A note about the t`Hooft`s ansatz for SU(N) real time guage theories

The t`Hooft's ansatz reduces the classical Yang--Mills theory to the $\lambda\phi^4$ one. It is shown that in the frame of this ansatz the real-time classical solutions for the arbitrary SU(N) gauge group is obtained by embedding $SU(2)\times SU(2)$ into SU(N). It is argued that this group structure is the only possibility in the frame of the considered ansatz. New explicit solutions for SU(3) and SU(5) gauge groups are shown

Hadamard states from null infinity

Free field theories on a four dimensional, globally hyperbolic spacetime, whose dynamics is ruled by a Green hyperbolic partial differential operator, can be quantized following the algebraic approach. It consists of a two-step procedure: In the first part one identifies the observables of the underlying physical system collecting them in a *-algebra which encodes their relational and structural properties. In the second step one must identify a quantum state, that is a positive, normalized linear functional on the *-algebra out of which one recovers the interpretation proper of quantum mechanical theories via the so-called Gelfand-Naimark-Segal theorem. In between the plethora of possible states, only few of them are considered physically acceptable and they are all characterized by the so-called Hadamard condition, a constraint on the singular structure of the associated two-point function. Goal of this paper is to outline a construction scheme for these states which can be applied whenever the underlying background possesses a null (conformal) boundary. We discuss in particular the examples of a real, massless conformally coupled scalar field and of linearized gravity on a globally hyperbolic and asymptotically flat spacetime.Comment: 23 pages, submitted to the Proceedings of the conference "Quantum Mathematical Physics", held in Regensburg from the 29th of September to the 02nd of October 201

Size-Dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium

The spatiotemporal dynamics of an excitable medium with multiple spiral defects is shown to vary smoothly with system size from short-lived transients for small systems to extensive chaos for large systems. A comparison of the Lyapunov dimension density with the average spiral defect density suggests an average dimension per spiral defect varying between three and seven. We discuss some implications of these results for experimental studies of excitable media.Comment: 5 pages, Latex, 4 figure

Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy

Propagation Failure in Excitable Media

We study a mechanism of pulse propagation failure in excitable media where stable traveling pulse solutions appear via a subcritical pitchfork bifurcation. The bifurcation plays a key role in that mechanism. Small perturbations, externally applied or from internal instabilities, may cause pulse propagation failure (wave breakup) provided the system is close enough to the bifurcation point. We derive relations showing how the pitchfork bifurcation is unfolded by weak curvature or advective field perturbations and use them to demonstrate wave breakup. We suggest that the recent observations of wave breakup in the Belousov-Zhabotinsky reaction induced either by an electric field or a transverse instability are manifestations of this mechanism.Comment: 8 pages. Aric Hagberg: http://cnls.lanl.gov/~aric; Ehud Meron:http://www.bgu.ac.il/BIDR/research/staff/meron.htm

The Dirac operator on generalized Taub-NUT spaces

We find sufficient conditions for the absence of harmonic $L^2$ spinors on spin manifolds constructed as cone bundles over a compact K\"ahler base. These conditions are fulfilled for certain perturbations of the Euclidean metric, and also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page

Green's functions and Hadamard parametrices for vector and tensor fields in general linear covariant gauges

We determine the retarded and advanced Green’s functions and Hadamard parametrices in curved spacetimes for linearized massive and massless gauge bosons and linearized Einstein gravity with a cosmological constant in general linear covariant gauges. These vector and tensor parametrices contain additional singular terms compared with their Feynman/de Donder-gauge counterpart. We also give explicit recursion relations for the Hadamard coefficients, and indicate their generalization to n dimensions. Furthermore, we express the divergence and trace of the vector and tensor Green’s functions in terms of derivatives of scalar and vector Green’s functions, and show how these relations appear as Ward identities in the free quantum theory

The Uses of Chiral Anomaly for Determination of the Number of Colors

The $N_c$-dependence of the vertices $PPP\gamma$, where $P$ is a pseudoscalar meson and $N_c$ is the number of colors, is analyzed with regard for the $N_c$-dependence of the quark charges. It is shown that the best processes for the determination of $N_c$ are the reactions $K\gamma \to K\pi$ and $\pi^pm\gamma\to\pi^\pm\eta$ as well as the decay \eta\ra\pi^+\pi^-\gamma. The measurement of the cross section \sigma(\pi^-\gamma\ra\pi^-\eta) at the VES facility at the IHEP agrees with the value $N_c=3$.Comment: 7 pages, 1 figure; accepted to Phys. Atom. Nucl., references adde

Assessment of the impact of CT calibration procedures for proton therapy planning on paediatric treatments

PURPOSE: Relative stopping powers (RSP) for proton therapy are estimated using single-energy CT (SECT), calibrated with standardised tissues of the adult male. It is assumed that those tissues are representative of tissues of all age and sex. Female, male and paediatric tissues differ from one another in density and composition. In this study, we use tabulated paediatric tissues and computational phantoms to investigate the impact of this assumption on paediatric proton therapy. The potential of dual-energy CT (DECT) to improve the accuracy of these calculations is explored. METHODS: We study 51 human body tissues, categorised into male/female for the age groups newborn, 1-, 5-, 10-, 15-year old and adult, with given compositions and densities. CT numbers are simulated and RSPs are estimated using SECT and DECT methods. Estimated tissue RSPs from each method are compared to theoretical RSP. The dose and range errors of each approach is evaluated on 3 computational phantoms (Ewing's sarcoma, salivary sarcoma, glioma) derived from paediatric proton therapy patients. RESULTS: With SECT, soft tissues have mean estimation errors and standard deviation up to (1.96 ± 4.18)% observed in newborns, compared to (0.20 ± 1.15)% in adult males. Mean estimation errors for bones are up to (-3.35 ± 4.76)% in paediatrics as opposed to (0.10 ± 0.66)% in adult males. With DECT, mean errors reduce to (0.17 ± 0.13)% and (0.23 ± 0.22)% in newborns (soft tissues/bones). With SECT, dose errors in a Ewing's sarcoma phantom are exceeding 5 Gy (10% of prescribed dose) at the distal end of the treatment field, with volumes of dose errors >5 Gy of Vdiff> 5 = 4630.7mm3 . Similar observations are made in the head and neck phantoms, with overdoses to healthy tissue exceeding 2 Gy (4%). A systematic Bragg peak shift resulting in either over- or underdosage of healthy tissues and target volumes depending on the crossed tissues RSP prediction errors is observed. Water equivalent range errors of single beams are between -1.53mm and 5.50mm (min, max) (Ewing's sarcoma phantom), -0.78mm and 3.62mm (salivary sarcoma phantom), and -0.43mm and 1.41mm (glioma phantom). DECT can reduce dose errors to <1 Gy and range errors to <1 mm. CONCLUSION: SECT estimates RSPs for paediatric tissues with systematic shifts. DECT improves the accuracy of RSPs and dose distributions in paediatric tissues compared to the SECT calibration curve based on adult males tissues