Gauge Definition and 685 Threads

hi~I am a beginner of Gauge theories,and I have some questions~ Why we need loacal phase invariance? Because i cannot understand why we assume phase depend on the position.Is there any theory leading to this asssumption?

Homework Statement Water flows at 0.25 L/s through a 9.0-m-long garden hose 2.0 cm in diameter that is lying flat on the ground. The temperature of the water is 20 ∘C. What is the gauge pressure of the water where it enters the hose? Side question: does the velocity of the water flow need to...

I have questions regarding the 24 gauge bosons of the SU(5) model. I keep seeing this matrix popping up in the documents I'm reading with no real explanation of why: First of all I'm wondering how this is constructed, which means I'm wondering what the V_{\mu}^{a} look like (I already have...

Hi! One of our professors told us once that in solving problems, always use absolute pressure in the computations. Then one time, I was solving some problems from Dr. Felder's Principles of Chemical Processes book, I often noticed that the pressures used in computations were not always in...

I know that we have a free parameter in the relativistic potential for electromagnetism. I also know that we can introduce this as a scalar field ψ which gives this free parameter. I understand that this can be related to U(1) by mapping ψ: ---> e^iψ, which is the U(1) group. It just seems a...

By fixing a gauge (thus breaking orspending the gauge symmetry), the model becomes something easier to analyse mathematically, such as a system of partial differential equations (in classical gauge theories) or a perturbative quantum field theory (in quantum gauge theories), though the...

I want to understand the 'vertex factor' of 3-bosons field and 4-bosons field but get confused. (I know the lagrangian and have computed the interaction vertices already) only need to understand the vertex factor. In other words, I want to learn how 3-boson vertex and 4-boson vertex are...

When we start by postulating local SU(2) gauge invariance for our weak isospin doublets \begin{align} \psi &= \begin{pmatrix} \nu_{e} \\ e^{-} \end{pmatrix}_{L} \end{align} etc., we have to introduce massless gauge fields to preserve the Lagrangian's invariance. For SU(2) this demands 3...

I hope someone with a deep conceptual understanding of terminologies would help me out here. I am having starting problems in understanding the approach of gauge theories. I have read suggested threads and I am still at a loss. I am an experimental physicist and know basics of electrodynamics...

Electromagnetism: Multivalued potential voltage? It's been my understanding that specifying the electric and magnetic potential at all points in a system determines the electric and magnetic fields--and more, that we can fix a particular gauge, and it all still works. Perhaps I've been naive...

Homework Statement Homework Equations Please see below. The Attempt at a Solution No idea about part (a). Trying to work out part (b), I asked my tutor and he said: I think it's this. We have the Dirac Equation $$\left ( i \hbar \gamma ^{\mu } \partial_{\mu }-mc\right )\Psi =0$$ but for a...

I recently learned that with (local) gauge invariance, functional quantization needs to factor out volume factor(Faddeev-Popov procedure). Why does this has to be done?Just to remove infinity? As far as I am concerned, ##\phi^4## theory contains invariance(for example ##\phi\to\phi\cdot e^{i...

Gauge transformation can be written as: ##\psi(\vec{r},t)\rightarrow e^{-i \frac{e}{\hbar c}f(\vec{r},t)}\psi(\vec{r},t)## http://quantummechanics.ucsd.edu/ph130a/130_notes/node296.html Does it have any sense that we choose such function ##f##, that all right side is constant in time. Is this...

Why is ##\bar{\psi}=e^{i\theta}\psi##, where ##\theta## is a real number, used as the global gauge transformation? Why ##e^{i \theta}##; what's the physical significance or benefit? Why is ##\bar{\psi} = e^{i \theta(x)} \psi## the local gauge transformation? What does ##\theta## being a...

Hello All May i ask a question? Could anyone give me a paper or a book that allows me to understand Gauge formalism from A-Z? I already have some ideas but i want more details. Thank you

It's well known when if we are working on problems related to particles in presence of an electromanetic field, the way we state the problem can be done using the next Hamiltonian: H=\dfrac{(p-\frac{e}{c}A)^2}{2m} +e \phi where the only condition for A is: \vec{\nabla } \times \vec{A} =\vec{B}...

