Chiral-Yang-Mills theory, non commutative differential geometry, and the need for a Lie super-algebra

In Yang-Mills theory, the charges of the left and right massless Fermions are independent of each other. We propose a new paradigm where we remove this freedom and densify the algebraic structure of Yang-Mills theory by integrating the scalar Higgs field into a new gauge-chiral 1-form which connects Fermions of opposite chiralities. Using the Bianchi identity, we prove that the corresponding covariant differential is associative if and only if we gauge a Lie-Kac super-algebra. In this model, spontaneous symmetry breakdown naturally occurs along an odd generator of the super-algebra and induces a representation of the Connes-Lott non commutative differential geometry of the 2-point finite space.Comment: 17 pages, no figur

Perturbative Study of the Supersymmetric Lattice Theory from Matrix Model

We study the lattice model for the supersymmetric Yang-Mills theory in two dimensions proposed by Cohen, Kaplan, Katz, and Unsal. We re-examine the formal proof for the absence of susy breaking counter terms as well as the stability of the vacuum by an explicit perturbative calculation for the case of U(2) gauge group. Introducing fermion masses and treating the bosonic zero momentum mode nonperturbatively, we avoid the infra-red divergences in the perturbative calculation. As a result, we find that there appear mass counter terms for finite volume which vanish in the infinite volume limit so that the theory needs no fine-tuning. We also find that the supersymmetry plays an important role in stabilizing the lattice space-time by the deconstruction.Comment: 36 pages, 18 figures; typos corrected, some definitions added, appendix including feynman dyagram delete

On the Structure of the Observable Algebra of QCD on the Lattice

The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic $C^{*}$-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3). The structure of the hadronic part, as presented in terms of a number of generators and relations, is studied in detail. It is shown that its irreducible representations are classified by triality. Using this, it is proved that the hadronic algebra is isomorphic to the commutant of the triality operator in the enveloping algebra of the Lie super algebra ${\rm sl(1/n)}$ (factorized by a certain ideal).Comment: 33 page

Phenol compounds for Electron Spin Resonance dosimetry in gamma and neutron field

The use of neutrons for cancer treatments has stimulated the research for beam characterization in order to optimize the therapy procedures in Neutron Capture Therapy (Altieri, 2008). Several research laboratories have shown an increasing interest aimed at extending the applicability of Electron Spin Resonance (ESR) dosimetry to radiotherapy with different types of radiation beams. In particular, ESR spectrometry provides absorbed dose measurements through the detection of the stable free radicals produced by ionizing radiations. The ESR dosimetric method has many advantages such as simple and rapid dose evaluation, the readout procedure is non-destructive, linear response of many organic and inorganic compounds (Baffa 2014). In this work we study the response of phenolic compounds with and without gadolinium addition for electron spin resonance (ESR) dosimetry exposed to a gamma and mixed (n, gamma) field mainly composed of thermal neutrons. The compound IRGANOX 1076 phenol gives a phenoxy radical stabilized by the presence of two bulky groups [3]. Moreover, its high molecular weight, the low volatility and the compatibility with the dosimeter binding material (paraffin) are advantages with respect to lower molecular weight phenols. In this work we report the ESR investigation of phenols pellets and thin films with and without Gd2O3 (5% by weight) exposed in the thermal column of the Triga Mark II reactor of LENA of Pavia. Thanks to their size, the phenolic films here presented are good devices for the dosimetry of beams with high dose gradient and which require accurate knowledge of the precise dose delivered. The choice of Gd as the additive nucleus has been made because we are interested in applications for mixed field (neutrons/photons) Gd-ESR dosimetry has an high neutron capture cross section and, furthermore, the high LET secondary particles release their energy entirely in the dosimeter. The low content of gadolinium guarantees a good tradeoff between the sensitivity to thermal neutrons. However, the use of gadolinium reduces or abolishes tissue equivalence because of its high atomic number (Marrale, 2015). The dosimetric features of these ESR dosimeters have been investigated. In particular, we analyzed the ESR spectra of these compounds and their dependence on microwave power and modulation amplitude, their response after gamma and neutron irradiations, the detection limits for both beam typologies, signal stability after irradiation. The results of ESR experiments are compared with Monte Carlo simulations aimed at obtaining information about the total dose measured by means of ESR dosimeters

Phenol compounds as new materials for Electron Paramagnetic Resonance dosimetry in clinical photon and electron beams,

