Integrable theories and loop spaces: fundamentals, applications and new developments

We review our proposal to generalize the standard two-dimensional flatness construction of Lax-Zakharov-Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang Mills theories are summarized. We also discuss other possibilities that have not yet been explored.Comment: 64 pages, 8 figure

Modeling skull-face anatomical/morphological correspondence for craniofacial superimposition-based identification

Craniofacial superimposition (CFS) is a forensic identification technique which studies the anatomical and morphological correspondence between a skull and a face. It involves the process of overlaying a variable number of facial images with the skull. This technique has great potential since nowadays the wide majority of the people have photographs where their faces are clearly visible. In addition, the skull is a bone that hardly degrades under the effect of fire, humidity, temperature changes, etc. Three consecutive stages for the CFS process have been distinguished: the acquisition and processing of the materials; the skull-face overlay; and the decision making. This final stage consists of determining the degree of support for a match based on the previous overlays. The final decision is guided by different criteria depending on the anatomical relations between the skull and the face. In previous approaches, we proposed a framework for automating this stage at different levels taking into consideration all the information and uncertainty sources involved. In this study, we model new anatomical skull-face regions and we tackle the last level of the hierarchical decision support system. For the first time, we present a complete system which provides a final degree of craniofacial correspondence. Furthermore, we validate our system as an automatic identification tool analyzing its capabilities in closed (known information or a potential list of those involved) and open lists (little or no idea at first who may be involved) and comparing its performance with the manual results achieved by experts, obtaining a remarkable performance. The proposed system has been demonstrated to be valid for sortlisting a given data set of initial candidates (in 62,5% of the cases the positive one is ranked in the first position) and to serve as an exclusion method (97,4% and 96% of true negatives in training and test, respectively)

Charges and fluxes in Maxwell theory on compact manifolds with boundary

We investigate the charges and fluxes that can occur in higher-order Abelian gauge theories defined on compact space-time manifolds with boundary. The boundary is necessary to supply a destination to the electric lines of force emanating from brane sources, thus allowing non-zero net electric charges, but it also introduces new types of electric and magnetic flux. The resulting structure of currents, charges, and fluxes is studied and expressed in the language of relative homology and de Rham cohomology and the corresponding abelian groups. These can be organised in terms of a pair of exact sequences related by the Poincar\'e-Lefschetz isomorphism and by a weaker flip symmetry exchanging the ends of the sequences. It is shown how all this structure is brought into play by the imposition of the appropriately generalised Maxwell's equations. The requirement that these equations be integrable restricts the world-volume of a permitted brane (assumed closed) to be homologous to a cycle on the boundary of space-time. All electric charges and magnetic fluxes are quantised and satisfy the Dirac quantisation condition. But through some boundary cycles there may be unquantised electric fluxes associated with quantised magnetic fluxes and so dyonic in nature.Comment: 28 pages, plain Te

Hopf instantons in Chern-Simons theory

We study an Abelian Chern-Simons and Fermion system in three dimensions. In the presence of a fixed prescribed background magnetic field we find an infinite number of fully three-dimensional solutions. These solutions are related to Hopf maps and are, therefore, labelled by the Hopf index. Further we discuss the interpretation of the background field.Comment: one minor error corrected, discussion of gauge fixing added, some references adde

Fermionic Determinant of the Massive Schwinger Model

A representation for the fermionic determinant of the massive Schwinger model, or $QED_2$, is obtained that makes a clean separation between the Schwinger model and its massive counterpart. From this it is shown that the index theorem for $QED_2$ follows from gauge invariance, that the Schwinger model's contribution to the determinant is canceled in the weak field limit, and that the determinant vanishes when the field strength is sufficiently strong to form a zero-energy bound state

Drug resistance in B and non-B subtypes amongst subjects recently diagnosed as primary/recent or chronic HIV-infected over the period 2013–2016: Impact on susceptibility to first-line strategies including integrase strand-transfer inhibitors

