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| {{Further|Ricci calculus|Special unitary group|Quantum chromodynamics}}
| | <br><br>It allows you to email to 3000 more members, bringing the total to 6000 every three days. Just obtain the [http://www.dev.adaptationlearning.net/hostgator-django-mysql HostGator 1 cent coupon] and avail all of the services of a regular package at free of price for a month. Reseller hosting is for webmasters who wish to start their own profitable hosting company. However, he apparently out of duty will erase all your data. Your hostgator billing invoices in GatorBill will be generated five days ahead. We are currently hosting our software code and an offsite backup service to use, so this is a no brainer and easy issue to resolve was. Selecting a web-hosting provider from the virtual melting pot is a critical decision. Highest quality hosting obtainable plus 24/7 support services which will answer every one of your questions as fast as attainable and to top it off, they offer money-back guarantee. That's one hundred dollars, each month, every month, as long as they're happy with your service! In certain cases a dedicated server can offer fewer overhead and a larger revenue in investments.<br><br><br><br>They have always been very helpful and they have saved my site on numerous occasions. It's not a full time job but it certainly helps if your saving for a particular thing. It's all quite simple really, nothing technical at all. Currently, HostGator enjoys a loyal [http://www.dict.cc/englisch-deutsch/client+population.html client population] of approximately 10 million members across the globe. If you choose the reseller package, you can have as many websites as your heart desires and more than 1,000 domain names. Next create a new WordPress account. 7) Join a relevant promotion group - Especially for romance authors, there exist websites entirely for book promotion. This eventually turned to 85 with a logo in the Attracta tool engine. |
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| {{quantum field theory}}
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| In [[theoretical physics|theoretical]] [[particle physics]], the '''gluon field''' is a [[four vector]] field characterizing the propagation of [[gluon]]s in the [[strong interaction]] between [[quark]]s. It plays the same role in [[quantum chromodynamics]] as the [[electromagnetic four-potential]] in [[quantum electrodynamics]] - the gluon field constructs the [[gluon field strength tensor]].
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| Throughout, Latin indices take values 1, 2, ..., 8 for the eight gluon [[color charge]]s, while Greek indices take values 0 for timelike components and 1, 2, 3 for spacelike components of four dimensional vectors and tensors in [[spacetime]]. Throughout all equations, the [[Einstein notation|summation convention]] is used on all color and tensor indices, unless explicitly stated otherwise.
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| ==Introduction==
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| Gluons can have eight [[colour charge]]s so there are eight fields, in contrast to photons which are neutral and so there is only one photon field.
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| The gluon fields for each color charge each have a "timelike" component analogous to the [[electric potential]], and three "spacelike" components analogous to the [[magnetic vector potential]]. Using similar symbols:<ref name="Martin and Shaw">{{cite book|title = Particle Physics |edition = 3rd |author = B.R. Martin, G. Shaw| series = Manchester Physics Series|pages=380–384|publisher = John Wiley & Sons|year=2009|isbn = 978-0-470-03294-7}}</ref>
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| :<math>\boldsymbol{\mathcal{A}}^n(\mathbf{r}, t) = [ \underbrace{\mathcal{A}^n_0(\mathbf{r}, t)}_{\text{timelike}} , \underbrace{\mathcal{A}^n_1(\mathbf{r}, t), \mathcal{A}^n_2(\mathbf{r}, t), \mathcal{A}^n_3(\mathbf{r}, t)}_{\text{spacelike}} ] = [\phi^n (\mathbf{r}, t), \mathbf{A}^n (\mathbf{r}, t)]</math>
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| where {{math|''n'' {{=}} 1, 2, ... 8}} are not [[exponent]]s but enumerate the eight gluon color charges, and all components depend on the [[position vector]] {{math|'''r'''}} of the gluon and time ''t''. Each <math>\mathcal{A}^a_\alpha </math> is a scalar field, for some component of spacetime and gluon color charge.
