviours of these extensions and exploit the constraints imposed by the embedding into a wider GUT scenario.Comment: 6 pages, 4 figures. Reference list updated. Contribution to the proceedings of the 8th International Workshop on QCD - Theory and Experiment (QCD@Work 2016), 27-30 Jun 2016. Martina Franca, Ital

Z′Z', Higgses and heavy neutrinos in U(1)′U(1)' models: from the LHC to the GUT scale

We study a class of non-exotic minimal $U(1) '$ extensions of the Standard Model, which includes all scenarios that are anomaly-free with the ordinary fermion content augmented by one Right-Handed neutrino per generation, wherein the new Abelian gauge group is spontaneously broken by the non-zero Vacuum Expectation Value of an additional Higgs singlet field, in turn providing mass to a $Z'$ state. By adopting the $B-L$ example, whose results can be recast into those pertaining to the whole aforementioned class, and allowing for both scalar and gauge mixing, we first extract the surviving parameter space in presence of up-to-date theoretical and experimental constraints. Over the corresponding parameter configurations, we then delineate the high energy behaviour of such constructs in terms of their stability and perturbativity. Finally, we highlight key production and decay channels of the new states entering the spectra of this class of models, i.e., heavy neutrinos, a second Higgs state and the $Z'$, which are amenable to experimental investigation at the Large Hadron Collider. We therefore set the stage to establish a direct link between measurements obtainable at the Electro-Weak scale and the dynamics of the underlying model up to those where a Grand Unification Theory embedding a $U(1)'$ can be realised.Comment: 32 pages, 59 figures, journal versio

Streamlined management of the built environment: the district and the building logbook as risk prevention tools

Management of information related to the real properties is a key topic both in private and public sector. In the Italian context, can be spotted an overall lack of organisation of the information concerning the real estate assets, from the building scale, to the neighbourhood, until the city and the territory. Moreover, management of the urban environment is characterised by the presence of different players asking for common needs in management and use of data. This research aims at proposing the Building Logbook and the District Logbook as tools for collection, organisation and management of information, in a perspective of streamlined real estate management process. Moreover, the Logbooks can be conceived as tools for risk management. They should be exploited especially in technical management phase of assets, as well as in the verification of compliance with laws, authorisations and licenses, since these issues often bear to disputes between public and private players. Often disputes concern that areas where the competences and responsibilities among different players are not clear (connections to system, property boundaries, licenses, occupation of public land etc.). In this situations, information management assumes a key role, since it could be a powerful mean to clarify responsibilities among players. Therefore, the scope of the research concerns the investigation on the relationships and related information flows among stakeholders in the real estate field. Altogether, it can be stated that the logbooks can streamline processes in the use phase of assets, despite they could be intended as rigid control tools. Through this paper these issues will deepened and clarified. The paper concludes with some considerations concerning the possible integration of the Logbooks in a digital environment, following the BIM approach

Spatio-temporal distribution pattern of COVID-19 in the Northern Italy during the first-wave scenario. The role of the highway network

Background: The rapid outbreak of Coronavirus disease 2019 (COVID-19) has posed several challenges to the scientific community. The goal of this paper is to investigate the spread of COVID-19 in Northern Italy during the so-called first wave scenario and to provide a qualitative comparison with the local highway net. Methods: Fixed a grid of days from February 27, 2020, the cumulative numbers of infections in each considered province have been compared to sequences of thresholds. As a consequence, a time-evolving classification of the state of danger in terms of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infections, in view of the smallest threshold overtaken by this comparison, has been obtained for each considered province. The provinces with a significant amount of cases have then been collected into matrices containing only the ones featuring a significant amount of cases. Results: The time evolution of the classification has then been qualitatively compared to the highway network, to identify similarities and thus linking the rapid spreading of COVID-19 and the highway connections. Conclusions: The obtained results demonstrate how the proposed model properly fits with the spread of COVID-19 along with the Italian highway transport network and could be implemented to analyze qualitatively other disease transmissions in different contexts and time periods

The maintenance paradox

This research will spot main features of servitization in real estate, placing main emphasis to current and future development of the trend. In manufacturing the servitization process has already been studied since the late 1980’s, whereas in real estate is a phenomenon not yet been clearly defined yet. Despite being a market characterised by low speed innovation, currently some changings in management of the built environment can be noticed: with new business models and financing structures, a shifting from a product-oriented market to a service-oriented one can be spotted. Therefore, through this research will be investigated the servitization process, with regard to maintenance management, no longer conceived as an optional non-core activity, after the transaction of the asset, but as part of the services included in the purchasing of the building and its facilities. Accordingly, the building is conceived more and more as a complex tangible and intangible entity, not only characterised by its production and location value, but also by its capability to offer provide users with a wide array of services to users. Thus, after a phase featured by the willingness to acquire legitimacy in the building process by the maintenance operators, we are witnessing to the maintenance paradox: the servitization of business model in real estate, leading to performing “the maintenance without maintenance”. The paper concludes with some considerations on future developments of the research and trends in the real estate marke