Objectives To characterize the prevalence of transmitted drug resistance mutations (TDRMs) by plasma analysis of 750 patients at the time of HIV diagnosis from January 1, 2013 to November 16, 2016 in the Veneto region (Italy), where all drugs included in the recommended first line therapies were prescribed, included integrase strand transfer inhibitors (InNSTI). Methods TDRMs were defined according to the Stanford HIV database algorithm. Results Subtype B was the most prevalent HIV clade (67.3%). A total of 92 patients (12.3%) were expected to be resistant to one drug at least, most with a single class mutation (60/68–88.2% in subtype B infected subjectsand 23/24–95.8% in non-B subjects) and affecting mainly NNRTIs. No significant differences were observed between the prevalence rates of TDRMs involving one or more drugs, except for the presence of E138A quite only in patients with B subtype and other NNRTI in subjects with non-B infection. The diagnosis of primary/recent infection was made in 73 patients (9.7%): they had almost only TDRMs involving a single class. Resistance to InSTI was studied in 484 subjects (53 with primary-recent infection), one patient had 143C in 2016, a total of thirteen 157Q mutations were detected (only one in primary/recent infection). Conclusions Only one major InSTI-TDRM was identified but monitoring of TDRMs should continue in the light of continuing presence of NNRTI-related mutation amongst newly diagnosed subjects, sometime impacting also to modern NNRTI drugs recommended in first-line therapy

Quantum equivalence of sigma models related by non Abelian Duality Transformations

Coupling constant renormalization is investigated in 2 dimensional sigma models related by non Abelian duality transformations. In this respect it is shown that in the one loop order of perturbation theory the duals of a one parameter family of models, interpolating between the SU(2) principal model and the O(3) sigma model, exhibit the same behaviour as the original models. For the O(3) model also the two loop equivalence is investigated, and is found to be broken just like in the already known example of the principal model.Comment: As a result of the collaboration of new authors the previously overlooked gauge contribution is inserted into eq.(43) changing not so much the formulae as part of the conclusion: for the models considered non Abelian duality is OK in one loo

Compact boson stars in K field theories

We study a scalar field theory with a non-standard kinetic term minimally coupled to gravity. We establish the existence of compact boson stars, that is, static solutions with compact support of the full system with self-gravitation taken into account. Concretely, there exist two types of solutions, namely compact balls on the one hand, and compact shells on the other hand. The compact balls have a naked singularity at the center. The inner boundary of the compact shells is singular, as well, but it is, at the same time, a Killing horizon. These singular, compact shells therefore resemble black holes.Comment: Latex, 45 pages, 25 figures, some references and comments adde

Identification of observables in quantum toboggans

Quantum systems with real energies generated by an apparently non-Hermitian Hamiltonian may re-acquire the consistent probabilistic interpretation via an ad hoc metric which specifies the set of observables in the updated Hilbert space of states. The recipe is extended here to quantum toboggans. In the first step the tobogganic integration path is rectified and the Schroedinger equation is given the generalized eigenvalue-problem form. In the second step the general double-series representation of the eligible metric operators is derived.Comment: 25 p

Binary systems of neutral mesons in Quantum Field Theory

Quasi-degenerate binary systems of neutral mesons of the kaon type are investigated in Quantum Field Theory (QFT). General constraints cast by analyticity and discrete symmetries P, C, CP, TCP on the propagator (and on its spectral function) are deduced. Its poles are the physical masses; this unambiguously defines the propagating eigenstates. It is diagonalized and its spectrum thoroughly investigated. The role of ``spurious'' states, of zero norm at the poles, is emphasized, in particular for unitarity and for the realization of TCP symmetry. The K_L-K_S mass splitting triggers a tiny difference between their CP violating parameters \epsilon_L and \epsilon_S, without any violation of TCP. A constant mass matrix like used in Quantum Mechanics (QM) can only be introduced in a linear approximation to the inverse propagator, which respects its analyticity and positivity properties; it is however unable to faithfully describe all features of neutral mesons as we determine them in QFT, nor to provide any sensible parameterization of eventual effects of TCP violation. The suitable way to diagonalize the propagator makes use of a bi-orthogonal basis; it is inequivalent to a bi-unitary transformation (unless the propagator is normal, which cannot occur here). Problems linked with the existence of different ``in'' and ``out'' eigenstates are smoothed out. We study phenomenological consequences of the differences between the QFT and QM treatments. The non-vanishing of semi-leptonic asymmetry \delta_S - \delta_L does not signal, unlike usually claimed, TCP violation, while A_TCP keeps vanishing when TCP is realized. We provide expressions invariant by the rephasing of K0 and K0bar.Comment: 44 pages, 2 figures. Version to appear in Int. J. Mod. Phys.