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| The [[Gell-Mann matrices]] {{math|''λ<sup>a</sup>''}} are eight 3 × 3 matrices which form matrix [[Representation theory|representation]]s of the [[special unitary group|''SU''(3) group]]. They are also [[Generating set of a group|generator]]s of the SU(3) group, in the context of quantum mechanics and field theory; a generator can be viewed as an [[operator (physics)|operator]] corresponding to a [[symmetry transformation]] (see [[symmetry in quantum mechanics]]). These matrices play an important role in QCD as QCD is a [[gauge theory]] of the SU(3) [[gauge group]] obtained by taking the color charge to define a local symmetry: each Gell-Mann matrix corresponds to a particular gluon color charge, which in turn can be used to define [[color charge operator]]s. Generators of a group can also form a [[basis (linear algebra)|basis]] for a [[vector space]], so the overall gluon field is a "[[Superposition principle|superposition]]" of all the color fields. In terms of the Gell-Mann matrices (divided by 2 for convenience),
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| :<math>t_a = \frac{\lambda_a}{2}\,,</math>
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| the components of the gluon field are represented by 3 × 3 matrices, given by: | |
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| :<math>\mathcal{A}_{\alpha} = t_a \mathcal{A}^a_\alpha \equiv t_1 \mathcal{A}^1_\alpha + t_2 \mathcal{A}^2_\alpha + \cdots t_8 \mathcal{A}^8_\alpha </math>
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| or collecting these into a vector of four 3 × 3 matrices:
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| :<math>\boldsymbol{\mathcal{A}}(\mathbf{r}, t) = [\mathcal{A}_0(\mathbf{r}, t),\mathcal{A}_1(\mathbf{r}, t),\mathcal{A}_2(\mathbf{r}, t),\mathcal{A}_3(\mathbf{r}, t)] </math>
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| the gluon field is:
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| :<math>\boldsymbol{\mathcal{A}} = t_a \boldsymbol{\mathcal{A}}^a \,.</math>
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| ==Gauge covariant derivative in QCD==
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| Below the definitions (and most of the notation) follow K. Yagi, T. Hatsuda, Y. Miake<ref name="Yagi, Hatsuda, Miake">{{cite book|title=Quark-Gluon Plasma: From Big Bang to Little Bang
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| |author=K. Yagi, T. Hatsuda, Y. Miake
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| |year=2005
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| |pages=17–18
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| |publisher=Cambridge University Press
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| |url=http://books.google.co.uk/books?id=C2bpxwUXJngC&pg=PA18&dq=equation+of+motion+gluon+field+strength&hl=en&sa=X&ei=RRtiUqXYGIq80QW4mIDQDA&ved=0CDkQ6AEwAQ#v=onepage&q=equation%20of%20motion%20gluon%20field%20strength&f=false
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| |isbn=0-521-561-086
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| |series=Cambridge monographs on particle physics, nuclear physics, and cosmology
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| |volume=23
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| }}</ref> and Greiner, Schäfer.<ref name="Greiner, Schäfer">{{cite book|title=Quantum Chromodynamics
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| |author=W. Greiner, G. Schäfer
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| |year=1994
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| |chapter=4
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| |publisher=Springer
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| |url=http://books.google.co.uk/books/about/Quantum_Chromodynamics.html?id=gzYHNhp9KTIC
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| |isbn=3-540-57103-5
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| }}</ref>
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| The gauge [[covariant derivative]] {{math|''D<sub>μ</sub>''}} is required to transform quark fields in [[manifest covariance]]; the [[partial derivative]]s that form the [[four-gradient]] {{math|''∂<sub>μ</sub>''}} alone are not enough. The components which act on the color triplet quark fields are given by:
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| :<math>D_\mu =\partial_\mu \pm ig_s t_a \mathcal{A}^a_\mu\,,</math>
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| wherein {{math|''i''}} is the [[imaginary unit]], and
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| :<math>g_s = \sqrt{4\pi \alpha_s}</math>
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| is the [[dimensional analysis|dimensionless]] [[coupling constant#QCD and asymptotic freedom|coupling constant for QCD]]. Different authors choose different signs.The [[partial derivative]] term includes a 3 × 3 [[identity matrix]], conventionally not written for simplicity.
