Gauge Definition and 685 Threads

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...

I've looked everywhere and I haven't found an explanation of why is it useful to introduce gauge conditions. I've also searched in this forum, and none of the existing threads I've read answered my question. I apologize if there is and I have failed to find it. My problem is that, as I see it...

When the cathode emits electrons which are accelerated towards the grid, usually on its way it will ionise a molecule in the vacuum. However at a certain low pressure there are too few molecules and therefore the electron will hit the grid and emit an x-ray. My question is, wouldn't electrons...

All we know the usual stress strain diagram obtained from tensile test from universal testing machine. As modulus of elasticity is material property that means till proportional limit slope will not change. As it is not a force vs elongation curve that means there will be no re-scaling to be...

Homework Statement objects A and b are submerged at a depth of 1m in a liquid with a specific gravity of 0.877. Given that the density of object B is one third that of Object A and that the gauge pressure of object A is 3atm, what is the gauge pressure of object B? assume atmospheric pressure...

Homework Statement For a gauge function G(t,q) where , does or have any alternative form or can they be expressed in any other way? Homework EquationsThe Attempt at a Solution

Well, I'm planning to learn from this book when i finish Shankar's Principles of Quantum Mechanics, if it fulfills the requiriments in this part, but from where i can learn the Special Relativity necessary to tackle this book?

Homework Statement A barrel contains a 0.110 m layer of oil and a density of 690 kg/m3 floating on water that is 0.300 m deep. What is the pressure at the bottom of the barrel? Homework EquationsThe Attempt at a Solution Poil + Pwater = Ptotal My question is why am I using this formula? I...

Hey I've built a speaker and the cone is about 20cm in diameter. I need help choosing the wire gauge for the voice coil though. When I look at this chart http://www.powerstream.com/Wire_Size.htm I can't really see anything that will work. My stereo puts out 50W and if I want the resistance to be...

Homework Statement We wish to make a precipitation meter shaped like a paraboloid ##z = x^2 + y^2, 0 \leq z \leq 10##. Devise a scale on the z-axis that tells you the amount of precipitation in cm. In other words, at what height ##z = h## is the surface of water in the dish when there has been...

Due to its form, gauge transformations for the typical electrodynamics potentials are "local" in nature. That`s: they exists for path connected topological spaces. So, there exists global gauge transformations or are all of them local in nature?. If the answer is "yes", i.e. if there are global...

I am trying to derive the potential based Lorentz gauge, but I am not sure if I am on the right track. Why the second partial derivative of vector potential must be 0? Please correct me where I got this wrong.

Hello everyone, I have been reading around that when performing the analytic continuation to Euclidean space (t\to-i\tau) one also has to continue the gauge field (A_t\to iA_4) in order to keep the gauge group compact. I already knew that the gauge field had to be continued as well but I didn't...

Homework Statement A person has a 5200 N/m^2 gauge pressure in a 0.01m radius artery, with blood flowing at 0.5 m/s. the gauge pressure outside the artery is 3200 N/m^2. When using her stethoscope, a physician hears a fluttering sound farther along the artery. the sound is a sign that the...

Hi, I am a little confused of derivation of Coulomb Gauage. (2) First, prime notation is adopted to describe the magnetic field density source current. Non-prime notation is for position that we are specifically interested in (ex. the position magnetic force acts on)...

A complex classical field Φ of particles is, by itself, invariant under global phase changes but not under local phase changes. It is made gauge invariant by coupling it with the EM potential, A, by substituting the covariant derivative for the normal partial derivative in the Lagrangian. But...

Spinors in $N=2, D=4$ supergravity can be simplified using gauge transformation and thus canonical spinors can be found. In the case of $N=2, D=4$ supergravity the gauge transformation Spin (3,1) is used. My question is how do we know which transformation can be used in a certain theory in order...

I'm having trouble reproducing some of the results regarding gravitational waves in the Wald's General Relativity In section 4.4 of gravitational radiation, eq.4.4.49 shows the far-field generated by a variable mass quadrupole: $$ \gamma_{i j}(t,r)=\frac{2}{3R} \frac{d^2 q_{i j}}{dt^2}...

Hello. I'm trying to wrap my head around how Lagrangians work in classical field theory. I have a book that is talking about the gauge invariance of the Lagrangian: \mathscr{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-J^\mu A_\mu. It shows that we can replace A^\mu with A^\mu+\partial^\mu\chi for...

Homework Statement Define n=(x + iy)/(2)½L and ñ=(x - iy)/(2)½L. Also, ∂n = L(∂x - i ∂y)/(2)½ and ∂ñ = L(∂x + i ∂y)/(2)½. with ∂n=∂/∂n, ∂x=∂/∂x, ∂y=∂/∂y, and L being the magnetic length. a=(1/2)ñ+∂n and a†=(1/2)n -∂ñ a and a† are the lowering and raising operators of quantum mechanics. Show...

A symmetry of a physical system is a physical or mathematical feature of the system that is preserved or remains unchanged under some transformation. For example, the speed of light is an example of symmetry and its value will always will always remain the same no matter where and what...

The part I understand: I understand that the spontaneous symmetry breaking of the Higgs produces the 'Mexican hat' potential, with two non-zero stable equilibria. I understand that as the Higgs is a complex field, there exists a phase component of the field. Under gauge transformations of...

