en>Gautehuus at 15:25, 11 August 2014

2014-08-11T15:25:41Z

en>Anrnusna: journal name, replaced: Proc. R. Sco., London → Proceedings of the Royal Society using AWB

2013-10-08T19:03:58Z

journal name, replaced: Proc. R. Sco., London → Proceedings of the Royal Society using AWB

← Older revision		Revision as of 21:03, 8 October 2013
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	They ~~accept all major credit cards such as Visa,~~ [~~http://Www~~.~~Alexa.com/search?q~~=~~Master+-&r~~=~~topsites_index&p~~=~~bigtop Master~~ -] ~~Card~~, ~~American Express~~, ~~Discover~~, ~~Pay - Pal and so on~~. ~~But maybe you can use your health savings account~~ (~~HSA~~) ~~Visa card instead~~. ~~com suggests that paying~~ a ~~holiday using a credit card is~~ the ~~best way to go~~. ~~[https:~~/~~/Paysafecardgeneratorcodes~~.~~Wordpress~~.~~com~~/ ~~paysafecard generator] You~~ can ~~take advantage~~ of ~~different kinds of sales that run all round~~ the year. ~~It also applies to those who are seeking to have their credit re~~-~~established~~. <~~br><br~~>~~In cases where they are not in~~ a ~~position to pro-actively expand rates~~, ~~they~~ are ~~going to obviously offer significant tariffs in~~ the ~~beginning, to ensure that individuals borrow fewer~~. ~~We're told that~~ this will ~~give smaller retailers~~ the ~~ability to "offer create and manage" targeted offers through~~ the ~~platform~~. ~~You might perhaps receive a several consumer support associate~~ to ~~keep up, and you'll obtain a various reply. Für~~ [~~jedenallejedwedenpraktisch jedenalle ernsthaftenjeden ernsthaften~~] ~~Internet Poker Fan ist es von Vorteil~~, ~~die Bonus Werbeangebote der besten Online Poker Seiten auszunutzen~~, ~~wie - ein Beispiel- durch Angabe des Party Poker Bonus Code PC100~~. ~~Any person may submit written comments concerning~~ the ~~proposed settlement within 60 days of its publication to John R.~~ <br><br>~~More women~~ are ~~finding an attraction to its expanding use as~~ e~~-commerce and retail accept it~~. ~~A great advantage~~ of ~~Pay - Safe - Card is easy for~~ the ~~user~~ to ~~be able~~ to ~~set up an account~~ with the ~~card~~. ~~The UK~~ and ~~Sweden cooperate very closely with America~~. ~~Such as �Road Assist�, which provides access to emergency service to travelers anywhere in~~ the US. ~~People of all ages~~ that ~~come~~ from ~~different walks of life enjoy~~ the ~~fun and excitement of online gambling~~. <br><br>~~From this point on~~, ~~you can then choose~~ the ~~bank account~~ that ~~you wish to withdraw to~~, and ~~then put~~ in the ~~amount of money that you want~~ to ~~move. Get lots additional data~~ on the ~~foremost reliable web site style port agencies for making a high~~-~~quality and custom on~~-~~line presence~~. ~~These days all Hotels and Car Rental companies along with many other businesses require you~~ to ~~have a credit card to guarantee their services. One unique thing about Ally~~ is ~~that they allow you~~ to ~~make electronic check deposits. A lot~~ of ~~nasty things can happen if they get access to your Pay~~ - ~~Pal account~~. <br><br>~~If you need~~ to ~~add positive credit, overcome a~~ "~~thin~~" ~~credit history or restore your credit scores~~, ~~the Vista Card or any form of prepaid card~~ is ~~a powerful solution that allows you~~ to ~~get credit for bills you pay all the time but have not been reporting~~ to ~~the major credit agencies~~. ~~While you get~~ to ~~keep your points for your full lifetime of your registration~~, ~~there's hardly any restrictions to~~ the ~~amount of bonuses you may score from your Capital One Platinum Master Card~~. ~~By substituting luxuriance with~~ a ~~bit of economy~~, ~~your tax refund could serve as~~ the ~~largest problem solver for any adversary financial position~~. ~~This is obviously limited~~ to ~~10 transfers a year but consider this example:~~. ~~One of the company's most recent and most buzzed-about apps~~ is ~~Master - Card Money - Send~~. ~~[https://Paysafecardgeneratorcodes~~.~~Wordpress~~.~~com~~/ ~~paysafecard generator~~]		{{Quantum field theory}}
			'''Center vortices''' are line-like [[topological defect]]s that exist in the [[vacuum state\|vacuum]] of [[Yang–Mills theory]] and [[Quantum chromodynamics\|QCD]]. They seem to play an important role in the [[color confinement\|confinement]] of [[quark]]s.

			==In SU(''N'') theories==
			Center vortices are line-like topological defect that carry a gauge charge equal to one of the [[center (group theory)\|center]] elements of the gauge group. In the case of SU(''N'') gauge theories, these are the constant matrices:
			:<math>z_n = e^{\frac{2\pi in}N} I\;,</math>
			where ''I'' is the unit matrix. These elements form the abelian subgroup [[modular arithmetic\|'''Z'''<sub>''N''</sub>]]. Under such center elements, quarks transform as
			:<math>\psi \to e^{\frac{2\pi in}N}\psi\;,</math>
			while [[gluon]]s are invariant. This means that, if quarks are free (like in the [[Deconfinement\|deconfined phase]]), the center symmetry will be broken. Restoration of the center symmetry will imply confinement. [[Gerard 't Hooft\|'t Hooft]] first put this on a more rigorous footing.<ref>{{cite journal\|author=G. 't Hooft\|authorlink=Gerard 't Hooft\|title=On the phase transition towards permanent quark confinement\|journal=Nucl. Phys.\|volume=B138\|year=1978\|pages=1\|doi=10.1016/0550-3213(78)90153-0\|bibcode = 1978NuPhB.138....1T }}</ref>

