412 research outputs found
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
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 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 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 -dependence of the vertices , where is a pseudoscalar
meson and is the number of colors, is analyzed with regard for the
-dependence of the quark charges. It is shown that the best processes for
the determination of are the reactions and
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 .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
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