New answers tagged quantum-field-theory
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Clarification Needed for The Klein-Gordon Field Acting on the Vacuum State (Peskin and Schroeder)
I think your confusion is because you have confused the vacuum state $\lvert 0 \rangle$ with the zero vector. The two are not the same thing; the first one is a non-zero vector in the Fock space with ...
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Why is entanglement entropy in QFT infinite?
I think the best way of making sense of this divergent entanglement entropy is to work with von Neumann algebras. Typical QFTs are type III von Neumann algebras, due to which the definition of a trace ...
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Renormalization in $\lambda\phi^4$-theory: Why renormalize at one-loop instead of renormalizing at order of the coupling constant $\lambda$?
OP is right that in perturbative QFT we ultimately want to calculate in order of the coupling constant $\lambda$, e.g. to determine the beta function. However, the following facts should be kept in ...
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vote
What happens when a photon interacts with a free electron?
In the classical theory, for a linearly polarized plane EM wave, the electron oscillates in the polarization direction, perpendicular to the propagation direction. An oscillating charge emits ...
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Do virtual particles actually physically exist?
Under the context and physical definition that theoretically these particles cannot be ever detected directly because their unstable nature and very tiny lifetime which is within the Heisenberg ...
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Can we regard metric as the Higgs field of gravity?
We will be using Trautman's unifying formulation of both general relativity and Yang-Mills gauge theories as theories of a $G$-principal bundle $P\to M$ over spacetime $M$. For an exposition of this ...
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Particle density operator in Fetter and Walecka
I believe the question remains as to why
$$
\sum_{i=1}^N \hat{a}(i) = \sum_{rr'}\hat{c}_r^\dagger \langle r| a|r'\rangle \hat{c}_{r'}
$$
holds. It is true that in first quantization, there is always ...
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Feynman diagrams in statistical physics
Using Feynmann diagrams for the Rennormalization group calculations is a relatively recent development. They have been extensively used in the context of Feynmann-Dyson expansion of quantities of ...
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2-point correlation function between two different fields
The story for a (connected) 2-point function of 2 different fields is very similar to what goes on for a 1-point function, cf. e.g. this & this related Phys.SE posts:
Either a symmetry ensures ...
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Question about proof of Weinberg-Witten theorem
So I guess the $t$ argument can just be ignored.
Per the link provided, $Q$ is a conserved charge. "Conserved" means that it doesn't change with time, so it is the same for all $t$:
$$
\...
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Why is the Gribov ambiguity not seen in perturbation theory?
In perturbation theory, Gribov copies do not pose a significant issue, and this can be understood through the work of Daniel Zwanziger. Zwanziger approached the Gribov problem differently, focusing on ...
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Particle Anti-Particle annihilation in Quantum Field Theory
What special distinction does the interaction of a particle with its anti particle have compared to an interaction with some other particle?
A particle and its antiparticle are described by the same ...
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Are quasi-particles really particles?
The following answer is from the Nobel laureate Frank Wilczek in a talk "Quasiparticles and Quasi-Worlds" (starting from 1:04:40). It seems that he gave the same talk at least three times ...
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About sending time to infinity in a slightly imaginary direction in QFT
TL;DR: In the Gell-Mann and Low theorem the $i\epsilon$ prescription in the complex time plane is equivalent to an adiabatic cutoff of interactions. Both serve as a regularization.
In more details: We ...
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What is the interpretation of Matsubara frequencies?
The imaginary-time Green-function is a periodic function on the interval $(- \hbar \beta , + \hbar \beta)$. Expanding this function w.r.t. its Fourier-series and using the periodicity-properties of ...
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Explicit form of Dirac field creation/annihilation operators?
You can recover them from the mode expansion of the field:
$$\psi(x) = \int \frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_p}}\sum\limits_s[a^s_p u^2(p) e^{-ipx} + b^{s\dagger}_p v^s(p) e^{ipx}]$$
You can ...
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What Do We Envision the Fabric of Space to Be? Physical or Immaterial?
Whatever spacetime is, we have to grant that it has the capacity to support propagation of gravitational waves.
