# Tagged Questions

Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use ...

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### Why every state evolving infinite time becomes the ground state in QFT?

For any state $|\phi \rangle$ evolving infinite time $$\lim\limits_{t\rightarrow \infty} e^{-iHt}|\phi\rangle=\lim\limits_{t\rightarrow \infty} e^{-iHt}|n\rangle\langle n|\phi\rangle$$ Let ...
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### The virtual particles are only a fictive tool in equations? DO they exist or DON'T? And if they exist, why do we call them VIRTUAL?

There is no "action at a distance" in nature. Attraction of a piece of iron by a magnet, attraction between distant electric charges of opposite sign, have to be mediated by something. The virtual ...
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### Why do we have different signs before the delta on the Klein-Gordon and the Dirac Green's function equation?

Let's read equation (2.56) on Peskin & Schroeder $$(\partial^2+m^2)D_R(x-y)=-i\delta^4(x-y).$$ Let's look now to equation (3.118) $$(i\gamma^{\nu}\partial_{\nu}-m)S_R(x-y)=i\delta^4(x-y).$$ ...
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### Higher-order gauge coupling terms in the Lagrangian

In QFT, one works with Lagrangians that are invariant with respect to a certain symmetry. Out of this invariance, one is able to write down interaction terms at first order in the gauge couplings. The ...
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### Chiral-Projection operator in a basis different than the Weyl basis

I was pretty confident that things are simple, but unfortunately I must have missed something. We can always change between between the bases for Dirac spinors, using unitary transformation, because ...
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### Proof that the effective action is the generating functional of one-particle-irreducible (1PI) correlation functions

In all text book and lecture notes that I have found, they write down the general statement ...
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### Renormalization condition

Can any on explain to me, why renormalization condition $$\Sigma(\gamma_\mu p^\mu=m)=0,$$ for one loop implies $$\Sigma_2(m)=m\delta_2-\delta_m~?$$ In the original $\Sigma_2$ we had $m_0$ which is ...
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### Path integral derivation of the state-operator correspondence in a CFT

Below, I paraphrase the path integral derivation of the state-operator correspondence in David Tong's notes on CFT (see pdf here). This is my interpretation of the text in that pdf, so please correct ...
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### Upper bound to annihilation cross section into heavy particles

For a process in which two relativistic particles annihilate to produce two or more heavy(er) particles of mass $M$: Is it true that the cross section $\sigma_{ann}$ cannot be larger than ...
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### Are relative phases observable for identical particles but not for non-identical ones?

In quantum mechanics, amplitudes are represented by complex numbers $e^{i\phi}$, which have phase angles $\phi$. These phase angles are clearly not observable in absolute terms. If I have two ...
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### Are Matsubara states pure states?

Generally in a non-interacting QFT one can solve the Klein-Gordon equation to get a (complete) set of states $\frac{e^{i\omega_k t-ikx}}{\sqrt{2\omega_k}}$. It is not clear to me how to construct the ...
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### Justification of not quantizing small extra dimensions

When dealing with extra dimensions ($x ^\mu$ represents $4D$ spacetime and $y$ the extra dimension) we use what's known as Kaluza-Klein decomposition (basically a Fourier transform), ...
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### Do physicists use agent based models?

I am hoping that this is a simple and specific question. I just wanted to know whether physicists from any branch of physics use agent based models as a tool in their research? If so, then in which ...
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### Are vacuum fluctuations really happening all the time?

In popular physics articles and even some physics classes I've been to, the vacuum of space is described as being constantly full of quantum fluctuations. Supposedly, all sorts of ...