Gauge Definition and 641 Threads

I think the story where abelian, i.e. U(1), gauge symmetry comes from is pretty straight-forward: We describe massless spin 1 particles, which have only two physical degrees of freedom, with a spin 1 field, which is represented by a four-vector. This four-vector has 4 entries and therefore too...

Hi there, I have just read that the gauge field term Fμν is proportional to the commutator of covariant derivatives [Dμ,Dν]. However, when I try to calculate this commatator, taking the symmetry group to be U(1), I get the following: \left[ { D }_{ \mu },{ D }_{ \nu } \right] =\left( {...

This is an interesting question that popped through my mind. Some of us should know what is meant by „gauge transformations”, „gauge invariance/symmetry” and are used to seeing these terms whenever lectures on quantum field theory are read. But the electromagnetic field in vacuum (described in a...

I've been studying TQFT and gauge theory. Dijkgraaf-Witten theory in particular. One learns that a topological field theory applied to a manifold outputs the number of principal G bundles of a manifold. My question is for the Physicists in the room, why do you want to know the number of...

My aim is to derive the photon propagator in an Coulomb gauge following Pokorski's book method. In this book the photon propagator in Lorenz gauge was obtained as follows: 1. Lorenz gauge: ##\partial_{\mu}A^{\mu}=0## 2. It's proved that ##\delta_{\mu}A^{\mu}_T=0##, where...

My aim is to derive the photon propagator in an Coulomb gauge following Pokorski's book method. In this book the photon propagator in Lorenz gauge was obtained as follows: Lorenz gauge: ##\partial_{\mu}A^{\mu}=0## It's proved that ##\delta_{\mu}A^{\mu}_T=0##, where...

2 sets of 6x LED strips, each 12v 8.1a 97.2W, powered by a single cv 240W PSU, in parallel. The 2 sets are split at the PSU end, each set getting 120W separately. Schematic below, What I don't know is what gauge wire to use at points A and B? Can you please explain what should be used and why...

Hello, I was reading about the Higgs mechanism and I must say that I did not really follow the argument of how the gauge symmetry is broken. I think that my problem has to do with the more general question of how does a gauge symmetry get broken in general? Thanks!

Hi all. I am new to this site and I would like to verify the following calculation. Is it correct to do it this way? Please advise. Thanks. Hydraulic Press: 15 tons (Enerpac RC1510) Gauge Max Pressure: 10000 psi Actual Gauge Reading: 2500 psi Actual pressure (tons) = (2500/10000) X 15 tons =...

The Higgs boson can be thought of as mediating a "fifth force" that is not a gauge force but a Yukawa interaction. What is the main difference between Yukawa and gauge interaction?

Can someone explain to me (or point me towards a source) how is the Lorenz Gauge derived? I am reading the Griffiths book and from what I understand we can do the transformation ##A' = A + \nabla \lambda## and at the same time ##V' = V - \frac{\partial \lambda}{\partial t}## and B and E remain...

Hi everyone, So I recently read a chapter in a math book that vaguely describe how connections on bundles occur in particle physics, but they are very cryptic about the physics part and I just want to know a little bit more about it. So I'll tell you what I read and then follow up with some...

Consider the following paragraph taken from page 15 of Thomas Hartman's lecture notes (http://www.hartmanhep.net/topics2015/) on Quantum Gravity: In gravity, local diffeomorphisms are gauge symmetries. They are redundancies. This means that local correlation functions like ##\langle...

Consider the following paragraph taken from page 15 of Thomas Hartman's lecture notes (http://www.hartmanhep.net/topics2015/) on Quantum Gravity: In an ordinary quantum field theory without gravity, in flat spacetime, there two types of physical observables that we most often talk about are...

In the framework of Einstein-Yang-Mills (EYM) theory, suppose the following action: \begin{equation}S=\int\left({\kappa R + \alpha tr(F_{\mu \nu}F^{\mu \nu})d^4 x}\right)\,,\end{equation} where F is the gauge curvature associated with a non-abelian Lie group G and a gauge connection A. Then...

1. Problem ##g_{uv}'=g_{uv}+\nabla_v C_u+\nabla_u C_v## If ##g_{uv}' ## is given by ##ds^2=dx^2+2\epsilon f'(y) dx dy + dy^2## And ##g_{uv}## is given by ##ds^2=dx^2+dy^2##, Show that ## C_u=2\epsilon(f(y),0)##? Homework Equations Since we are in flatspace we have ##g_{uv}'=g_{uv}+\partial_v...