In the last decades several research laboratories have shown an increasing interest aimed at extending the applicability of Electron Paramagnetic Resonance (EPR) dosimetry to radiotherapy with different types of radiation beams. EPR is a spectroscopic method for investigating the structure and dynamics of such paramagnetic species. Free radicals are known to be produced when a compound is irradiated with ionizing radiations. The concentration of radiation-induced free radicals is proportional to the energy released inside in the medium and this allows for dosimetric measurements through EPR technique. The use of alanine as a dosimetric material gave the possibility to apply EPR spectroscopy for high-dose standardization and dose control in radiation processing (Marrale 2016). The EPR dosimetric method has many advantages such as simple and rapid dose evaluation, the readout procedure is non-destructive, linear response of many organic and inorganic compounds. EPR detectors show a behavior that suggest possible applications for various kinds of beams used for radiation therapy. Nowadays, the most widely used organic compound as a dosimeter is the alanine. However, many researches are in progress with the aim at improving sensitivity of EPR dosimetry for doses much smaller than 1 Gy. More sensitive materials than alanine are needed to make the EPR dosimeter competitive with other dosimetry systems. Our research group has started an investigation of the EPR response of some phenols compounds for possible EPR dosimetric applications suitable features, such as high efficiency of radiation-matter energy transfer and radical stability at room temperature. Phenols are compounds possessing a benzene ring attached to a OH group. After irradiation the final product is a stable phenoxy radical. The stability of such radical can be improved by adding other alkyl chains which can be attached to the benzene ring. The phenol octadecyl-3-(3,5-di-tert.butyl-4-hydroxyphenyl)-propionate gave interesting results. Moreover, its high molecular weight, the low volatility and the compatibility with the dosimeter binding material (wax) are advantages with respect to lower molecular weight phenols. In this work we report the EPR investigation of phenols exposed to clinical photon and electron beams (Gallo, 2016). The dosimetric features of these EPR dosimeters (dependence on microwave power and modulation amplitude, their response after gamma and electron irradiations, dependence on beam type and energy, the detection limits for both beam typologies, signal stability after irradiation) were investigated and the results are reported

A Viewing Angle - Kinetic Luminosity Unification Scheme For BL Lacertae Objects

We propose a unified classification for BL Lac objects (BLs), focusing on the synchrotron peak frequency of the spectral energy distribution. The unification scheme is based on the angle Theta that describes the orientation of the relativistic jet and on the electron kinetic luminosity Lambda of the jet. We assume that Lambda scales with the size of the jet r in a self-similar fashion (Lambda propto r^2), as supported by observational data. The jets are self-similar in geometry and have the same pressure and median magnetic field at the inlet, independent of size. The self-similarity is broken for the highest energy electrons, which radiate mainly at high frequencies, since for large sources they suffer more severe radiative energy losses over a given fraction of the jet length. We calculate the optically thin synchrotron spectrum using an accelerating inner jet model based on simple relativistic gas dynamics and show that it can fit the observed infrared to X-ray spectrum of PKS 2155--304. We couple the accelerating jet model to the unification scheme and compare the results to complete samples of BLs. The negative apparent evolution of X-ray selected BLs is explained as a result of positive evolution of the jet electron kinetic luminosity $\Lambda_{kin}$. We review observational arguments in favor of the existence of scaled-down accretion disks and broad emission-line regions in BLs. The proposed unification scheme can explain the lack of observed broad emission lines in X-ray selected BLs, as well as the existence of those lines preferentially in luminous radio-selected BLs. Finally, we review observational arguments that suggest the extension of this unification scheme to all blazars.Comment: 32 pages, 8 figures, to be published in the ApJ (Oct 20, 1998

On the complexity of color-avoiding site and bond percolation

The mathematical analysis of robustness and error-tolerance of complex networks has been in the center of research interest. On the other hand, little work has been done when the attack-tolerance of the vertices or edges are not independent but certain classes of vertices or edges share a mutual vulnerability. In this study, we consider a graph and we assign colors to the vertices or edges, where the color-classes correspond to the shared vulnerabilities. An important problem is to find robustly connected vertex sets: nodes that remain connected to each other by paths providing any type of error (i.e. erasing any vertices or edges of the given color). This is also known as color-avoiding percolation. In this paper, we study various possible modeling approaches of shared vulnerabilities, we analyze the computational complexity of finding the robustly (color-avoiding) connected components. We find that the presented approaches differ significantly regarding their complexity.Comment: 14 page