Yang-mills Definition and 47 Threads

Can a single bivector field ##\mathcal{A}_\mu##, defined within a Clifford algebra framework, mediate the following four standard field equations using a covariant derivative ##D_\mu = \partial_\mu + [\mathcal{A}_\mu, \cdot]##? The standard equations are: \textbf{Yang-Mills Equation}: $$D_\mu...

For many years now, the theorist Nima Arkani-Hamed has lent his prestige and energy to a research program that aims to transform our understanding of quantum field theory, by using symmetries in the sums of Feynman diagrams to uncover perspectives on the theory not based in ordinary space-time...

It's given as ##T_{\mu \nu} = - \mathrm{tr}(F_{\mu \lambda} {F_{\nu}}^{\lambda} - \frac{1}{4} g_{\mu \nu} F_{\alpha \beta} F^{\alpha \beta})##. Can somebody explain the notation, i.e. what is the meaning here of the trace? (usually I would interpret the trace of a matrix as the number...

From: https://en.wikipedia.org/wiki/Axiomatic_quantum_field_theory But, that seems like a fairly abstract place to begin the kind of QFT construction that was asked of us by Witten in 2012: At the bottom of that page on axiomatic QFT are the "Euclidean CFT axioms": Are there any examples of...

Hi! So I have just been studying Yang-Mills theory advanced quantum field theory. In chapter 72 of Srednicki's book Quantum Field Theory they list the Feynman rules for non-abelian gauge theory. I was asked if I could show some sample allowed diagrams but I could not.. In standard particle...

While revising Yang-Mills theory, I have stumbled upon a certain problem, which I solved in a somewhat trivial way so I would like to check whether my reasoning is correct. Let's say we have a multicomponent matter field ##\{\phi^m(x)\}## which transforms according to some Lie group ##G## of...

Hello everyone, I am stuck in the derivation of the three gauge-boson-vertex in Yang-Mills theories. The relevant interaction term in the Lagrangian is$$\mathcal{L}_{YM} \supset g \,f^{ijk}A_{\mu}{}^{(j)} A_{\nu}{}^{(k)} \partial^{\mu} A^{\nu}{}^{(i)} $$ I have rewritten this term using...

I'm trying yo verify the relation \begin{equation} [D_{\mu},D_{\nu}]\Phi=F_{\mu\nu}\Phi, \end{equation} where the scalar field is valued in the lie algebra of a Yang-Mills theory. Here, \begin{equation} D_{\mu}=\partial_{\mu} + [A_{\mu},\Phi], \end{equation} and \begin{equation}...

I am sorry for asking this stupid question, but in the Yang-Mills lagrangian, there is a term ##Tr(F^{\mu \nu}F_{\mu \nu})##. Isn't ##F^{\mu \nu}F_{\mu \nu}## a number?

Hi all, I'm not certain if this is the correct section of the forum for this thread but I'm trying to understand ghosts and BRST symmetry and my starting point is chapter 16 of Peskin and Schroeder where I've found a nagging issue. My issue is regarding the derivation of equation (16.6) on...

Hello Everyone. I Was Wondering how excatly the Gauge invariance of the trace of the Energy-momentum tensor in Yang-Mills theory connects with the trace of an Holonomy. To be precise in what I'm asking: The Yang-Mills Tensor is defined as: $$F_{\mu \nu} (x) = \partial_{\mu} B_{\nu}(x)-...

Does someone know which episode from Sliders did they mention Yang-Mills? I want to watch this episode for nostalgia sake. If you want to move this post to other subforum then it's fine by me. Cheers!

Let us consider a classical field theory with gauge fields ##A_{\mu}^{a}## and a scalar ##\phi^{a}## such that the Lagrangian is gauge-invariant under the transformation of 1. the gauge fields ##A_{\mu}^{a}## in the adjoint representation, with dimension ##D_{\bf R}##, of the gauge group...

The Yang-MIlls Lagrangian is given by ##\mathcal{L}_{\text{gauge}} = F_{\mu\nu}^{a}F^{\mu\nu a} + j_{\mu}^{a}A^{\mu a}.## We can rescale ##A_{\mu}^{a} \to \frac{1}{g}A_{\mu}^{a}## and then we have ##\frac{1}{g^{2}}F_{\mu\nu}^{a}F^{\mu\nu a}.## How does the second term change? Does the...