Lightcone gauge is ##X^u=\tau=1/\sqrt{2}(X^0+X^{D-1})## (1) The mode expansions are: My book says 'it is possible to solve for one of the oscillators in terms of all the others' with this relation. What is a oscillator? Is this any of the ##X^{D}## coordinates, what exactly does ##n##...

In Yang-Mills theory, the gauge transformations $$\psi \to (1 \pm i\theta^{a}T^{a}_{\bf R})\psi$$ and $$A^{a}_{\mu} \to A_{\mu}^{a} \pm \partial_{\mu}\theta^{a} \pm f^{abc}A_{\mu}^{b}\theta^{c}$$ induce the gauge transformation$$F_{\mu\nu}^{a} \to F_{\mu\nu}^{a} -...

In some Yang-Mills theory with gauge group ##G##, the gauge fields ##A_{\mu}^{a}## transform as $$A_{\mu}^{a} \to A_{\mu}^{a} \pm \partial_{\mu}\theta^{a} \pm f^{abc}A_{\mu}^{b}\theta^{c}$$ $$A_{\mu}^{a} \to A_{\mu}^{a} \pm...

Consider the following facts: 1. For a particle with momentum ##k##, the two transverse polarization vectors ##\epsilon({\bf k}, \lambda_{1})## and ##\epsilon({\bf k}, \lambda_{1})## are purely spatial and orthogonal to ##\bf k##, that is, ##\epsilon^{0}({\bf k}, \lambda_{1}) = 0,##...

Usually, one defines large gauge transformations as those elements of ##SU(2)## that can't be smoothly transformed to the identity transformation. The group ##SU(2)## is simply connected and thus I'm wondering why there are transformations that are not connected to the identity. (Another way to...

The coupling of the Higgs boson to the electroweak gauge bosons in the Standard model is given by $$\mathcal{L}_{\text{H-g}} = - \left( \frac{H}{v} + \frac{H^{2}}{2v^{2}} \right) \left(2M_{W}^{2}W_{\mu}^{+}W^{-\mu} + M_{Z}^{2}Z_{\mu}Z^{\mu} \right).$$ However, in Cliff Burgess' textbook 'The...

The mantra in theoretical physics is that global gauge transformations are physical symmetries of a theory, whereas local gauge transformations are simply redundancies (representing redundant degrees of freedom (dof)) of a theory. My question is, what distinguishes them (other than being...

Hi, I read in a QFT book that the free massive vector boson Lagrangian is ## \mathcal{L}_W = - \frac{1}{4} (\partial_\mu W^\dagger_\nu - \partial_\nu W_\mu^\dagger ) (\partial^\mu W^\nu - \partial^\nu W^\mu ) + M^2_W W^\dagger_\mu W^\mu ## gives the propagator in momentum space by: ## i...

Hello! I will be attending a course on condensed matter physics with emphasis on geometrical phases and I was wondering if the are any good books on gauge transformations, gauge symmetry and geometrical phases that you know of. Thanks in advance!

The lagrangian of a non interacting quark is made to be invariant under local SU(3) transformations by introduction of a new field, the gauge field, giving rise to the gluon. This gives us a locally gauge invariant lagrangian for the quark field and together with the construction of a locally...

Consider the following Lagrangian: ##YHLN_{1}^{c} + Y^{c}H^{\dagger}L^{c}N_{1} + \text {h.c.},## where ##L=(N_{0}, E')## and ##L^{c} = (E^{'c}, N_{0}^{c})## are a pair of ##SU (2)## doublets and ##N_{1}## and ##N_{1}^{c}## are a pair of neutral Majorana fermions...

Homework Statement A barrel contains 0.130-m layer of oil floating on water that is 0.290 m deep. The density of the oil is 610 kg/m3 What is the gauge pressure at the bottom of the barrel? Homework Equations P [/B]= ρ(g)(h) The Attempt at a Solution I found the pressure of the oil which...

Do a particle influence another particle by exchange of gauge bosons? If so, how?

Homework Statement I need to gauge the symmetry: \phi \rightarrow \phi + a(x) for the Lagrangian: L=\partial_\mu\phi\partial^\mu\phi Homework EquationsThe Attempt at a Solution We did this in class for the Dirac equation with a phase transformation and I understood the method, but...

Hi, is correct to say that there is no interaction between four photons because the gauge group of QED is U (1) while there are interactions of four gluons or four W's because the gauge group of QCD is SU (3) and EW's one is SU (2) xU (1)? I know that the interaction between four photons is not...

I know that, in the presence of a magnetic field, the momentum of a charge particle changes from ##p_{i}## to ##\pi_{i}\equiv p_{i}+eA_{i}##, where ##e## is the charge of the particle. I was wondering if this definition of momentum is gauge-invariant? How about ##\tilde{\pi}_{i}=p_{i}-eA_{i}##?

