Reconstructing Quantum Field Theory from an Educational Perspective

The research work concerns the analysis of the foundations of Quantum Field Theory carried out from an educational perspective. The whole research has been driven by two questions: • How the concept of object changes when moving from classical to contemporary physics? • How are the concepts of field and interaction shaped and conceptualized within contemporary physics? What makes quantum field and interaction similar to and what makes them different from the classical ones? The whole work has been developed through several studies: 1. A study aimed to analyze the formal and conceptual structures characterizing the description of the continuous systems that remain invariant in the transition from classical to contemporary physics. 2. A study aimed to analyze the changes in the meanings of the concepts of field and interaction in the transition to quantum field theory. 3. A detailed study of the Klein-Gordon equation aimed at analyzing, in a case considered emblematic, some interpretative (conceptual and didactical) problems in the concept of field that the university textbooks do not address explicitly. 4. A study concerning the application of the “Discipline-Culture” Model elaborated by I. Galili to the analysis of the Klein-Gordon equation, in order to reconstruct the meanings of the equation from a cultural perspective. 5. A critical analysis, in the light of the results of the studies mentioned above, of the existing proposals for teaching basic concepts of Quantum Field Theory and particle physics at the secondary school level or in introductory physics university courses.

Quantum Integrability in Non-Linear Sigma Models related to Gauge/String Correspondences

The Thermodynamic Bethe Ansatz analysis is carried out for the extended-CP^N class of integrable 2-dimensional Non-Linear Sigma Models related to the low energy limit of the AdS_4xCP^3 type IIA superstring theory. The principal aim of this program is to obtain further non-perturbative consistency check to the S-matrix proposed to describe the scattering processes between the fundamental excitations of the theory by analyzing the structure of the Renormalization Group flow. As a noteworthy byproduct we eventually obtain a novel class of TBA models which fits in the known classification but with several important differences. The TBA framework allows the evaluation of some exact quantities related to the conformal UV limit of the model: effective central charge, conformal dimension of the perturbing operator and field content of the underlying CFT. The knowledge of this physical quantities has led to the possibility of conjecturing a perturbed CFT realization of the integrable models in terms of coset Kac-Moody CFT. The set of numerical tools and programs developed ad hoc to solve the problem at hand is also discussed in some detail with references to the code.

Ab initio quantum mechanical investigation of structural and chemical-physical properties of selected minerals for minero-petrological, structural ceramic and biomaterial applications

The purpose of this thesis is the atomic-scale simulation of the crystal-chemical and physical (phonon, energetic) properties of some strategically important minerals for structural ceramics, biomedical and petrological applications. These properties affect the thermodynamic stability and rule the mineral-environment interface phenomena, with important economical, (bio)technological, petrological and environmental implications. The minerals of interest belong to the family of phyllosilicates (talc, pyrophyllite and muscovite) and apatite (OHAp), chosen for their importance in industrial and biomedical applications (structural ceramics) and petrophysics. In this thesis work we have applicated quantum mechanics methods, formulas and knowledge to the resolution of mineralogical problems ("Quantum Mineralogy”). The chosen theoretical approach is the Density Functional Theory (DFT), along with periodic boundary conditions to limit the portion of the mineral in analysis to the crystallographic cell and the hybrid functional B3LYP. The crystalline orbitals were simulated by linear combination of Gaussian functions (GTO). The dispersive forces, which are important for the structural determination of phyllosilicates and not properly con-sidered in pure DFT method, have been included by means of a semi-empirical correction. The phonon and the mechanical properties were also calculated. The equation of state, both in athermal conditions and in a wide temperature range, has been obtained by means of variations in the volume of the cell and quasi-harmonic approximation. Some thermo-chemical properties of the minerals (isochoric and isobaric thermal capacity) were calculated, because of their considerable applicative importance. For the first time three-dimensional charts related to these properties at different pressures and temperatures were provided. The hydroxylapatite has been studied from the standpoint of structural and phonon properties for its biotechnological role. In fact, biological apatite represents the inorganic phase of vertebrate hard tissues. Numerous carbonated (hydroxyl)apatite structures were modelled by QM to cover the broadest spectrum of possible biological structural variations to fulfil bioceramics applications.

Exploring Quantum Speed-up Through Cluster-state Computers

The aim of this thesis is to investigate the nature of quantum computation and the question of the quantum speed-up over classical computation by comparing two different quantum computational frameworks, the traditional quantum circuit model and the cluster-state quantum computer. After an introductory survey of the theoretical and epistemological questions concerning quantum computation, the first part of this thesis provides a presentation of cluster-state computation suitable for a philosophical audience. In spite of the computational equivalence between the two frameworks, their differences can be considered as structural. Entanglement is shown to play a fundamental role in both quantum circuits and cluster-state computers; this supports, from a new perspective, the argument that entanglement can reasonably explain the quantum speed-up over classical computation. However, quantum circuits and cluster-state computers diverge with regard to one of the explanations of quantum computation that actually accords a central role to entanglement, i.e. the Everett interpretation. It is argued that, while cluster-state quantum computation does not show an Everettian failure in accounting for the computational processes, it threatens that interpretation of being not-explanatory. This analysis presented here should be integrated in a more general work in order to include also further frameworks of quantum computation, e.g. topological quantum computation. However, what is revealed by this work is that the speed-up question does not capture all that is at stake: both quantum circuits and cluster-state computers achieve the speed-up, but the challenges that they posit go besides that specific question. Then, the existence of alternative equivalent quantum computational models suggests that the ultimate question should be moved from the speed-up to a sort of “representation theorem” for quantum computation, to be meant as the general goal of identifying the physical features underlying these alternative frameworks that allow for labelling those frameworks as “quantum computation”.