The LIGO observatory registers the passage of gravitational waves. The frequency range ...
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How to find probability density function of this quantum particle
The Born Rule states that the probability is the square of the modulus of the wave function:
$$ P(x, t) = \Psi^*(x, t)\Psi(x, t) $$
Since $\Psi$ is not an eigenstate, it has time dependence.
The time ...
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What are the dimensions, width and length, of a photon?
It’s a great question. In college, my professor was rather unclear on this topic.
Electrons are experimentally point sources. No matter how high an energy is used to smash them together no size is ...
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The most general procedure for quantization
I will give you a more general answer, in fact, a very mathematical answer that defines quantization.
Setup:
k is a characteristic 0 field, and K = k[[h]]
Deformation
A Deformation algebra is a ...
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Why don't we study spin-3/2 fields?
There is a theorem by Weinberg that spin-1 massless particles can only enter an interacting theory as gauge bosons and spin-2 massless particles as gravitons. This was extended by Grisaru Pendleton ...
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Why do the subatomic particles like electron exhibits Dual-nature? And how does the particle knows when to change their state?
This question has troubled physicists for a century. What you're referring to is defined as the 'Measurement problem,' wherein a particle, initially described as a wave (i.e., a wavefunction), ...
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Calculation of $ \gamma(\lambda) $ in massless renormalizable scalar field theory
At first one has to realize that the calculation of (12.49-51) is a generalization of the $\phi^4$ case. A couple of theories could be concerned like $\phi^3$ in 6 dimensions described by Srednicki or ...
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Does the Standard Model have a Landau pole?
The value on Wikipedia I'm finding for the Landau Pole energy is $10^{286}~\mathrm{eV}$. I question the significance of the pole, because this is so far beyond anything observed or understood. The ...
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Renormalization in Classical Field Theory
Sorta, yes, there is a classical analogue to renormalization groups that is native to classical field theory - at least in the case of scalar fields. I will demonstrate it here. Whether/how it can be ...
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Does the probability wave of a photon determine its color?
Probability waves are are math calculation used to predict the outcome and do not determine anything physically. Yes the double slit experiment would have different results when performed with red ...
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Expectation value of the exponential of a quadratic term in fields
Oh, well, this is the classic seat-of-the-pants stunt Polyakov is famous for, like Landau or Feynman, etc, a formal wisecrack.
The idea is to integrate over a high momentum slice where h fluctuates ...
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Whether vacuum energy gravitate?
Pertubation fields, that are introduced to correct the ill adapted, nearly free Lagrangians for interacting fields, are no invariant parts of the energy-momentum tensor.
Generally, the perturbation ...
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Euler-Lagrange for Dirac Lagrangian - is $\bar \psi$ independent of $\psi$?
While $\psi$ and $\bar{\psi}$ do not appear to be independent, the key point is that they are linearly independent. This is because the operation of complex conjugation (in the hermitian conjugate) is ...
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Feynman diagrams with no lines crossing
By no crossing lines, I shall assume you mean no vertices.
In that case, that means that you have particles just propagating. For example, if you have just one line connecting two points a, and b, ...
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Euler-Lagrange for Dirac Lagrangian - is $\bar \psi$ independent of $\psi$?
We generally treat $\psi$ and $\bar\psi$ as independent variables. This follows from the fact that the most general form of $\psi$ (and consequently the implied form of $\psi^\dagger$, where $\bar\psi=...
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Can we regard metric as the Higgs field of gravity?
A version of this idea is discussed at the end of section 1.1.1 of
https://inspirehep.net/literature/1823987
which also cites the following as precursors
https://inspirehep.net/literature/150700
https:...
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Energy density proportional to the cube of the frequencies
So I just found this in reference to finding out if frequency cubed had any significance in physics. I used E^2=(mc^2)^2+(pc)^2 and ...
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Some calculation in Mahan book, p73
On page 73 of Mahan, Many-particle physics, 3d edition, one finds
$$
_0\langle|S(-\infty,0) = e^{-iL}_0\langle|S(\infty,-\infty)S(-\infty,0).
$$
I'm wondering why this is true, as in the previous page ...
