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Discrepance between gauge symmetry and Noether's first theorem

There's no conserved charge associated with the local symmetry. The reason for that is that gauge "symmetry" is not a physical symmetry. The current for the EM Lagrangian is $J^\mu=\partial_\...
Lucky Charms's user avatar
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Can the potential of a point charge be considered one-dimensional?

Mathematically, we can indeed think of it as being one-dimensional, since it depends on only one variable. Therefore you can describe its full behavior by plotting it along a line. But the potential ...
Codename 47's user avatar
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Explanation of homogeneity of space and time by giving examples?

For now, I am only commenting on homogeneity. Homogeneity of space and time It is my understanding that the homogeneity of space and homogeneity of time is invoked when we develops the rules to ...
Michael Levy's user avatar
2 votes

How do we know at the operator-level that the tadpole $\langle\Omega|\phi(x)|\Omega\rangle=0$ vanishes in scalar $\phi^4$ theory?

I think you are basically there: Let $\hat{U}$ be the unitary operation you defined, $\hat{U} \hat{\phi}(x) \hat{U}^\dagger \equiv -\hat{\phi}(x)$. This is a definition. We then assume (or check) that ...
Lucas Baldo's user avatar
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1 vote

How to know the position of an object when calculating the center of mass, without using integrals?

Try to balance the 1/4 piece of pizza with one finger.
Hyperon's user avatar
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0 votes

Conserved current transforming under adjoint

Charges are constructed by integrating currents, $$ Q^a = \int_\Sigma n^\mu j_\mu^a $$ $Q^a$ transforms in the adjoint, therefore $j^a_\mu(x)$ must transform in the adjoint.
Prahar's user avatar
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Conserved current transforming under adjoint

It's straightforward, provided you appreciate the currents and their charges are the vectors (states) of the adjoint, not its transformation matrices/generators. Ignoring normalizations and ...
Cosmas Zachos's user avatar
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What is the gravity in the center of Earth?

The gravitational potential itself has zero gradient at the centre of the Earth or the Sun. However there is a very strong effect buoyancy, as your density will be inferior to that of your ...
my2cts's user avatar
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What is the gravity in the center of Earth?

Or in other words - If I would be in the center of the sun, would I be in a weightlessness state or would I be torn to pieces? From Newton's shell theorem, there are no net forces acting on a ...
KDP's user avatar
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What is the gravity in the center of Earth?

The gravitational field $\textbf{g}$ is governed by Poisson's equation for Newtonian gravity $$\nabla\cdot\textbf{g}=-4\pi G\rho \tag{1}$$ where $G$ is the gravitational constant and $\rho$ is the ...
Thomas Fritsch's user avatar
-2 votes

How to show that an $N$-dimensional SHO's dynamics symmetry is $SU(N)$?

It is easy to show that the following operator commutes with the hamiltionian $$A_{ij} = \frac{1}{2} \hbar \omega (a_i a_j^+ + a_i^+ a_j)$$
user398568's user avatar
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Relating the different "notions of charges" in field theory

The 3 charges you mentioned are essencially the same. There is a 'Noether charge theorem' which states that the Noether charge should be the quantum generator of the transformation (Weinberg Chapter 7)...
zixuan feng's user avatar
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How to tell whether Hamiltonian has rotational invariance? Conservation of angular momentum?

In the classical framework, the exchange interaction term S$_{i}$ $\cdot$ S$_{j}$ satisfies the rotation invariance of the x,y,z-direction, but the uniaxial anisotropy term ${(S_{i}^{z})}^2$ breaks ...
Xin's user avatar
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Question regarding time dilation

In SR, if two people are moving relative to each other at constant velocity, each person will be equally time dilated in the frame of the other person. In those circumstances, the movements of the ...
Marco Ocram's user avatar
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Question regarding time dilation

Suppose you know that my clock currently says 3:00PM. Does that tell how anything about how fast it ticks? Answer: Of course not. No matter how fast or slow my clock runs, I can always set it to ...
WillO's user avatar
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-3 votes

Question regarding time dilation

Einstein himself answered this question in his paper here. What Einstein said pretty well contradicts with the other answers above. He says is that you cannot look at special relativity alone. You ...
foolishmuse's user avatar
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Magnetic Field in the plane of a circular current carrying loop

So your argumentation using Amperes law and rotational symmetry does hold. But as mentioned in the comments you need to take care of the direction you are looking at. Your argumentation tells you, ...
Zaph's user avatar
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Why is the charge distribution on the outer surface of a hollow conducting sphere uniform and independent of the charge placed inside it?

