There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

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Table Of Integrals Series And Products

第12次 아시아ㆍ太平洋 矯政局長會議 參加記

Recent lattice data have reported an infrared suppressed, positivity violating gluon propagator which is nonvanishing at zero momentum and a ghost propagator which is no longer enhanced. This paper discusses how to obtain analytical results which are in qualitative agreement with these lattice data within the Gribov-Zwanziger framework. This framework allows one to take into account effects related to the existence of gauge copies, by restricting the domain of integration in the path integral to the Gribov region. We elaborate to great extent on a previous short paper by presenting additional results, also confirmed by the numerical simulations. A detailed discussion on the soft breaking of the Becchi-Rouet-Stora-Tyutin symmetry arising in the Gribov-Zwanziger approach is provided.

Refinement of the Gribov-Zwanziger approach in the Landau gauge: Infrared propagators in harmony with the lattice results

So far, the infrared behavior of the gluon and ghost propagator based on the Gribov-Zwanziger approach predicted a positivity violating gluon propagator vanishing at zero momentum, and an infrared enhanced ghost propagator. However, recent data based on huge lattices have revealed a positivity violating gluon propagator which turns out to attain a finite nonvanishing value very close to zero momentum. At the same time the ghost propagator does not seem to be infrared enhanced anymore. We point out that these new features can be accounted for by yet unexploited dynamical effects within the Gribov-Zwanziger approach, leading to an infrared behavior in qualitatively good agreement with the new data.

New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach

We present an analytic description of numerical results for the Landau-gauge SU(2) gluon propagator $D({p}^{2})$, obtained from lattice simulations (in the scaling region) for the largest lattice sizes to date, in $d=2$, 3 and 4 space-time dimensions. Fits to the gluon data in $3d$ and in $4d$ show very good agreement with the tree-level prediction of the refined Gribov-Zwanziger (RGZ) framework, supporting a massive behavior for $D({p}^{2})$ in the infrared limit. In particular, we investigate the propagator's pole structure and provide estimates of the dynamical mass scales that can be associated with dimension-two condensates in the theory. In the $2d$ case, fitting the data requires a noninteger power of the momentum $p$ in the numerator of the expression for $D({p}^{2})$. In this case, an infinite-volume-limit extrapolation gives $D(0)=0$. Our analysis suggests that this result is related to a particular symmetry in the complex-pole structure of the propagator and not to purely imaginary poles, as would be expected in the original Gribov-Zwanziger scenario.

Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates

We consider the gluon propagator $D({p}^{2})$ at various lattice sizes and spacings in the case of pure SU(3) Yang-Mills gauge theories using the Landau gauge fixing. We discuss a class of fits in the infrared region in order to (in)validate the tree level analytical prediction in terms of the (refined) Gribov-Zwanziger framework. It turns out that an important role is played by the presence of the widely studied dimension two gluon condensate $⟨{A}^{2}⟩$. Including this effect allows to obtain an acceptable fit around 1 to 1.5 GeV, while corroborating the refined Gribov-Zwanziger prediction for the gluon propagator. We also discuss the infinite volume extrapolation, leading to the estimate $D(0)=8.3\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{ }{\mathrm{GeV}}^{\ensuremath{-}2}$. As a by-product, we can also provide the prediction $⟨{g}^{2}{A}^{2}⟩\ensuremath{\approx}3\text{ }\text{ }{\mathrm{GeV}}^{2}$ obtained at the renormalization scale $\ensuremath{\mu}=10\text{ }\text{ }\mathrm{GeV}$.

/pdf/indirect-lattice-evidence-for-the-refined-gribov-zwanziger-sxtpjaptf2.pdf

Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate in the Landau gauge

In recent years, the Gribov-Zwanziger action was refined by taking into account certain dimension 2 condensates. In this fashion, one succeeded in bringing the gluon and the ghost propagator obtained from the Gribov-Zwanziger model in qualitative and quantitative agreement with the lattice data. In this paper, we shall elaborate further on this aspect. First, we shall show that more dimension 2 condensates can be taken into account than considered so far and, in addition, we shall give firm evidence that these condensates are in fact present by discussing the effective potential. It follows thus that the Gribov-Zwanziger action dynamically transforms itself into the refined version, thereby showing that the continuum nonperturbative Landau gauge fixing, as implemented by the Gribov-Zwanziger approach, is consistent with lattice simulations.

David Dudal

Papers

Refinement of the Gribov-Zwanziger approach in the Landau gauge: Infrared propagators in harmony with the lattice results

New features of the gluon and ghost propagator in the infrared region from the Gribov-Zwanziger approach

Modeling the Gluon Propagator in Landau Gauge: Lattice Estimates of Pole Masses and Dimension-Two Condensates

Indirect lattice evidence for the refined Gribov-Zwanziger formalism and the gluon condensate in the Landau gauge

Dynamical origin of the refinement of the Gribov-Zwanziger theory