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| The [[Color charge#Quark and gluon fields and color charges|quark fields in triplet representation]] are written as [[column vector]]s:
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| :<math>\psi=\begin{pmatrix}\psi_{1}\\
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| \psi_{2}\\
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| \psi_{3}
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| \end{pmatrix},\overline{\psi}=\begin{pmatrix}\overline{\psi}^*_{1}\\
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| \overline{\psi}^*_{2}\\
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| \overline{\psi}^*_{3}
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| \end{pmatrix}
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| </math>
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| The quark field {{math|ψ}} belongs to the [[fundamental representation]] ('''3''') and the [[antiparticle|anti]]quark field {{math|{{overline|ψ}}}} belongs to the [[Hermitian conjugate|complex conjugate representation]] ('''3<sup>*</sup>'''), [[complex conjugate]] is denoted by {{math|*}} (not overbar).
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| ==Gauge transformations==
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| {{main|gauge theory}}
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| The [[gauge transformation]] of each gluon field <math>\mathcal{A}^n_\alpha</math> which leaves the gluon field strength tensor unchanged is;<ref name="Greiner, Schäfer"/>
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| :<math>\mathcal{A}^n_\alpha\rightarrow e^{i\bar{\theta}(\mathbf{r},t)} \left(\mathcal{A}^n_\alpha + \frac{i}{g_s}\partial_\alpha\right)e^{-i\bar{\theta}(\mathbf{r},t)}</math>
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| where
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| :<math>\bar{\theta}(\mathbf{r},t) = t_n \theta^n(\mathbf{r},t)\,,</math>
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| is a 3 × 3 matrix constructed from the {{math|''t<sup>n</sup>''}} matrices above and {{math|''θ''<sup>''n''</sup> {{=}} ''θ''<sup>''n''</sup>('''r''', ''t'')}} are eight [[Gauge theory|gauge functions]] dependent on spatial position {{math|'''r'''}} and time ''t''. [[Matrix exponentiation]] is used in the transformation. The gauge covariant derivative transforms similarly. The functions {{math|''θ''<sup>''n''</sup>}} here are similar to the gauge function {{math|''χ''('''r''', ''t'')}} when changing the [[electromagnetic four potential]] {{math|''A''}}, in spacetime components:
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| :<math>A'_\alpha (\mathbf{r},t) = A_\alpha (\mathbf{r},t) - \partial_\alpha \chi (\mathbf{r},t) \,</math>
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| leaving the electromagnetic tensor {{math|''F''}} invariant.
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| The quark fields are invariant under the [[gauge transformation]];<ref name="Greiner, Schäfer"/>
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| :<math>\psi(\mathbf{r},t) \rightarrow e^{ig\bar{\theta}(\mathbf{r},t)}\psi(\mathbf{r},t) </math>
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| ==See also==
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| * [[Quark confinement]]
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| * [[Gell-Mann matrices]]
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| * [[Field (physics)]]
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| * [[Einstein tensor]]
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| * [[Symmetry in quantum mechanics]]
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| * [[Wilson loop]]
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| * [[Wess–Zumino gauge]]
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| ==References==
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| ===Notes===
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| {{reflist}}
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| ===Further reading===
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| ====Books====
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| *{{cite book|title = An Introduction to the Standard Model of Particle Physics|edition = |author = W. N. Cottingham, D. A. Greenwood| series = |publisher = Cambridge University Press|year=2007|isbn = 113-946-221-0|url=http://books.google.co.uk/books?id=Dm36BYq9iu0C&pg=PA156&dq=gluon+field+equation&hl=en&sa=X&ei=-HliUsaAJ4KW0AXq44DQBA&redir_esc=y#v=onepage&q=gluon%20field%20equation&f=false}}