			The two phases in the theory can be distinguished based on the behavior of the vortices.<ref name="Engelhardt">{{cite journal\|author=M. Engelhardt\|author2=K. Langfeld\|author3=H. Reinhardt\|author4=O. Tennert\|title=Deconfinement in SU(2) Yang-Mills theory as a center vortex percolation transition\|journal=Phys. Rev.\|volume=D61\|pages=054504\|year=2000\|doi=10.1103/PhysRevD.61.054504\|arxiv = hep-lat/9904004 \|bibcode = 2000PhRvD..61e4504E }}</ref> When considering a certain [[Wilson loop]], if the vortices are generally long, most vortices will only pierce the surface within the Wilson loop once. Furthermore the number of vortices piercing this surface will grow in proportion to the area of the surface. Due to the vortices suppressing the value of the [[vacuum expectation value]] of the Wilson loop, this will lead to an area-law, i.e. the Wilson loop ''W''(''C'') behaves like
			:<math>\langle W(C)\rangle \propto e^{-\sigma A}\;,</math>
			where ''A'' is the area spanned by the loop. The constant σ is called the string tension. This behavior is typical of confinement. However, when considering a regime where vortices are generally short — i.e. they form small loops — they will usually pierce the surface of the Wislon loop twice in opposite directions, thus leading to the two contributions canceling. Only vortex loops near the Wilson loop itself will pierce it once, thus leading to a contribution scaling like the perimeter:
			:<math>\langle W(C)\rangle \propto e^{-\alpha L}\;,</math>
			with ''L'' the length of the Wilson loop, and α some constant. This behavior signals there is ''no'' confinement.

			In [[Lattice gauge theory\|lattice simulations]] this behavior is indeed seen.<ref name="Engelhardt"/> At low temperatures (where there is confinement) vortices form large, complex clusters and percolate through space. At higher temperatures (above the deconfinement phase transition) vortices form small loops. Furthermore it has been seen that the string tension almost drops to zero when center vortices are removed from the simulation.<ref name="Faber">{{cite journal\|author=M. Faber\|author2=J. Greensite\|author3=&Scaron;. Olejník\|title=Direct laplacian center gauge\|journal=JHEP\|volume=11\|pages=053\|year=2001\|doi=10.1088/1126-6708/2001/11/053\|arxiv = hep-lat/0106017 \|bibcode = 2001JHEP...11..053F }}</ref> At the other hand, the string tension remains approximately unchanged when removing everything ''except'' for the center vortices. This clearly shows the close relation between center vortices and confinement. Aside from this it has also been shown in simulations that the vortices have a finite density in the continuum limit (meaning they are not a lattice artifact, but they do exist in reality), and that they are also linked with chiral symmetry breaking and topological charge.<ref name="Faber"/>

			One subtlety concerns the string tension at intermediate range and in the [[1/N expansion\|large-''N'' limit]]. According to the center vortex picture, the string tension should depend on the way the matter fields transform under the center, i.e. their so-called ''N''-ality. This seems to be correct for the large-distance string tension, but at smaller distances the string tension is instead proportional to the quadratic [[Casimir invariant\|Casimir]] of the representation — so-called Casimir scaling. This has been explained by domain formation around center vortices.<ref name="domains">{{cite journal\|author=J. Greensite\|author2=K. Langfeld\|author3=&Scaron;. Olejník\|author4=H. Reinhardt\|author5=T. Tok\|title=Color screening, Casimir scaling, and domain structure in G(2) and SU(N) gauge theories\|journal=Phys. Rev.\|volume=D75\|pages=034501\|year=2007\|doi=10.1103/PhysRevD.75.034501\|arxiv = hep-lat/0609050 \|bibcode = 2007PhRvD..75c4501G }}</ref> In the large-''N'' limit, this Casimir scaling goes all the way to large distances.<ref name="Greensite">{{cite journal\|author=J. Greensite\|title=The confinement problem in lattice gauge theory\|journal=Prog. Part. Nucl. Phys.\|volume=51\|year=2003\|pages=1\|doi=10.1016/S0146-6410(03)90012-3\|arxiv = hep-lat/0301023 \|bibcode = 2003PrPNP..51....1G }}</ref>

			==In gauge theories with trivial center==
			A gauge group like SO(3) has a trivial center, but SO(3) gauge theory is expected to be identical to SU(2) gauge theory. This discrepancy is due to the fact that, rather than the center, it is really the [[homotopy group]] π<sub>1</sub> which should be considered.<ref name="Greensite"/> Also mark that a theory like [[G2 (mathematics)\|'''G'''<sub>2</sub>]] gauge theory does not have a long-range string tension, which is consistent with the center vortex picture. In this theory, gluons can screen quarks, leading to color singlet states with the quantum number of quarks. Casimir scaling is, however, still present at intermediate ranges, i.e. before string breaking occurs. This can be explained by domain formation.<ref name="domains"/>

			==See also==
			* [[QCD vacuum]]

			==References==
			{{reflist\|2}}

			[[Category:Gauge theories]]
			[[Category:Quantum chromodynamics]]

en>Malcolma: added Category:Fluid dynamics; removed {{uncategorized}} using HotCat

2011-12-07T09:31:18Z

added Category:Fluid dynamics; removed {{uncategorized}} using HotCat

New page

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Kinematic wave - Revision history

en>Gautehuus at 15:25, 11 August 2014

en>Anrnusna: journal name, replaced: Proc. R. Sco., London → Proceedings of the Royal Society using AWB

en>Malcolma: added Category:Fluid dynamics; removed {{uncategorized}} using HotCat