DJBunk
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What is the massless limit of massive electromagnetism?
6 votes

Starting with the Lagrangian for a massive $U(1)$ vector boson $A_\mu$ which like you said has 3 DOF: $$\mathcal{L} = - \frac{1}{4 e^2} F^{\mu \nu} F_{\mu \nu} - m^2 A^\mu A_\mu$$ now if we change ...

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About calculation of anomalous dimension in Peskin and Schroeder's book.
1 votes

The anomalous dimension for the field strength is defined as (eqn 12.63 Peskin): $\gamma = \frac{1}{2} \frac{M}{Z} \frac{\partial Z}{\partial M} = \frac{1}{2} \frac{\partial \log Z}{\partial \log M} ...

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Pauli matrices and the Levi-Civita symbol
2 votes

Unless I am missing something the relation is trivial since starting with $$\epsilon^{klm}\sigma^m = \sigma^m \epsilon^{mkl}$$ and permuting the $m$ past the $l$ gives a factor of -1 $$(-1)\...

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Comprehensive book on group theory for physicists?
5 votes

I personally recommend Georgi's book with a particular focus on SU(3). And there is also Ramond's book, which is along the same lines as Georgi's textbook. Also online there are some notes ...

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De Broglie wavelength of slow moving macroscopic objects
1 votes

Building on DavePhD's answer, you need to have some sort of experiment in order to measure/resolve such a length, and this would be done with an interference experiment. In order to have any meaning, ...

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Physical question on an RLC circuit
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5 votes

Inductors resist changes in current. So in a circuit like the one you describe, for short times after the switch is closed, the inductor acts like a broken wire. This is consistent with the statement ...

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Can dimensional regularization solve the fine-tuning problem?
2 votes

The fine tuning you describe isn't present in the $\phi^4$ model. You need some some other heavy fields around to see it. For example, couple your $\phi$ to a heavy fermion of mass M, Then when you ...

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What exactly are we doing when we set $c=1$?
7 votes

If you are getting used to 'natural' units I think its best to think of it like this: we are basically defining a new time variable $t' \equiv c t$ to work in. $t '$ has units of distance. We can ...

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Time inside a Black hole
1 votes

The time dilation you speak of is a description of the apparent time an observer outside witnesses someone falling into a black hole. That is, if you are standing outside the black hole (some distance ...

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The paradoxical nature of Hawking radiation
3 votes

First of all, by electromagnetic radiation we basically mean photons. That is particles are radiated by a black hole. Hawking radiation in general can be any type of particles, as in the same way in ...

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Potential in Relativistic Scalar Field Theory
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1 votes

Any term in the action that does not transform under any symmetries is allowed. This means for a scalar field you can have any power $\phi^n$ in your Lagrangian. In equation (92.2) Scrednicki just ...

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Different approaches to calculating the Christoffel symbols
Accepted answer
3 votes

The first one is probably correct, and you are likely not counting correctly in the second method. You should compare you result $\ddot{t}+ 2 \frac{\partial U}{\partial x^{i}} \dot{x}_i \dot{t}=0$ ...

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Density operator in second quantization
4 votes

You can find this by noting the the photon potential $A_\mu$ couples to the electromagnetic current $J_\mu$ in the form $\mathcal{L}_{int} = A^\mu J_\mu. $ Where $J_\mu$ obeys the continuity ...

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Is Feynman's explanation of how the moon stays in orbit wrong?
3 votes

Picture this. Take your desk and put in top of the tallest building on earth. Put a penny on the desk and flick it with your finger. (The point of this is that we are only giving the penny a ...

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Finite square well
Accepted answer
4 votes

I think you are asking for a finite well of width L that is from $ -L/2< x< L/2$. Why do we only use $\psi(x) = A e^{+\kappa x} $ for $ x<-L/2 $ and $\psi(x) = B e^{-\kappa x} $ for $ ...

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A partial differential equation for kinetic energy
Accepted answer
1 votes

I can't see where this has any utility at all. The point of having any equation, differential or algebraic, is to put constraints on a system. We then solve these equations to obtain an unknown ...

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Can't find the mass scale; calculation using the modified minimal subtraction scheme and dimensional regularisation
1 votes

Your $\mu^\epsilon$ is still there, it's just that you have expanded in small $\epsilon$ so you got $$ \mu^\epsilon \approx 1 + \epsilon \log \mu = 1 - \epsilon \log \frac{1}{\mu} $$ The $\log \...

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Calculating force of impact
0 votes

First of all just to refine your notion of force and acceleration by `force = mass X acceleration' what we mean is the relationship between the vectors: $\vec{F}_{net} = m \vec{a}$ that is, its the ...

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Fourier transform between $x$ and $p$
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4 votes

As far as where you put things like the $2 \pi$ and the $\hbar$ in the Fourier transform or Inverse Fourier transform, it doesn't really matter. What really matters is that the operations are the ...

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Strong interaction and the Lagrangian for electromagnetic interaction
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1 votes

If you take your Lagrangian, including the $A^\alpha A_\alpha$ and vary it with respect to $A^\alpha$, you will get the classical equation of motion: $\partial_\beta \partial^\beta A^\alpha + \mu^2 ...

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Electric field lines
-1 votes

This: Which I borrowed from: enter link description here The lines go off to infinity and never terminate. EDIT: As per your comment, you seem to be asking about the difference between an electric ...

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The direction of friction for a car wheel
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1 votes

The truck is indeed moving up the hill, and the tires are not slipping. There are a couple of ways to see why the friction points in the direction of the motion of the truck. One way is to keep in ...

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Trilinear gauge couplings: Spin
3 votes

The massive verse massless cases are different. Massive vector bosons are a bit more 'honest' in their representation of the Lorentz group in that they have all 3 DOF implied by the $j=1$ ...

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Why use Fourier expansion in Quantum Field Theory?
Accepted answer
5 votes

First of all, this is just a change of basis, which is up to us to make. Furthermore we should always choose a basis that makes our calculations easier, and hopefully makes things more intuitive. For ...

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Feynman Rules for massive vector boson interactions
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3 votes

Your first interaction term is bilinear in 2 gauge fields. Terms of this form indicate that you need to diagonalize your mass matrix. So you could work out the Feynman rules for your first interaction,...

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Why don’t photons interact with the Higgs field?
7 votes

There is an aspect to this question that nobody seems to have addressed and that is, although the higgs (the 'radial' component of the field) is neutral, and therefore doesn't interact with the photon ...

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Is single photon annihination of electron-positron pair prohibited by Feynman diagram analysis?
4 votes

If you want to see this from a straightforward implementation of the Feynman rules: You can always calculate the diagram for $e^- e^+ \rightarrow \gamma$ and for arbitrary momentum it will be nonzero. ...

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What makes a Feynman diagram real or virtual?
7 votes

If I understand your question correctly its just a matter of what you are calculating whether you put the external particles on shell or not. If you are, for example, calculating an amplitude to use ...

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Is the braket notation of the Dirac delta function symmetric?
2 votes

Either way is fine: $\delta(x-x')= \langle x| x' \rangle= \delta(x' - x) =\langle x'| x \rangle$. You can see this either from the fact that in the limiting definition $\delta (x-x') = \lim_{\...

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Photons and uncertainty principle
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2 votes

In your post when you say you 'know' the position and momentum of a single photon you really don't know anything, you are just making a prediction, not making a measurement. In your head you are ...

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