Questions tagged [quantum-field-theory]
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 this tag for many-body quantum-mechanical problems and the theory of particle physics. Don’t combine with the [quantum-mechanics] tag.
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Transition Amplitude
Question referring to this question
Transition Amplitude in Free Field Theory
The previous person shows an example with a two particle to one, what would happen if we were to get more particles out, ...
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The emergence of space-time from entangled states
I recently read an article by Yasunori Nomura (https://arxiv.org/abs/1711.05263), in which he says that space-time is an emerging phenomenon. At the same time, space-time disappears when the ...
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Change in vertex factors for inverse process
Recently I have started learning the "Effective Field Theory". As a part of learning, I was trying to calculate the vertex factor for a process where two unknown neutral spin-1 bosons $Y$ ...
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Matrix Element in QFT - Sign of Terms When Swapping
Let's consider the process $e^{-} \ (p_1) \ \mu^{-} \ (p_2) \rightarrow e^{-} \ (p_3) \ \mu^{-} \ (p_4)$. In our scriptum, we proved that the matrix element for this process is
$$i\mathcal M_{fi} = \...
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Integrating amplitude for electron scattering from Coulomb potential
I am following Zee's QFT book in Section II.6. I have found the amplitude for an electron to scatter from a static Coulomb potential as
\begin{align*}
\mathcal{M}&=ie\!\int\!d^4x\,\big\langle ...
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(Anti)commutation of creation and annhilation operators for different fermion fields
The Fourier expansion of the fermion field operator is such that
$$ \hat\psi=\int\!d^3p\,\left[ f_b(p)\hat b(p) +f_d(p)\hat d^\dagger\!(p) \right] ~~, $$
for some sufficiently complicated $f_b$ and $...
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Measurements, QFT and Wightman's axiom 3
I think I might have misconceptions about the conceptual core of QFT. Let me explain where I am puzzled.
In QM, the measurement process is accounted by the postulate of collapse of the wave function: ...
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About the steps in a book about Quantum Field Theory [duplicate]
I have a question about the steps in the book "An Introduction To Quantum Field Theory" By Peskin & Schroeder.
In page 213, i don't understand why the $e^{iPx}$ before the $<\Omega|$ ...
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Question about Weinberg-Witten theorem
From Weinberg-Witten theorem, people say that the graviton (which has spin 2) can not be composite. But it seems that graviton can still be composite particle by combining spin-3/2 particles. Is ...
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Use of Cauchy's integral formula in the derivation of the Feynman propagator
In deriving the Feynman propagator in Timo Weigand's 2014 QFT2 notes, at the top of page 37, (equation 1.170), we use Cauchy's integral formula:
$$g(z_0)=\frac{1}{2\pi i}\oint_{C_1}\frac{g(z)}{z-z_0}\...
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Wilsonian Renormalization in Curved Spacetimes
One way of seeing the Wilsonian renormalization in flat spacetimes is to consider a quantum field theory in a lattice, where the spacings between the lattice elements depend on the energy scale under ...
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Electron scattering from Coulomb potential in canonical formalism
I am trying to follow Zee's computation of the amplitude for the pictured process. I have already done it using the Feynman rules for writing amplitudes and now I am confirming the result in the ...
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Why must there always exist a real particle with the same mass of the virtual particle of a certain force field?
I've tried to ask this question before, but I've never quite got a satisfying answer so I'm going to simplify my question.
As I understand it, virtual particles are just 'internal legs of a Feynman ...
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Formation of hydrogen atom by electron proton collision [duplicate]
Suppose we have an electron $e$ and a proton $p$ colliding to form a hydrogen atom that is the reaction
$e+p\rightarrow H + \gamma$ where $H$ is an hydrogen atom and $\gamma$ is some photon.
The ...
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Tunneling in quantum field theory
Tunneling in QM is well defined phenomenon since for a real potential the number of particles remain constant. But when we switch to field theory the number of particles need not to remain constant ...
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Does microcausality plus the time-slice property imply local primitive causality?
In quantum field theory, observables are associated with regions of spacetime. One of the basic principles of relativistic quantum field theory is microcausality, which says that observables ...
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Fermionic Version of the effective Action
For a scalar field theory one introduces the partition function with external sources
$$
Z[j] = \int \mathscr{D} \varphi \, \exp \left( -S[\varphi] + \int j \, \varphi \right) \text{,}
$$
the analogon ...