I was wondering since the Vector supermultiplet in N=2 SUSY can be built from a Chiral and a Vector supermultiplet from N=1, in order to make up the off-shell degrees of freedom, would you include the two auxiliary fields from the N=1 theory (traditionally F from the Chiral and D from the vector...

I was thinking about hadrons in general Yang-Mills theory and I have some doubts that I'd like to discuss with you. Suppose that we have a Yang-Mills theory that, like QCD, tend to bind quarks into color singlet states. So far nothing strange, even QED tend to bind electromagnetic charges to...

What is the difference between Yang-Mills and QED theories? Yukawa and QCD? specially in terms of the lagrangians. I really want to get into this subject with a previously first sight.

Hi! I'm trying to show that the differential from equation $$D \star F = 0$$ transform homogeneously under the adjoint action ##F \mapsto gFg^{-1}## of the lie group ##G##, where ##D## denotes the covariant exterior derivative ##D\alpha = d \alpha + A \wedge \alpha## for some lie algebra valued...

I remember hearing this, but not sure if it's true.

I have been teaching myself QFT and General Relativity. The mathematics of those fields is daunting, and I find that what I have come across is very difficult to master. Of course it will take work, but can someone recommend a good text for self-leaning differential geometry with application...

What exactly is a Yang-Mills Theory? Is it a general theory, based on SU(N) symmetry, which can then be applied for particular cases (ElectroWeak, Chromodynamics) ? Is it like a general mathematical model of gauge theory ?

I've come across countless sources that gauge fix SU(N) Yang-Mills fields using the typical U(1) gauges (e.g. Lorenz gauge, coulomb gauge, temporal gauge, etc). However, I can't find a single one where they prove that this gauge fixing is valid for all field configurations... I've tried to...

Hello all, my teacher assigned a problem related to the yang-mills equation in my general relativity class and I just wanted to ask a couple of questions about this problem. I believe it is a simplified version of the Yang-Mills you encounter in particle physics. Basicly assuming that...

In reading Ryder's book on quantum field theory he advocates reading off the Feynman rules directly from the Lagrangian in the path integral quantization method. I can sort of do this in phi-four theory, but it is not obvious in for example Yang-Mills theory, so I wondered if someone could...

Hi. I'm reading about non-abelian theories and have thus far an understanding that a gauge invariant Lagrangian is something to strive for. I previously thought that the Yang-Mills gauge boson free field term ##-1/4 F^2 ## was gauge invariant, but now after realizing that the field strength...

I've been doing some self-study in Peskin and Schroeder and been struggling a bit in Part III. Right now, I am stuck on the last two terms in 16.6 (Lagrangian for Yang-Mills). Presumably these come from (-1/4) (F^{a}_{\mu\nu})^2, but I am getting stuck on getting the indices to work out...

What are the consequences of a possible solution to Yang-Mills existence and mass gap problem? Are the consequences only physical or they will also have applications to other branches of science or life? If yes, what are they?

Homework Statement 1. Derive the Yang-Mills-Higgs equations of motion (D_{v}F^{\mu, v})^{a} = - \epsilon^{abc}\phi^{b}(D^{\mu}\phi)^{c} and (D_{\mu}D^{\mu}\phi)^{a} = - c(|\phi|^{2} - v^{2}) \phi^{a} from \mathcal{L} = - \frac{1}{4} F^{a}_{\mu v}F^{\mu v a} +...

By "physical particle" I mean color-singlet particles which have asymptotic T=\pm \infty states. How many stable particles exist in the theory? Only one? SU(2), SU(3), and SU(N) gauge groups can all be discussed.

http://arxiv.org/abs/1106.2121 Abstract: Gravitational and electroweak interactions can be unified in analogy with the unification in the Weinberg-Salam theory. The Yang-Mills framework is generalized to include space-time translational group T(4), whose generators $T_{\mu}(=\p/\p x^{\mu})$...