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vote
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Feynman propagator from Hadamard propagator
If you use
$$
\theta(x)+\theta(-x) =1
$$
You will see that they are the same.
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Quantization of charge from the path integral
First, let me rewrite the conserved current as a one-form, $j = j_\mu \mathrm{d}{x^\mu}$. This allows me to rewrite the charge as
$$Q[\Sigma] = \int_\Sigma \star j,\tag{1}$$
where $\Sigma$ is any ...
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Numerator of Massive Vector Propagator and Polarization Sum
Setup
For a massive spin-1 particle, there are three physical polarization states. The polarization vectors $\epsilon_i^\mu$ describe these states. The sum over polarization vectors essentially sums ...
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Finding scalar propagators in QFT for specific spacetime dimension $d$ and mass $m$
I will attempt to aid you in finding a solution to your problem. First, start with the recipe
$$G^E(it,\vec{x})=-iG^F(t,\vec{x})$$
and then consider the definition of $G^F(t,\vec{x})$, i.e.
$$G^F(t,\...
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vote
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Gibbs state and creation and annihilation operators
I think this is already answered in the comments, but it can put more clearly as follows.
Suppose there is a way to label the $p$ states, as $p_1,p_2,\ldots$. Then, the many-body state in the ...
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How to show a propagator of massive spin-1 field is the Green function to its equation of motion?
I will try to answer your question. If something does not make sense, you can always comment so that I can edit my answer.
You are looking at two different types of commutators. Their definitions are ...
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Why 5D gauge theory is non-renormalizable?
Concerning OP's 1st question:
If we scale the gauge field $A_{\mu}$ so that the quadratic term $-\frac{1}{2}{\rm tr}F_{\mu\nu}^2$ in the Lagrangian density $ {\cal L}$ is canonically normalized, then ...
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Gibbs state and creation and annihilation operators
There is an identity that is useful when you need to compute commutations with exponentiated operators for boson operators. It is
$$ \exp(\hat{X})\hat{Y}\exp(-\hat{X})=\hat{Y}+[\hat{X},\hat{Y}] +\frac{...
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Is impact parameter a initial condition for collision in colliders?
By classical mechanics, the impact parameter is the distance of line of the free movement to its parallel line through the collision center.
The impact parameter, as a vector, cross multiplied by ...
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Non-vanishing amplitude outside light cone doesn't violate causality?
A propagator like
$\langle 0 | \phi(x) \phi(y)|0 \rangle$
(or a time-ordered correlation)
is an expression of the correlation of field values at different space-time points. Nonzero correlations over ...
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Non-vanishing amplitude outside light cone doesn't violate causality?
The point of the first calculation is to show that our naive idea of what makes a QFT causal needs to be replaced with the idea that field operators commute at spacelike distances. If you look a ...
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Physical intuition for spatially constant motion in the XY-model in 2+1D
Looking back, I realize that he is thinking of the XY model as an approximation to a Bose-Hubbard type model at large filling. There, you expand around some integer filling $N_0$ to get your rotor ...
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Special relativity, quantum mechanics and non-conservation of particle number
you said, "I'm guessing ..." ... and i say keep guessing because you've pretty much almost answered your own question. So take a QM particle jack in the box and apply energy uncertainty with ...
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How do we interpret disconnected diagrams in scattering theory?
I've recently discovered that the extra delta function for the amplitude is exactly what is needed for cluster decomposition principle. I'm too lazy to write details here.
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How is a Fock state from QFT related to the wave function from quantum mechanics?
In QFT, Fock states are indeed the analogs of quantum mechanical states, constructed from vacuum states using creation operators. For spinor fields, these creation operators create states with ...
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Path Integral Measure Transformation as $(DetU)^{-1}$
Grassmannian integrals satisfy (this is a definition)
$$
\int d \theta \theta = 1 \tag{1}
$$
Let $\theta' = A \theta$. Then,
$$
1 = \int d \theta' \theta' = \int d (A\theta) (A\theta) = A \int d (A\...
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