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Amplitude for electron scattering off structureless stationary nucleon
In Zee's QFT book, Section II.6, he gives the amplitude for this pictured process of an electron scattering from a structureless nucleon as
$$ \mathcal{M}(P,P_N) = \cfrac{-ie^2}{k^2-m_\gamma^2} \,\...
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One-loop exactness of self-dual Yang-Mills theory
The self-dual Yang-Mills theory (gauge group $G$) with the action:
$$
\mathcal{S} = \int_{M} \text{Tr} (B^{+} \wedge F)
$$
where $B^{+}$ is a self-dual field, transforming in the adjoint ...
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What does Art Hobson mean/explain in his article "There are no particles, there are only fields" regarding the double slit experiment?
So I have been reading about fields in physics. I am reading Art Hobson's "There are no particles, there are only fields" published in The American Journal of Physics in 2013, and I am ...
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Integrating out bosons/fermions when the action is quadratic
Arovas and Auerbach, in their paper titled "Functional integral theories of low-dimensional quantum Heisenberg models" try to compute the free energy of $SU(N)$ models with the large $N$ ...
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Meson operator treated as an elementary field in effective action?
I have seen in many papers, with this as the earliest example I can find, that the meson chiral order operator $M_j^{\,\,\,i}(x)=\overline{\psi}^i(1+\gamma_5)\psi_j(x)$ is treated as an elementary ...
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Are unstable particles created with an exact mass, or masses distributed in resonances?
I'm pretty comfortable with QFT, but this is a conceptual point I feel shaky on. For example, when creating $Z$ bosons in a process like $e^+ e^- \rightarrow Z Z \rightarrow f^+ f^- f^+ f^-$, the $Z$ ...
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Why commutator of positive and negative parts of scalar field is equal to the Feynman propagator?
Peskin & Schroeder state that the contraction of two fields, defined as the commutator:
$$ [\phi^+(x),\phi^-(y)]\qquad \text{assuming}\ x^0>y^0$$
is equal to the Feynman propagator $D_F(x-y)$. ...
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IR Wilson-Fisher fixed point
I was wondering how we define IR-fixed point, when we have more then one coupling.
When the coupling is unique, it is simple, because we can look at the beta function of the coupling and determine ...
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Feynman diagram for the 2-point one-loop 1PI diagram
If I have the $\phi^3$-interactive theory. How can I draw the Feynman diagram for the 2-point one-loop 1PI diagram?
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How to understand the negative specific heat of a massless Majorana fermion in one dimension?
Let us consider a massless Majorana fermion on a ring of length $L$ with a periodic boundary condition at a temperature $T$.
Then the conformal field theory calculation tells us that the quantum ...
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Harmonic oscillator in QFT
Given a single bosonic mode with frequency $\omega_0$, such that $\hat{H}=\hbar\omega_0(\frac{1}{2}+\hat{a}^{\dagger}\hat{a})$ how should one show the equivalence between the coherent state path ...
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Unruh particles
When we accelerate, an event horizon forms behind us resulting in Unruh radiation. In this kind of scenario, the existence of the radiation particles themselves is observer dependent.
My question is: ...
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Vacuum space has mass/energy?
It is said that vacuum spaces contain particles and antiparticles, my question is if so whether empty space has mass/energy?
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Question about vacuum state of fields in Quantum Field Theory
Are the fields in their empty state a single indivisible and static entity? I would also like to know if the gravitational field also has a vacuum state and if the other fields are permanently linked ...
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Could we have a position-independent picture for quantum fields?
Here's what I understood. In quantum mechanics, there is two equivalent of treating time:
Scrödinger's picture where operators are time-independent and states are time-dependent.
Heisenberg's ...
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Is spin associated with rotations or boosts?
EDIT:
It seems that I made an error and it was $S^{ij}$ that was used after all. I will not delete the question though because even though it is erroneous, the answer given below is rather insightful.
...
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QCD quark self-energy, is the propagator momentum in the right direction?
For the quark self-energy diagram the amplitude is giving by:
The fermion propagator is given by $\frac{i}{\not p + l}$ in the lecture. It is not supposed to be $\frac{i}{\not p - l}$? It's seems ...