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| *{{cite book|title = Quarks: the stuff of matter|edition = |author = H. Fritzsch| series = |publisher = Allen lane|year=1982|isbn = 0-7139-15331}}
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| *{{cite book|title = The Physics of the Quark-Gluon Plasma: Introductory Lectures|edition = |author = S. Sarkar, H. Satz, B. Sinha|publisher = Springer|year=2009|isbn = 3642022855|url=http://books.google.co.uk/books?id=1WPV0NSenZ4C&pg=PA344&dq=gluon+field+strength+tensor&hl=en&sa=X&ei=TaXtUMa8H8jL0QWa3IHYCQ&ved=0CD4Q6AEwAQ#v=onepage&q=gluon%20field%20strength%20tensor&f=false}}
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| *{{cite book|title = Hadrons, Quarks and Gluons: Proceedings of the Hadronic Session of the Twenty-Second Rencontre de Moriond, Les Arcs-Savoie-France|edition = |author= J. Thanh Van Tran (editor)|publisher = Atlantica Séguier Frontières|year=1987|isbn = 2863320483|url=http://books.google.co.uk/books?id=Vo48UfeBaG4C&pg=PA615&dq=gluon+field+strength+tensor&hl=en&sa=X&ei=jaXtUPXdI6vO0AWUyICQAg&ved=0CEMQ6AEwAg#v=onepage&q=gluon%20field%20strength%20tensor&f=false}}
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| *{{cite book|title = Chiral Quark Dynamics|edition = |author= R. Alkofer, H. Reinhart|publisher = Springer|year=1995 |isbn = 3540601376|url=http://books.google.co.uk/books?id=fDENwIMAc50C&pg=PA7&dq=gluon+field+strength+tensor&hl=en&sa=X&ei=jaXtUPXdI6vO0AWUyICQAg&ved=0CE0Q6AEwBA#v=onepage&q=gluon%20field%20strength%20tensor&f=false}}
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| *{{cite book|title = Hadronic Production of ''ψ''(2S) Cross Section and Polarization|edition = |author= K. Chung|publisher = ProQuest|year=2008 |isbn = 0549597743|url=http://books.google.co.uk/books?id=ETrMNvqLrXUC&pg=PA2&dq=gluon+field+strength+tensor&hl=en&sa=X&ei=jaXtUPXdI6vO0AWUyICQAg&ved=0CFgQ6AEwBg#v=onepage&q=gluon%20field%20strength%20tensor&f=false}}
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| *{{cite book|title = Foundations of Perturbative QCD|edition = |author= J. Collins|publisher = Cambridge University Press|year=2011 |isbn = 0521855330|url= http://books.google.co.uk/books?id=0xGi1KW9vykC&pg=PA233&dq=gluon+field+strength+tensor&hl=en&sa=X&ei=kKjtULjaOIa-0QW4woGgBg&ved=0CFMQ6AEwBQ#v=onepage&q=gluon%20field%20strength%20tensor&f=false}}
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| *{{cite book|title = Standard Model of Particle Physics|edition = |author= W.N.A. Cottingham, D.A.A. Greenwood|publisher = Cambridge University Press|year=1998 |isbn = 0521588324|url= http://books.google.co.uk/books?id=XSseBp7y19MC&pg=PR16&dq=gluon+field+strength+tensor&hl=en&sa=X&ei=gantUO_cIuWd0QWp_4A4&ved=0CDMQ6AEwADgK#v=onepage&q=gluon%20field%20strength%20tensor&f=false}}
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| ====Selected papers====
| |
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| *{{cite news|title=QCD evolutions of twist-3 chirality-odd operators
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| |author=J.P. Maa, Q. Wang, G.P. Zhang
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| |year=2012
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| |location=Beijing, China
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| |publisher=Elsevier
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| |journal=Physics Letters B
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| |url=http://www.journals.elsevier.com/physics-letters-b
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| }}
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| *{{cite news|title=Field strength correlators in full QCD
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| |author=M. D’Elia, A. Di Giacomo, E. Meggiolaro
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| |year=1997
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| |location=Pisa, Italy
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| |publisher=
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| |journal=Physics Letters B
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| |arxiv = hep-lat/9705032
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| |url=http://arxiv.org/pdf/hep-lat/9705032v1.pdf
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| }}
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| *{{cite news|title=Gauge Invariant Field Strength Correlators In QCD