I asked this question to PhysicsStackExchange too but to no avail so far. I'm trying to understand the way that the Higgs Mechanism is applied in the context of a U(1) symmetry breaking scenario, meaning that I have a Higgs complex field \phi=e^{i\xi}\frac{\left(\rho+v\right)}{\sqrt{2}} and...

Is there a physical reason why all gauge groups considered in SM and especially beyond are always semisimple? [+ U(1)] What would happen if they were solvable?

I've heard the claim that the gauge freedom of the general Lagrangian can be used to derive the Lorentz force on a charged particle. I understand that Langrangian gauge freedom allows A⋅v -∇φ to be unaffected by the gauge freedom in defining the EM potentials, but this seems like a convenient...

From what I have read: Gauge Pressure: The amount by which the pressure measured in a fluid exceeds that of the atmosphere. and Absolute pressure: Total pressure at a point in a fluid equaling the sum of the gauge and the atmospheric pressures.So Absolute pressure= Patm+ P-Patm= P (Which is...

Hi! I'm in a situation with threads that are being torqued, and unthreaded, and then torqued again hundreds of times per day. While torqued they are required to lift thousands of pounds of load. We've experienced failures where the threads appear to have worn/galled to the point that they...

Homework Statement Homework Equations The Attempt at a Solution I'm trying to find the principal strain, then from that find stress. The poisons ratio should be around 0.3 for this experiment. My result is about 100 micro strain higher than what my class mates got. Can anyone see...

Homework Statement To determine the maximum and minimum principal strains Homework Equations The Attempt at a Solution I think Poissons ratio is supposed to be 0.3. If someone who knows this stuff can see where I'm going wrong it would be greatly appreciated.

Homework Statement Objects A and B are submerged at depth of 1m in a liquid with specific gravity of 0.877. Given that density of object B is one third that of object A and that the gauge pressure of object A is 3atm, what is the gauge pressure of object B? (assume atmos pres is 1 atm and that...

Can there be interactions that are symmetric under low temperatures but exhibit spontaneous symmetry breaking under extremely low temperatures? (Maybe that symmetry breaking temperature is so low that it couldn't be discovered in experiments) Does electromagnetism split into electricity and...

I've having trouble understanding one of the consequences of using the length gauge. The length gauge is obtained by the gauge transformation ##\mathbf{A} \rightarrow \mathbf{A} + \nabla \chi## with ##\chi = - \mathbf{r} \cdot \mathbf{A}##. Starting from the Coulomb gauge, we have $$...

please explain what gauge symmetry is, gauge transformation is, gauge invariance is, and also how gauge invariance deletes the timelike polarization of a massless vector boson. without fancy math and formulas.

Urs Schreiber submitted a new PF Insights post Examples of Prequantum Field Theories II: Higher Gauge Fields Continue reading the Original PF Insights Post.

Although I have a good understanding of how to do calculations in gauge field theory, I am still dissatisfied with my understanding of why we use them in the first place. From a philosophical point, it should be possible to characterize a gauge theory in terms of observables only. I suppose one...

Urs Schreiber submitted a new PF Insights post Examples of Prequantum Field Theories I: Gauge Fields Continue reading the Original PF Insights Post.

If a theory is gauge invariant and one chooses to fix a particular gauge, having done this is it then possible to make a gauge transformation from this chosen gauge to another gauge, or have we already "spent" the gauge symmetry? Apologies if this is a really basic question, but I've got myself...

Homework Statement The lagrangian is given by: L = -\frac{1}{4} F^2_{\mu \nu} + (\partial_{\mu} \phi_1 - m_1 A_{\mu})^2 + (\partial_{\mu} \phi_2 - m_2 A_{\mu})^2 Homework Equations Find the gauge transformation of the fields that corresponds to a symmetry. Find the combination of scalar...

Is anyone able to explain in basic terms a thick EE student could understand, the significance and a bit about what Guage Fixing, or maybe gauge theory in general is? (or especially for FE simulation) making heads or tails of https://en.wikipedia.org/wiki/Gauge_fixing is not easy. A nice simple...

Buried in a recent talk by John Ellis, the following passage: Reference 92 is Weinberg & Witten 1980, reference 93 is a talk by Zohar Komargodski at the same meeting.

<<Mentor note: Moved from other thread.>> I have 4 questions: 1. Why Weinberg angle affects neutral boson mixing, while W+ and W- are unaffected? 2. Is there any relation between Weinberg angle and CP violation angle? Are they absolutely independent? 3. How our world would be different if...

From a recent thread: Is this true of gluons? Doesn't the color charge invert under CPT? (For example, a red-antigreen gluon's antiparticle would be a green-antired antigluon.)

So, I am following the PI lecture series by Neil Turok. He starts with the following description of harmonic gauge condition $$g^{\mu \nu}\Gamma^{\lambda}_{\mu \nu}=0$$ He then claims that for linearized gravity (weak field) i.e. $$g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} $$ with $$ |h_{\mu...

If I have a theory withsome gauge symmetry, I don't understand why we want to fix a gauge. It seems to me to be 1. artificial 2. ignoring a real symmetry of the equations For example in electromagnetism, we can use the lorentz gauge, but why would I? It removes a degree of freedom that should...