It's well known when if we are working on problems related to particles in presence of an electromanetic field, the way we state the problem can be done using the next Hamiltonian: H=\dfrac{(p-\frac{e}{c}A)^2}{2m} +e \phi where the only condition for A is: \vec{\nabla } \times \vec{A} =\vec{B}...

Hello everyone, I'm trying to write down a Lagrangian invariant under local ISO(3) (rotations+shifts) transformations. I'm working at classical level and there will be no quantization of any kind so the theory shouldn't have any ghost pathology. However, I found that, out of the 6 gauge fields...

Hello everyone. Does anyone know if it is possible to build a gauge theory with a local ISO(3) symmetry (say a Yang-Mills theory)? By ISO(3) I mean the group composed by three-dimensional rotations and translations, i.e. if ##\phi^I## are three scalars, I'm looking for a symmetry under: $$...

Homework Statement [/B] The Lagrangian ##\mathcal{L}\frac{1}{2}(\partial_\mu\phi^\nu)^2+\frac{1}{2}(\partial_\mu\phi^\mu)^2+\frac{m^2}{2}(\phi_\mu\phi^\mu)^2## for the vector field ##\phi^\mu## is not invariant with respect to the gauge transformation ##\phi^\mu\rightarrow...

Hello, I was wondering if anyone can help me out with this one. I am installing a 350 ohm strain gauge as shown in attached figure. I am expecting to see 350ohm value between terminal 1 and 2. I have checked the values for the following terminals. 1) 5 & 6 = 350ohm (PASS) 2) 3 & 4= 350ohm...

Using R = ρL/A, I am trying to get this formula, which is the change in resistance due to change in length, area, and resistivity. ΔR = (∂R/∂L)ΔL + (∂R/∂A)ΔA + (∂R/∂ρ)Δρ I understand the above conceptually, but I am confused about why we are multiplying by terms ΔL, ΔA, and Δρ. Intuitively, I...

Why must the gauge group be in a complex representation so that chirality of the fermions is respected? thanks

Do all forces of nature have to support gauge symmetry? Are there none gauge forces? Or what if there is a force but it is not gauge.. then what do you call it? For example. The quantum vacuum are very complex thing and can act like medium where other forces may propagate, what principles...

Hey guys, So I have a question about the gauge invariance of the weak field approximation. So if I write the approximation as \Box h^{\mu\nu} -\partial_{\alpha}(\partial^{\mu}h^{\nu\alpha}+\partial^{\nu}h^{\mu\alpha})+\partial^{\mu}\partial^{\nu}h=0 then this is invariant under the gauge...

Refering to this paper "Theoretical Aspects of Massive Gravity" (http://arxiv.org/abs/1105.3735) about the spin-2 boson field and GR. The author uses the Fierz-Pauli action ( I quote the massless part) ##-\frac{1}{2}\partial_\lambda h_{\mu\nu}\partial^\lambda h^{\mu\nu} + \partial_\mu...

My book says that in this case $$e^+e^- \rightarrow \gamma \gamma $$ gauge invariance requires that $$k_{1\nu}(A^{\mu\nu} + \tilde{A}^{\mu\nu})=0=k_{2\mu}(A^{\mu\nu} + \tilde{A}^{\mu\nu})$$ Please see attachment. My question is how does this statement hold?

Homework Statement Given your average Wheatstone Bridge with R1 R2 and R3 unknown resistor values and R4=RG= strain gauge, how to solve for the resistor values given only input voltage and the value of the resistances between the resistors?[/B]Homework Equations Not Sure[/B]The Attempt at a...

Homework Statement I want to built a simple ultrasonic thickness gauge for my final project. I have already search in google about that simple electronic circuit but i can't found it and also i have already looking for tutorial video in youtube about how to built simple ultrasonic...

Homework Statement Approximately how deep into water must a diver dive to reach the point where the gauge pressure is 1 atm. (1 atm = 1.013 x 10^5 N/m^2) (assume fresh water) Homework Equations gauge pressure = pgd density of fresh water p = 1 kg/m^3 The Attempt at a Solution pgd = (1...

I was trying to prove all those little things you spend long as the local invariance in the free Lagrangian of electroweak interaction. Taking into account the appropriate SU(2) transformations (without covariant derivatives), came to the following expression \mathcal{L}_{\text{ferm.}} =...

