Two-dimensional Quantum Field Models (with applications to Statistical Mechanics)

Two dimensional toy models display, in a gentler setting, manysalient aspects of Quantum Field Theory. Here I discuss a concrete two dimensional case, the Thirring model, which illustrates several important concepts of this theory: the anomalous dimension of the fields; the exact solvability; the anomalies of the Ward-Takahashi identities. Besides, I give a glimpse of the decisive role that this model plays in the study of an apparently unrelated topic: correlation critical exponents of two dimensional lattice systems of Statistical Mechanics.Comment: 10 pages; International Conference on Mathematical Physics 2012 - Topical Section: Quantum Field Theor

Universality of one-dimensional Fermi systems, I. Response functions and critical exponents

The critical behavior of one-dimensional interacting Fermi systems is expected to display universality features, called Luttinger liquid behavior. Critical exponents and certain thermodynamic quantities are expected to be related among each others by model-independent formulas. We establish such relations, the proof of which has represented a challenging mathematical problem, for a general model of spinning fermions on a one dimensional lattice; interactions are short ranged and satisfy a positivity condition which makes the model critical at zero temperature. Proofs are reported in two papers: in the present one, we demonstrate that the zero temperature response functions in the thermodynamic limit are Borel summable and have anomalous power-law decay with multiplicative logarithmic corrections. Critical exponents are expressed in terms of convergent expansions and depend on all the model details. All results are valid for the special case of the Hubbard model.Comment: 56 pages, 2 figures. arXiv admin note: text overlap with arXiv:1106.035

Case Report: Morphologic and Functional Characteristics of Intestinal Mucosa in a Child With Short Bowel Syndrome After Treatment With Teduglutide: Evidence in Favor of GLP-2 Analog Safety

Teduglutide is a glucagon-like peptide-2 (GLP-2) analog employed in patients with short bowel syndrome (SBS) to reduce the need of parenteral nutrition in these patients, by virtue of its effects on enteric function. The experimental studies reported that the stimulating action of GLP-2 on epithelial turnover implies the potential development of dysplastic and neoplastic lesion. However, the clinical trials could not detect preneoplastic lesions on histologic material, and in a recent pilot study the occurrence of polyps was similar before and after treatment and included only low-grade dysplastic lesions. Another clue in GLP-2 function in stimulating mucosal restore is its enhancement through cooperation with epidermal growth factor (EGF). In this study, we analyzed gastroscopy and colonoscopy samplings from a child successfully weaned off parenteral nutrition with teduglutide. Villous and crypt structure was regular both in duodenal and in colonic samplings; in properly oriented villi, villus/crypt ratio was regular. The absorptive epithelium demonstrated a regular morphology. No atypia was detected in enterocytes, along epithelial structures. At the ultrastructural analysis, only a few enterocytes with vacuolized cytoplasm were observed. An S-phase marker Ki67 stained nuclei in the transitional amplifying zone, while nuclei stained by the cell cycle regulatory proteins p21 and p27 were placed in the differentiated epithelium of the duodenal villi and colonic crypts, as in the control cases. The counts of enterocytes immunostained with the same antisera, evaluated with image analysis software, were in the range of control cases. The ratio of the number of epidermal growth factor receptor (EGFR) signals/the number of centromere probe of chromosome 7 (CEP7) signals was less than 2. The findings available from this single patient are consistent with good preservation of functional capability of intestinal epithelium after treatment with GLP-2, given the histologic and ultrastructural features of enterocytes. In addition, the findings from cell cycle regulatory proteins immunolocalization and quantitative analysis show that cell renewal machinery in our case is comparable to control cases. The gene of the receptor EGFR is regularly expressed in enteric epithelium of our case. Morphologic and functional data from our patient improve evidence in favor of the safety of GLP-2 employ in SBS

Renormalization Group and Asymptotic Spin--Charge separation for Chiral Luttinger liquids

The phenomenon of Spin-Charge separation in non-Fermi liquids is well understood only in certain solvable d=1 fermionic systems. In this paper we furnish the first example of asymptotic Spin-Charge separation in a d=1 non solvable model. This goal is achieved using Renormalization Group approach combined with Ward-Identities and Schwinger-Dyson equations, corrected by the presence of a bandwidth cut-offs. Such methods, contrary to bosonization, could be in principle applied also to lattice or higher dimensional systems.Comment: 45 pages, 11 figure

Kosterlitz-Thouless Transition Line for the Two Dimensional Coulomb Gas

With a rigorous renormalization group approach, we study the pressure of the two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless transition line, i.e. the boundary of the dipole region in the activity-temperature phase-space.Comment: 61 pages, 2 figure

The addition of Capsicum baccatum to Calabrian monovarietal extra virgin olive oils leads to flavoured olive oils with enhanced oxidative stability

This study aimed to evaluate the influence of Capsicum baccatum L. Aji Angelo and Bishop crown cultivars to the quality parameters of flavoured olive oils (FOOs) obtained by the addition of both fresh and dried pepper powders (1%) to Dolce di Rossano and Roggianella monovarietal extra virgin olive oils (EVOOs). First, pepper extracts were investigated for their total phenolic, flavonoid, carotenoid content as well as phenolic acids, fatty acid profile, and vitamin C and E content. In order to evaluate the impact of both fresh and dried peppers on the oxidative stability of FOOs, the Rancimat test was applied. 2,2-Azinobis(3-ethylbenzothiazoline-6-sulfonic) acid (ABTS), 2,2-diphenyl-1-picrylhydrazyl (DPPH), ?-carotene bleaching (B-CB) and ferric reducing antioxidant power (FRAP) assays were used to investigate the antioxidant potential. Bishop crown dried extracts showed the highest phenolic, carotenoid and vitamin content, whereas Aji Angelo had the highest amount of capsaicinoids. Among EVOOs, Roggianella EVOO showed the highest antioxidant activity as well as the highest induction time (39.6 h). Remarkably, FOO obtained by the addition of Bishop crown dried pepper extract to Roggianella EVOO showed a higher induction time (44.9 h) with respect to the corresponding EVOO