In QCD, quark is in fundamental representation of SU(3) and thus it has to have 3 charges (what we came to call "colors"). Gauge bosons are in adjoint representation and there are 8 of them. The choice how to assign color charges to them is not unique, one popular choice is based on Gell-Mann...

Consider the covariant derivative ##D_{\mu}=\partial_{\mu}+ieA_{\mu}## of scalar QED. I understand that ##D_{\mu}\phi## is invariant under the simultaneous phase rotation ##\phi \rightarrow e^{i\Lambda}\phi## of the field ##\phi## and the gauge transformation ##A_{\mu}\rightarrow...

What would be the ramifications of discovering that a) dark matter radiates something non-electromagnetic, and that b) this radiation always travels at a constant velocity according to all inertial reference frames, but c) this constant velocity is equal to, say, c times pi?

Hello, friends! My textbook, Gettys's Physics, says that the Lorenz gauge choice uses the magnetic vector potential $$\mathbf{A}(\mathbf{x},t):=\frac{\mu_0}{4\pi}\int \frac{\mathbf{J}(\mathbf{y},t-c^{-1}\|\mathbf{x}-\mathbf{y}\|)}{\|\mathbf{x}-\mathbf{y}\|}d^3y $$and the electric potential...

The common presentation for free field quantization proceeds with the Lorentz and Coulomb (##\phi = 0, \,\nabla \cdot \mathbf{A} = 0 ##) constraints. Then ##A## can be defined $$\mathbf{A} \propto \iint \frac{d^3 p}{\sqrt{2\omega_p}}\sum_{\lambda} \Big(e^{i\mathbf{p}\cdot...

Hi How can I measure, shaft power (watts or HP) of a vertical turbine using dead weight blocks Turbine diameter - 18 inches RPM - 450 ( Zero Load)

haushofer submitted a new PF Insights post General Relativity as a Gauge Theory Continue reading the Original PF Insights Post.

Based on this lecture notes http://www.helsinki.fi/~hkurkisu/CosPer.pdf For a given coordinate system in the background spacetime, there are many possible coordinate systems in the perturbed spacetime, all close to each other, that we could use. As indicated in figure 2, the coordinate system...

Hi, I have a question that has been bugging me recently. It's about the berry phase and something that I find contradictory. One can see that it is possible to get rid of 2π x (integer) part of the Berry phase by means of a gauge transformation. This in general applies to phases (gauge...

In gauge theories, the counterterms in the equation to balance the gauge freedom (like the phase in electrodynamics) produce the forces of nature. In GR.. what is the equivalent of the counterterms and what is the equivalent of the phase or isospins freedom in electroweak)?

Homework Statement Hi Physics gurus, this question was in my Chem Eng exam, and I can't agree with my lecturer's answer. He makes a LOT of mistakes, so it's hard to know when he's being clever or reallllly dumb. The question I have issue with is: "Is the pressure a manometric or an absolute...

I'm reading the ## \frac 1 N ## chapter of Sidney Coleman's "Aspects of Symmetry". Equation 3.5, gives the gluon propagator as below: ## A^a_{\mu b}(x)A^c_{\nu d}(y)=\left( \delta^a_d \delta^c_b-\frac 1 N \delta^a_b \delta^c_d \right) D_{\mu \nu}(x-y)##. Then he explains that the term...

Dear all I have a question is the dual of the field strength ( of abelian gauge theory) in 3 dimensional space the same as the gauge field? I have a formula for the dual field strength and am trying to bring that of gauge field! Thank you

Hello! Can someone explain to me what exactly a local gauge invariance is? I am reading my first particle physics book and it seems that putting this local gauge invariance to different lagrangians you obtain most of the standard model. The math makes sense to me, I just don't see what is the...

Dear all I am trying to prove that the action resulting from studying conformal gauge theory is invariant under SO(2,4)*diff. Can anyone give me a hint to start from thank. I considering several papers: E.A.Ivanov and J.Niederie and others...

It has been sometime since I have been thinking about this question and I have been quite successful in confusing myself. In Einstein's General Relativity, we say that the general coordinate transformations (or diffeomorphisms) on a manifold are the gauge transformations of the theory. The local...

micromass submitted a new PF Insights post Omissions in Mathematics Education: Gauge Integration Continue reading the Original PF Insights Post.

I am looking for guidance on how to successfully measure vacuum using a device similar to a pirani gauge, my device however is a tungsten filament which is heated electrically to about 90*C, and it's current draw is a measure of vacuum.The problem I am having is how to relate specifically the...