Hi folks -- it is my understanding that only non-Abelian gauge theories can be asymptotically free. But can anyone provide me with a canonical reference showing that such symmetries can be dynamically broken and still retain that status? I gather that this is the case (from reading the...

A twisted cylindrial rod has the cross sectional symmetry so that it's not posible to tell whether it is twisted or not without knowing if there is any torsional energy. now drawing a line on the surface of it can tell us whether or not it's twisted. It might not be a straight line.. there are...

Is there any significance to the fact that: The electromagnetic and strong interactions have gauge bosons with no electric charge that are massless; and The weak interaction has two massive gauge bosons which do have electric charge. If there is a significance to this 'observation' then where...

Lets take QED just to simplify. When we are doing Path Integrals and we want to "fix the Gauge": 1 we add in the integral a delta(F) -meaning that we are going to integrate only in one representative of each class of equivalent configuration- 2 We take some factors out because they are constant...

Homework Statement Demonstrate the equivalence between the gauge fields A1=(0,bx,0) and A2=)-yB/2,xB/2,0) and find the scalar field Φ for which A1= A2 + ∇ΦHomework Equations B = ∇XA The Attempt at a Solution The first part is fine, you just plug it into the above relevant equation and you get...

I was walking around at work today to find an AC amp Gauge on a DC breaker (1000KW, 250 VDC), Which made me scratch my head if there is any difference between the two gauges for this application? Any idea? Thanks.

See the passage attached below. Consider the 1-loop vertex correction (c.f. p.2 of http://bolvan.ph.utexas.edu/~vadim/classes/2012f/vertex.pdf) and vacuum polarization diagrams in QED. A very simple UV regulator that makes the integrals for the amplitude very simple is the prescription that we...

I've seen explanations that when a neutrino with a W+ Boson comes near a neutron, it affects one of the bottom quarks and changes it to a up quark which effectively turns the neutron into a proton. The neutrino then turns into an electron. Source: (2:20 onwards) I've seen other explanations...

Can some one explain what are the so called "large gauge transformations" and where do they play important role in physics? Explanations with less mathematical rigor will be greatly appreciated.

Hello Community! I can't find a good answer(if there is) to my question. When in statistical mechanics we can define the order parameter for to study some phase transition. we need to define a order parameter. Now, I want to know if we can to define/find some "order parameter" for to...

Anyone can help me how to argue that interaction lagrangian is invariant under gauge transformation?

Hello, I'm trying to design a strain gauge load cell for force measurments. I have few questions regarding that. Q1: how to calculate the minimum froce that my load cell can detect? Q2: how to calculate the FSO(full scale output) of my load cell? Q3: Is there any way to measure the...

Hello, I would like to know, how to calculate the number of grid lines( or loops) in a strain gauge. I'm trying to calculate the output form the each grid lines. Thanks in advance

In the presence of a magnetic field with vector potential \vec A and an electric field, the Schrodinger equation for a charged particle with charge q and mass m becomes: \frac{1}{2m} (\frac{\hbar}{i} \vec \nabla-q\vec A)^2 \psi =(E-q \phi)\psi Another fact is that, Schrodinger equation...

Hi folks -- does anyone know of a good survey article on the topic of whether local gauge invariance is a requirement of a fundamental theory within QFT -- hence of an asymptotically safe theory? I only have a few scattered remarks to this effect (by F. Wilczek mostly), so any good...

I have a question about this classical invariance problem I'm working on. I'm almost done, and I understand the theory I think, so my question may seem a bit more math-oriented (it's been a few years since crunching equations). I have found that under a gauge transformation for a single particle...

Well I'm trying to understand the difference between these propagators: \frac{g_{\mu \nu}}{k^{2} - m^2 + i \epsilon} and \frac{g_{\mu \nu}+ \frac{ k_{\mu} k_{\nu}}{m^{2}}}{k^{2} - m^2 + i \epsilon} My professor told me that they are different gauges, and the from the second you rule out...

Do gauge fields work the same way as the Higgs field? Are gauge fields all encompassing too, like the Higgs field? What are the differences between the functioning of gauge fields and Higgs field?

I have a problem concerning gauge invariance in QM. QM should be invariant of electromagnetic gauge. However, the following two physically equivalent vector potential: 1. A = (-\frac{1}{2}By, \frac{1}{2}Bx, 0 ) 2. A = (-By, 0 , 0 ) generates the following hamitonian: 1. H =...