Just to review a little bit: In general, for a gauge field with Yang-Mills Lagrangian \mathcal L=-\frac{1}{4}F^{c}_{\mu \nu}F^{c \mu \nu} for each c it is impossible to find the resulting free Green's function G(k) in momentum space: (g^{\mu \nu}k^2-k^{\mu}k^{\nu})G_{\nu...

Here and there some rumors come out about this relevant problem. I have read the following article in Wikipedia http://en.wikipedia.org/wiki/Yang–Mills_existence_and_mass_gap and the talk page http://en.wikipedia.org/wiki/Talk:Yang–Mills_existence_and_mass_gap but people cited there...

Right, so in Yang-Mills theory, the vector potential is modified from: F = dA To: F = dA + A\wedge A However, it is my understanding that the exterior/wedge product is anticommutitive, so that for a given exterior algebra over a vector space, V: \omega \wedge \omega = 0, \forall...

Hello, suppose you start with Yang Mills theory with some gauge group G, for example SU(5). Then you turn on a gauge bundle, say a U(1) bundle, and the group breaks down. I know that from hearsay but I wonder how would you describe that explicitly in formulas? meha

When N=1, is the superspace formulation of 10D SYM the same as the 4D SYM, except the differences of the coefficient and gamma matrices? For the extended SUSY in 10D, are the superspace formulation available for N=2, 4? How about N=8, 16, and 32? Thanks for any tips you may tell me.

Even though classical (as opposed to quantized) non-abelian gauge theories do not have any physical applications at this time, it is mathematically valid to say that these classical Yang-Mills fields generalize Maxwell's equations of E&M in some sense i.e. the Yang-Mills equations reduce to the...

Since it appears (so far) I am infringing no rule, here is another shameless copy/paste of a thread I started on another forum, where I didn't get too much help - rather, folk tried, but confused me even further! See if you guys can do better. (Note:I am not a physicist) The mathematics here...

In developing the Yang-Mills Lagrangian, Wikipedia defines the covariant derivative as \ D_ \mu = \partial _\mu + A _\mu (x) . Is A_mu to be taken as a 1-form, so that \ D _\mu \Phi = \partial _\mu \Phi + A _\mu (x) or an operator on \Phi, such that \ D _\mu \Phi = \partial...

I was aware that this theory can be solved exactly and is trivial, i.e. there is no dynamics. I was also convinced that this result is due to 't Hooft. Could you confirm this view and put out some relevant refs about? Thanks beforehand. Jon

Why a magnetic current obviously must be C- parity odd in the (exact) SU(2) theory? (C^{-1} J_M C=-J_M). Best regard. Leonid

I was wondering why for [tex] F_{\mu \nu} = [D_{\mu},D_{\nu}] = \partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}+[A_{\mu},A_{\nu}] [\tex] the term [tex] A_{\mu}\partial_{\nu} - A_{\nu}\partial_{\mu} [\tex] vanishes.

From Trees to Loops and Back Andreas Brandhuber, Bill Spence, Gabriele Travaglini 49 pages, 17 figures http://www.arxiv.org/abs/hep-th/0510253 We argue that generic one-loop scattering amplitudes in supersymmetric Yang-Mills theories can be computed equivalently with MHV diagrams or with...

Can someone give me some references on Yang-Mills theories formulated with light-cone coordinates? (preferably on-line) Thank you very much in advance.

Could someone rephrase in a short and casual manner the famous Millenium Problem of the Clay Math institute ? http://www.claymath.org/millennium/Yang-Mills_Theory/ Thank you for help !

What in simple terms is a Yang-Mills field? What has it got to do with the standard model of particle physics and why are all particles in the standard model massless - is this something to do with getting the standard model to be consistent with the Higgs field? Do we need the standard...

(1) Is it true that when a pair of particles is created from a Photon, that the Photon Energy (h x nu) is equal to 2(msub0)c^2 ? If say an electron and positron are created does the photon Energy equal (at least) twice the mass of one electron 2(9.109 x 10^-31 kg)times c^2? (2) Could anyone...

In what way is the Yang-Mills theory a mathematical problem? Because this problem was one of the 7 millennium problems on the Clay Mathematica Institute.