"Minimal geometric data" approach to Dirac algebra, spinor groups and field theories

The three first sections contain an updated, not-so-short account of a partly original approach to spinor geometry and field theories introduced by Jadczyk and myself; it is based on an intrisic treatment of 2-spinor geometry in which the needed background structures do not need to be assumed, but rather arise naturally from a unique geometric datum: a vector bundle with complex 2-dimensional fibres over a real 4-dimensional manifold. The two following sections deal with Dirac algebra and 4-spinor groups in terms of two spinors, showing various aspects of spinor geometry from a different perspective. The last section examines particle momenta in 2-spinor terms and the bundle structure of 4-spinor space over momentum space.Comment: 33 pages, typos corrected and one inexact statement eliminate

Fermi transport of spinors and free QED states in curved spacetime

Fermi transport of spinors can be precisely understood in terms of 2-spinor geometry. By using a partly original, previously developed treatment of 2-spinors and classical fields, we describe the family of all transports, along a given 1-dimensional timelike submanifold of spacetime, which yield the standard Fermi transport of vectors. Moreover we show that this family has a distinguished member, whose relation to the Fermi transport of vectors is similar to the relation between the spinor connection and spacetime connection. Various properties of the Fermi transport of spinors are discussed, and applied to the construction of free electron states for a detector-dependent QED formalism introduced in a previous paper.Comment: 18 page

Tetrad gravity, electroweak geometry and conformal symmetry

A partly original description of gauge fields and electroweak geometry is proposed. A discussion of the breaking of conformal symmetry and the nature of the dilaton in the proposed setting indicates that such questions cannot be definitely answered in the context of electroweak geometry.Comment: 21 pages - accepted by International Journal of Geometric Methods in Modern Physics - v2: some minor changes, mostly corrections of misprint

Hermitian vector fields and covariant quantum mechanics of a spin particle

In the context of Covariant Quantum Mechanics for a spin particle, we classify the ``quantum vector fields'', i.e. the projectable Hermitian vector fields of a complex bundle of complex dimension 2 over spacetime. Indeed, we prove that the Lie algebra of quantum vector fields is naturally isomorphic to a certain Lie algebra of functions of the classical phase space, called ``special phase functions''. This result provides a covariant procedure to achieve the quantum operators generated by the quantum vector fields and the corresponding observables described by the special phase functions.Comment: 23 page

Hermitian vector fields and special phase functions

We start by analysing the Lie algebra of Hermitian vector fields of a Hermitian line bundle. Then, we specify the base space of the above bundle by considering a Galilei, or an Einstein spacetime. Namely, in the first case, we consider, a fibred manifold over absolute time equipped with a spacelike Riemannian metric, a spacetime connection (preserving the time fibring and the spacelike metric) and an electromagnetic field. In the second case, we consider a spacetime equipped with a Lorentzian metric and an electromagnetic field. In both cases, we exhibit a natural Lie algebra of special phase functions and show that the Lie algebra of Hermitian vector fields turns out to be naturally isomorphic to the Lie algebra of special phase functions. Eventually, we compare the Galilei and Einstein cases

Two-spinor Formulation of First Order Gravity coupled to Dirac Fields

Two-spinor formalism for Einstein Lagrangian is developed. The gravitational field is regarded as a composite object derived from soldering forms. Our formalism is geometrically and globally well-defined and may be used in virtually any 4m-dimensional manifold with arbitrary signature as well as without any stringent topological requirement on space-time, such as parallelizability. Interactions and feedbacks between gravity and spinor fields are considered. As is well known, the Hilbert-Einstein Lagrangian is second order also when expressed in terms of soldering forms. A covariant splitting is then analysed leading to a first order Lagrangian which is recognized to play a fundamental role in the theory of conserved quantities. The splitting and thence the first order Lagrangian depend on a reference spin connection which is physically interpreted as setting the zero level for conserved quantities. A complete and detailed treatment of conserved quantities is then presented.Comment: 16 pages, Plain TE