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Derivative interaction of scalar fields
I'm studying derivative interactions and I'm trying to gain a better intuition for the formal process of arriving at the vertex factor. In particular, I'm trying to evaluate the vertex factor ...
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Matrix element of the currents associated with the broken generators between the vacuum and Goldstone's bosons
Let $G$ be a Lie group and $L^i$ the generators of this group. Suppose we have $L^{j}|0\rangle \neq 0$ where $|0\rangle \neq 0$ denotes the vacuum. If $G$ is associated with a symmetry of the ...
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Unruh effect: should Minkowski vacuum transform according to different observers?
It's known that the Minkowski vacuum is observed as a thermal bath for Rindler observers, in paticular:
$\langle0_{M}|N_{M}|0_{M}\rangle=0 \space\space\space\space\space\space\space $ (1)
$\...
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Quantum Field Theory, questions about fields and their vacuum state [closed]
Are the fields in their empty state a single indivisible and static entity? I would also like to know if the gravitational field also has a vacuum state and if the other fields are permanently linked ...
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0
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Derivation of matter potential from QFT
I'm trying to derive the matter potential as experienced by neutrinos from QFT. The paper I am looking at is unfortunately not publicly available online (https://doi.org/10.1103/PhysRevD.40.259) and ...
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Why, when you eject an electron from a metal, do you get exactly one electron and not part of an electron?
Let's assume you have a metal with an electron sea so the electrons are very delocalized. The electrons are described by some wave function
$$\Psi(\vec x_1,\dots,\vec x_N).$$
Now an electron is ...
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Wick's time ordering operator
I am working on Wolfgang Nolting's . And I feel confused about the time ordering operator.Below is how he introduced the Wick's time ordering operator.
My understanding is that the $\epsilon$ in the ...
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Why is an RG fixed point scale invariant?
I cannot understand why people say RG fixed point is scale invariant.
Scale invariant means the action $S[\phi]$ of the theory is invariant under scale transformation like $\phi(x)\to\lambda^{-\Delta}...
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Path integral formulation for Green's functions
In the first place, I am struggling when trying to derive the path integral formulation of the Green function for non-interacting particles
$$G_{ij}(\tau)=-\frac{1}{Z}\int D(\bar{\psi},\psi) \psi_i(\...
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How to use principal value in propagator definition?
The propagator for a scalar particle can be written as
$$
\frac{1}{x + i\epsilon} = {\rm PV}\left( \frac{1}{x} \right) - i\pi\delta(x), \quad x = p^2 - m^2, \tag{1}
$$
where $p, m$ are the momentum ...
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Is this measure employed in the Faddeev-Popov procedure related to the Haar measure?
In the Faddeev-Popov procedure one defines the Faddeev-Popov determinant through the formula $$\int {\mathcal{D}\alpha \ } \delta\big[G(A^\alpha)\big]\Delta[A]=1,\tag{1}$$
where $G(A^\alpha)$ is the ...
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Adjusting the rate of proton decay in the standard $\rm SU(5)$ grand unified theory
The proton decay rate in the standard $SU(5)$ grand unified theory is given by
$$
\Gamma \sim \left(\frac{g^2}{M_x^2}\right)^2 m_p^5 =\frac{g^4}{M_x^4}m_p^5
$$
Naively we could push up the bound for ...
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Dual Bra of the ground state of interacting theory
I'm currently reading Peskin's "An introduction to Quantum Field Theory", but I'm stuck on page 87; I don't understand why he gets such a Bra for the vaccum state of the interacting theory, ...
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Effective Field Theory vs Ostrogradsky
The low-energy effective description of a given QFT is an expansion of the form
$$
\mathcal L_\mathrm{IR}\sim\sum_{n,m} \lambda_{n,m}\phi^n\partial^ m\phi
$$
where we include all terms that are ...
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1
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Reference request for Effective field theories
Situation
I've taken a course on QFT, covering canonical quantization (of the scalar, EM and Spinor fields), Feynman diagrams and rules, etc. --- it was your basic one-semester introduction to QFT.
I'...
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Does the concept of a "momenton" make sense?
Looking at the QED-Lagrangian
$$\mathcal L = -\bar\psi(\not\!p + e\not\!\!A + m)\psi -\frac14 F_{\mu\nu} F^{\mu\nu} $$
I was wondering: While $\bar\psi\not\!\!A\psi$ describes the interaction between ...
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