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| |author=A. Di Giacomo, M. D’elia, H. Panagopoulos, E. Meggiolaro
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| |year=1998
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| |location=Pisa (Italy), Nicosia (Cyprus), Heidelberg (Germany)
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| |publisher=
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| |journal=
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| |arxiv = hep-lat/9808056
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| |url=http://arxiv.org/pdf/hep-lat/9808056v2.pdf
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| }}
| |
| *{{cite news|title=A Virial Theorem for the Kinetic Energy of a Heavy Quark inside Hadrons
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| |author=M. Neubert
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| |year=1993
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| |location=Geneva (CERN), Switzerland
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| |publisher=
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| |journal=Physics Letters B
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| |arxiv = hep-ph/9311232
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| |url=http://arxiv.org/pdf/hep-ph/9311232v1.pdf
| |
| }}
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| *{{cite news|title=Field strength correlators and dual effective dynamics in QCD
| |
| |author=M. Neubert, N. Brambilla, H.G. Dosch, A. Vairo
| |
| |year=1998
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| |location=Washington, USA
| |
| |publisher=
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| |journal=Physical Review D
| |
| |arxiv = hep-ph/9311232
| |
| |doi=10.1103/PhysRevD.58.034010
| |
| |url=http://link.aps.org/doi/10.1103/PhysRevD.58.034010
| |
| }}
| |
| *{{cite news|title=Gluon field distribution between three infinitely spaced quarks
| |
| |author=V. Dzhunushaliev
| |
| |year=2011
| |
| |location=Eurasian National University
| |
| |publisher=
| |
| |journal=
| |
| |arxiv = 1101.5845v1
| |
| |url=http://arxiv.org/abs/1101.5845v1
| |
| }}
| |
| | |
| ==External links==
| |
| *{{cite news|title=QCD
| |
| |author=K. Ellis
| |
| |year=2005
| |
| |location=Fermilab, USA
| |
| |journal=
| |
| |url=http://theory.fnal.gov/people/ellis/Talks/FNAL/l1_s.pdf
| |
| }}
| |
| | |
| *{{cite web|accessdate=2013-10-17
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| |title=Chapter 2: The QCD Lagrangian
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| |location=Technische Universität München
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| |url=http://www.t39.ph.tum.de/T39_files/Lectures_files/StrongInteraction2011/QCDkap2.pdf}}
| |
| | |
| [[Category:Particle physics]]
| |
| [[Category:Quantum field theory]]
| |
| [[Category:Quantum chromodynamics]]
| |
It allows you to email to 3000 more members, bringing the total to 6000 every three days. Just obtain the HostGator 1 cent coupon and avail all of the services of a regular package at free of price for a month. Reseller hosting is for webmasters who wish to start their own profitable hosting company. However, he apparently out of duty will erase all your data. Your hostgator billing invoices in GatorBill will be generated five days ahead. We are currently hosting our software code and an offsite backup service to use, so this is a no brainer and easy issue to resolve was. Selecting a web-hosting provider from the virtual melting pot is a critical decision. Highest quality hosting obtainable plus 24/7 support services which will answer every one of your questions as fast as attainable and to top it off, they offer money-back guarantee. That's one hundred dollars, each month, every month, as long as they're happy with your service! In certain cases a dedicated server can offer fewer overhead and a larger revenue in investments.
They have always been very helpful and they have saved my site on numerous occasions. It's not a full time job but it certainly helps if your saving for a particular thing. It's all quite simple really, nothing technical at all. Currently, HostGator enjoys a loyal client population of approximately 10 million members across the globe. If you choose the reseller package, you can have as many websites as your heart desires and more than 1,000 domain names. Next create a new WordPress account. 7) Join a relevant promotion group - Especially for romance authors, there exist websites entirely for book promotion. This eventually turned to 85 with a logo in the Attracta tool engine.