Consider first the conducting sphere is grounded, then using the method of images there is a point charge q' outside the sphere which gives zero potential at the surface of the sphere. Now if we wish ...
Yuan Fang's user avatar
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Review: If true, what makes the vacuum of a local ${\rm U(1)}$ gauge theory unique?

I want to present a "counter"example to Ruben's answer --- a state that preserves local gauge symmetry but breaks the global symmetry. The issue is rooted in the thermodynamic limit. For ...
Yuan Yao's user avatar
1 vote

Question regarding time dilation

Time dilation is indeed symmetric, since velocity is relative. But if a rocket ship turns around, it's definition of simultaneity changes, and it has to take that into account when calculating the ...
Eric Smith's user avatar
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0 votes

Question regarding time dilation

This is basically the problem of the "twin paradox". It seems at first that there should be no difference between the observers on earth and those on the ship since there is symmetry between ...
Albertus Magnus's user avatar
0 votes

Question regarding time dilation

Suppose that there are several synchronized clocks in the Earth's frame along the ship's path. Each time that the ship passes by one of that clocks, the difference with respect to the clock inside the ...
Claudio Saspinski's user avatar
26 votes
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Have all the symmetries of the standard model of particle physics been found?

The standard model of particle physics is entirely determined by writing down its Lagrangian or, equivalently, writing down the corresponding system of PDEs. Actually, this isn't true -- it is true ...
Andrew's user avatar
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3 votes

Are loops counted twice in Feynman diagrams?

Well, the self-loop propagator $D(z-z)$ in OP's Feynman diagram occupies 2 of the 4 legs of the 4-vertex. It is also responsible for a symmetry factor $S=2$ that the diagram should be divided with.
Qmechanic's user avatar
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3 votes

Are loops counted twice in Feynman diagrams?

Propagators correspond to line segments; since there are three line segments, there are three propagators. Two 'offshoots' of the vertex are covered by one propagator (the loop), but you'll notice ...
John Dumancic's user avatar
0 votes

Why $n-1$ point function vanishes in $D=0$ scalar theory?

More generally, for a complex scalar $\phi^n$ theory$^1$ where $n\in\mathbb{N}$ with a global $\mathbb{Z}_n$-symmetry $\phi\to e^{2\pi i/n}\phi$, then the $m$-point function $\langle\phi^m\rangle_{J=0}...
Qmechanic's user avatar
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2 votes

Why $n-1$ point function vanishes in $D=0$ scalar theory?

In the absence of space-time coordinates ($D=0$), the functional integral of the (Euclidean) "field" theory with the Lagrangian $g \phi^n$ reduces to an ordinary integral and the generating ...
Hyperon's user avatar
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2 votes

What is the real shape of Earth?

Yes, Earth does take the shape of an oblate spheroid, but only to a very marginal extent, such that it is barely noticeable. If you are looking for a planet that more obviously takes the shape of an ...
cookiecainsy's user avatar
1 vote

What is the real shape of Earth?

The shape of the earth is called the geoid. An ellipsoid is just an approximation, and the geoid deviates from the reference ellipsoid by up to 106 m. A sphere is, in turn, an approximation to the ...
Dale's user avatar
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1 vote

What is the real shape of Earth?

Well the truth is that NASA doesn't have pictures of around Earth. However, your point is well taken in that the pictures certainly look like they show a round Earth. Even though the Earth is indeed ...
Albertus Magnus's user avatar
1 vote

What is the real shape of Earth?

An oblate spheroid does not need to be very oblate to qualify as oblate. This one is not. It's that simple. The shape of the Earth is, of course, considerably more complex than any idealized shape, ...
StephenG - Help Ukraine's user avatar
1 vote

$\mathbf F'=\mathbf F$ in special relativity

The covariant Minkowski force can be written in terms of the three-vector force as \begin{equation} {\cal F}^\mu=\left[\gamma\frac{dW}{dt},\gamma{\bf F}\right], \end{equation} where $\bf F$ is three-...
Jerrold Franklin's user avatar
1 vote

Phase transitions in the XXZ model

For the second question, what should be the case is the moment you get to $T>0$, the "quantum-classical correspondence" with $d+1$ dimension breaks down, and it becomes simply like a $d$ ...
Jun_Gitef17's user avatar
0 votes

Is there an spherical symmetric Einstein vacuum solution which has circular orbits with flat velocities? Or a proof that it cannot exist?

There is a spherically symmetric Einstein vacuum solution for flat circular velocities. Its line element is the general spherically symmetric line element [1][2] $$\mathrm{d}s^2=\left(\frac{r_S}{C}-1 \...
Franz Unterleitner's user avatar

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