jpm
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Are there forces which do not involve a change in momentum?
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20 votes

Actually Newton's second law is better stated as $$F=\frac{dp}{dt}$$ and this is even valid in relativity, both SR and GR, expressed in the right way $$ f^\mu = \frac{dp^\mu}{d\tau}=m\frac{du^\mu}{d\...

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Do gamma matrices form a basis?
18 votes

As previous answers have correctly noted gamma matrices do not forma a basis of $M(4,\mathbb{C})$. Nevertheless you can construct one from them in the following way 1 the identity matrix $\mathbb{1}$ ...

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Symmetries of the theory that are not symmetries of the action nor of the measure?
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9 votes

The theory of a chiral fermion $\psi$ coupled to a Maxwell field in four dimensions has a famous anomaly in the chiral transformations $$ \psi \rightarrow \psi'=e^{i \gamma_5 \theta} \psi $$ which ...

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Confusion with LSZ reduction formula
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6 votes

$|\Omega\rangle$ is the vacuum of the full interacting theory and $|0\rangle$ is the vacuum of the free theory. They are related in the following way $$ |\Omega\rangle = \lim_{T\rightarrow(1-i\epsilon)...

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Multivariable Dirac Delta and Faddeev-Popov Determinant
5 votes

Again assuming it only has a zero $x^i=x_0^i$ what you have is $$ \delta(f(x^i)) = \frac{\delta(x^1-x_0^1)}{\left|\frac{\partial f}{\partial x^1}\right|_{x^i=x_0^i}} \frac{\delta(x^2-x_0^2)}{\left|\...

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How to verify this statement in optical theorem?
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4 votes

I believe they are just describing in words the following equation $$\frac{1}{p^2- m^2 \pm i\epsilon} = P\frac{1}{p^2- m^2} \,\mp\,i\pi \delta(p^2- m^2) $$ where $P$ denotes the principal part. ...

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Killing vector contractions along isometric curves
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4 votes

Let $\lambda$ be an affine parameter of the integral curves of $\xi^{\nu}$ then you question translates as $$ \frac{d}{d\lambda}(\xi_{\nu}\xi^{\nu}) = \xi^\mu \nabla_\mu(\xi_{\nu}\xi^{\nu}) = (\xi^\mu ...

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Monopole operator: correlation functions
3 votes

“Monopole operators” only exist as local operators in three dimensions. For free Maxwell theory in that dimension an easy way to think about them is in terms of the dual compact scalar, as you ...

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From representations to field theories
3 votes

I don't think such a thing exists. Usually reps only help you classify the kind of objects you have (i.e the quantum numbers that identify them) and how they transform under the corresponding group. ...

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Electomagnetic Field Quantization
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3 votes

That factor is there because they quantize the field in a box and not in the continuum. When you take the continuum limit one gets $$ \int d^3k \rightarrow \sum_k \sqrt{\frac{\hbar c^2}{V}} $$ by ...

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Why in the relativistic quantum mechanics $ \gamma_4$ name is not used instead of $ \gamma_5$?
3 votes

I don't know is there is a historical reason I just assumed that was just no to mistake it with $\gamma^3$ which would be called $\gamma^4$ if your Lorentz indices run from $\mu=1,2,3,4$ instead of ...

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Dirac equation in QFT vs relativistic QM
3 votes

The field is not interpreted as a wave function but as an operator $\hat{\psi}$ which creates/annihilates particles. This quantisation procedure is done by expanding the field in its Fourier ...

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Why does this amplitude not factorise into subamplitudes?
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2 votes

What you found is precisely that the amplitude factorizes since the correct statement of factorization is $$ \lim_{P^2\rightarrow0} M(1,\cdots,n) = \sum_{ i\in \text{helicities}} M(1,\cdots,k,P^i)\...

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Coulomb repulsion in superconductivity
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2 votes

Take a look at the beautiful TASI lectures by Polchinski on Effective Field Theory and the Fermi Surface. In Lecture 2 he explains the EFT point of view on BCS condensation and he derives the one-loop ...

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Does 4D ${\cal N} = 3$ supersymmetry exist?
2 votes

Weinberg's argument relies on the existence of Lagrangian/weak coupling regime. Genuine $\mathcal{N}=3$ theories were recently found in this paper. As expected, they are strongly coupled and believed ...

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Quantum symmetries: $S$ or $Z$?
2 votes

People sometimes talk about on-shell symmetries: symmetries of the equations of motion or the S-matrix, which do not hold off-shell (i.e. at the level of the action, path integral, correlators, etc). ...

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What will be the relative speed of a photon in a light ray to another photon of opposite direction light ray?
2 votes

The question of what is the velocity of a photon relative to another photon does not make sense. Neither it does asking what is the velocity of anything relative to a photon. This is because in ...

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When can i separate spin from the wavefunction?
2 votes

@ChrisWhite is right I believe you don't need to worry about that since using the tensor product notation $|x s\rangle = |x \rangle \otimes |s\rangle$ and the angular momentum and spin operators just ...

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Comparing predictions and reality for the gravitational attraction due to light beams
2 votes

Usually the Newtonian limit is described as taking $v << c$ but a much better way to express it is saying that the kinetic energy is much less than the rest energy $$ \frac{1}{2}m v^2 << m ...

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Normalization of the Chern-Simons action in the Dijkgraaf-Witten paper
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1 votes

Let me answer the second part of your question: In the Abelian case there is no trace at all. The term $$\frac{1}{8\pi^2} \int F\wedge F$$ is indeed the second Chern number of the $U(1)$ bundle. This ...

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Faster ways of computing feynman diagrams
1 votes

Nowadays, less and less people use Feynman diagrams for precision calculations (that is, anything beyond a tree level 4 or 5 point amplitude). There is a whole field dedicated to finding better ...

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Energy of quarks and the mass of the proton
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1 votes

Yes it fluctuates but it is a very small fluctuation. Note that unstable particles have a decay rate or width $\Gamma$ that is related to its lifetime $\tau$ by $$ \Gamma=\frac{\hbar}{\tau} $$ when ...

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A simple question about the scattering amplitude $\mathcal{M}$ in QFT
1 votes

All Lorentz indices are summed over, but it is more subtle than you might think. The amplitude for particles of helicity/spin greater than zero is not a scalar. The reason for this is that the ...

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What causes here an apparent violation of Elitzur's theorem?
0 votes

Gauge symmetries are not real symmetries but redundancies. Any two states related by a gauge transformation are physically equivalent. So if there isn’t a symmetry to begin with, it cannot be ...

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Why we can't write low energy effective field theory for a gapless system?
0 votes

For the notion of effective theory to make sense you need a separation of scales. This is so that experiments at low energies (with respect to that scale) do not excite the heavy modes too much. In ...

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