Lentiviral haemopoietic stem/progenitor cell gene therapy for treatment of Wiskott-Aldrich syndrome: interim results of a non-randomised, open-label, phase 1/2 clinical study

Background Wiskott-Aldrich syndrome is a rare, life-threatening, X-linked primary immunodeficiency characterised by microthrombocytopenia, infections, eczema, autoimmunity, and malignant disease. Lentiviral vector-mediated haemopoietic stem/progenitor cell (HSPC) gene therapy is a potentially curative treatment that represents an alternative to allogeneic HSPC transplantation. Here, we report safety and efficacy data from an interim analysis of patients with severe Wiskott-Aldrich syndrome who received lentiviral vector-derived gene therapy. Methods We did a non-randomised, open-label, phase 1/2 clinical study in paediatric patients with severe Wiskott-Aldrich syndrome, defined by either WAS gene mutation or absent Wiskott-Aldrich syndrome protein (WASP) expression or a Zhu clinical score of 3 or higher. We included patients who had no HLA-identical sibling donor available or, for children younger than 5 years of age, no suitable 10/10 matched unrelated donor or 6/6 unrelated cord blood donor. After treatment with rituximab and a reduced-intensity conditioning regimen of busulfan and fludarabine, patients received one intravenous infusion of autologous CD34+ cells genetically modified with a lentiviral vector encoding for human WAS cDNA. The primary safety endpoints were safety of the conditioning regimen and safety of lentiviral gene transfer into HSPCs. The primary efficacy endpoints were overall survival, sustained engraftment of genetically corrected HSPCs, expression of vector-derived WASP, improved T-cell function, antigen-specific responses to vaccinations, and improved platelet count and mean platelet volume normalisation. This interim analysis was done when the first six patients treated had completed at least 3 years of follow-up. The planned analyses are presented for the intention-to-treat population. This trial is registered with ClinicalTrials.gov (number NCT01515462) and EudraCT (number 2009-017346-32). Findings Between April 20, 2010, and Feb 26, 2015, nine patients (all male) were enrolled of whom one was excluded after screening; the age range of the eight treated children was 1·1–12·4 years. At the time of the interim analysis (data cutoff April 29, 2016), median follow-up was 3·6 years (range 0·5–5·6). Overall survival was 100%. Engraftment of genetically corrected HSPCs was successful and sustained in all patients. The fraction of WASP-positive lymphocytes increased from a median of 3·9% (range 1·8–35·6) before gene therapy to 66·7% (55·7–98·6) at 12 months after gene therapy, whereas WASP-positive platelets increased from 19·1% (range 4·1–31·0) to 76·6% (53·1–98·4). Improvement of immune function was shown by normalisation of in-vitro T-cell function and successful discontinuation of immunoglobulin supplementation in seven patients with follow-up longer than 1 year, followed by positive antigen-specific response to vaccination. Severe infections fell from 2·38 (95% CI 1·44–3·72) per patient-year of observation (PYO) in the year before gene therapy to 0·31 (0·04–1·11) per PYO in the second year after gene therapy and 0·17 (0·00–0·93) per PYO in the third year after gene therapy. Before gene therapy, platelet counts were lower than 20 × 109 per L in seven of eight patients. At the last follow-up visit, the platelet count had increased to 20–50 × 109 per L in one patient, 50–100 × 109 per L in five patients, and more than 100 × 109 per L in two patients, which resulted in independence from platelet transfusions and absence of severe bleeding events. 27 serious adverse events in six patients occurred after gene therapy, 23 (85%) of which were infectious (pyrexia [five events in three patients], device-related infections, including one case of sepsis [four events in three patients], and gastroenteritis, including one case due to rotavirus [three events in two patients]); these occurred mainly in the first 6 months of follow-up. No adverse reactions to the investigational drug product and no abnormal clonal proliferation or leukaemia were reported after gene therapy. Interpretation Data from this study show that gene therapy provides a valuable treatment option for patients with severe Wiskott-Aldrich syndrome, particularly for those who do not have a suitable HSPC donor available