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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54 views

How to determine the sign of coupling constant in quantum field theory?

Experimentally, we determine the value of the coupling constant by measuring the scattering cross-section and compare it with the results calculated by the scattering amplitude. However, in the ...
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Overall constant for the scalar propagator in AdS background

I am trying to solve Exercise 3.3 in TASI Lectures on AdS/CFT by João Penedones. It is solving for the scalar propagator $\Pi(X,Y)$ in AdS, and states as follows: $$ \begin{align} \frac{1}{2} J_{AB}J^...
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51 views

Why is the operator ${\cal O}_k(E_k,z_k,\bar{z}_k)$ in the celestial sphere written in this form?

I have one probably very silly confusion about a footnote in the paper "2D Kac-Moody symmetry of 4D Yang-Mills theory ". In section (4) the authors consider ${\cal O}_k(E_k,z_k,\bar{z}_k)$ ...
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$\varphi^4$ via renormalization group with hard cut-off

I am studying the application of the renormalization group to the $\varphi^4$ theory: $$\mathcal{L} = -\frac{1}{2} \varphi (\Box + m^2)\varphi -\frac{\lambda}{4!}\varphi^4.$$ In particular I wanted to ...
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58 views

Vacuum polarization or electron with structure?

Is it possible to construct some charge density $ρ(r)$ to get the Uehling-Potential? $${\displaystyle V_{\text{Uehling}}(r)\approx -Z\alpha \hbar c{\frac {1}{r}}\left(1+{\frac {\alpha }{8\pi ^{2}{\...
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Does this is an onshell propagator?

This image is from here (page 6-7). My question refers to Eq. 26 and 27 The denominator changed from $(p_1 -p_3)^2 - m^2$ to $p_3^2 - 2p_3p_1$. So they used $p_1^2 = m^2$. But I thought, this relation ...
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How to calculate the path integral (or partition function) of a set of phonons with continuous frequencies?

I have a system of phonons with continuous frequencies so that the Hamiltonian of this system is $H=\int_0^{k_0} h(k) a_k^\dagger a_k \mathrm{d}k$. How do I calculate the partition function of this ...
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In/out states in scattering theory, Weinberg vol 1

Chapter 3 of volume 1 of Weinberg's QFT says the following regarding in and out states in scattering theory: Implicit in the definition of the states is a choice of the inertial frame from which the ...
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Is The Seiberg-Witten Map Unique?

From my understanding the Seiberg-Witten map is a way to convert a non-commutative field theory into a commutative field theory. For example for the commutative relation between positions $[x, y]=i \...
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How is Schwinger's quantum action principle related to least action?

The principle of least action says that a body moves in such a way that the action value $S=\int L dt$ is stationary (often minimal). The principle is written as $$\delta S =0 \ .$$ In contrast, ...
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Quantum Optics Question Involving Coherent States

Given the quantum-optics coherent states $|\alpha \rangle = \exp \Big(-\frac{|\alpha|^2}{2}\Big) \sum_{n=0}^{\infty} \frac{\alpha^n}{\sqrt{n!}} |n \rangle$ Show that $\langle (\Delta X)^2 \rangle_{\...
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Fermions from lattice model

In TASI Lectures on Emergence of Supersymmetry, Gauge Theory and String in Condensed Matter Systems from lattice Hamiltonian, which describe fermions on honeycomb lattice: $$ H_f = -t_f \sum_{\langle ...
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Perturbative expansion and self-contractions in functional integral

Consider a one-dimensional integral $$I(g)=\int dx\, e^{-x^2-gx^4}$$ One can formally expand it perturbatively order by order in $g$ so that $$I(g)=\left<1\right>-g\left<x^4\right>+\frac{g^...
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Uncertainty principle from QFT

Is it possible to derive uncertainty principle from QFT? Which kinds of perturbation (particles, monopoles, ...) are rule out by this principle?
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$1+1D$ $U(1)$ gauge theory is a quantum mechanical system

In article Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory there is statement (page 13): Ordinary $1 + 1$-dimensional $U(1)$ gauge theory is effectively a quantum ...
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Stability and topological charge of kink (anti-kink) solutions (soliton)

I am reading the book << Gauge theory of elementary particle physics >>. In chapter 15, it presents a model having finite-energy solution. First, we have a $1+1D$ spacetime model \begin{...
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Solving the Poisson-Schrodinger equations numerically

I need to find the solution to the Poisson- Schrodinger equation in the newtonian approximation, which are basically coupled differential equations given by: \begin{equation} \nabla^2 V=8\pi G M^{2}\...
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Conformal field theory in 2 dimensions and Riemann sphere

In many introductory textbooks on conformal field theories in two dimensions, the flat Euclidean manifold $\mathbb{R}^2$ is considered. Later, when the global conformal transformation is derived, $\...
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Why is Gell-Mann and Low theorem valid only for non-degenerate non-perturbed states?

Second the Gell-Mann and Low theorem, if a quantum system has a hamiltnian $H = H_{0} + V$, and $H_{0} | \Phi_{0} \rangle = E_{0} | \Phi_{0} \rangle$, then the following quantity $$ | \Psi \rangle = \...
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Time reversal symmetry implies that fermions are massless?

In TASI Lectures on Emergence of Supersymmetry, Gauge Theory and String in Condensed Matter Systems some continuous limit of lattice model with fermions considered. And on page 6 there is a statement: ...
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Textbook for parton distributions?

Are there any textbooks, or good pedagogical review articles, on the subject of parton distributions? I'm looking for such sources that cover all the standard topics, such as: Generalized parton ...
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What is the form of a many-body hamiltonian that are subject to the measurement of the position?

Suppose there is a $N$ body hamiltonian, suppose $N=2$ for simplicity: $$ H = - \frac{1}{2} \nabla_1^2 - \frac{1}{2} \nabla_2^2 + V(r_1,r_2) + \frac{1}{|r_1 - r_2|}. $$ If we make a measurement for ...
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What is the flavour problem? In particular the leptonic flavour problem

I'm studying from these lecture notes by S. Pascoli. She mentions several times the leptonic flavour problem but she never actually defines it. I've looked a bit online but I only found vague ...
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What does it mean for an extended operator to possess “local excitations”?

In the context of defect conformal field theory, we consider in operator product expansions "local excitations" of the defect (see e.g. text between eq. $(1.1)$ and $(1.2)$ in the paper ...
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Where does this formula for normal ordering in QFT come from? [duplicate]

On this Wikipedia page you can find the following equation for free fields $$:\phi(x)\chi(y):=\phi(x)\chi(y)-\langle0| \phi(x)\chi(y)|0\rangle\tag{1}$$ But I don't understand where this comes from ...
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110 views

Is virtual particle a relativistic or non-relativistic effect?

A virtual particle is defined to be the internal line in a Feynman diagram which usually mediates force. I'm wondering if it's a pure relativistic effect? If the system is non-relativistic (quantum ...
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33 views

Experimental foundation of particle number conservation

How can we prove that the charge is conserved in particle experiment? Or lepton and baryon conservation. I think it is easy to say that the charge is conserved, but might be hard to measure. I guess ...
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34 views

Physical intuition for spatially constant motion in the XY-model in 2+1D

The XY-model on a 2-torus ($L_1,L_2$) has a lagrangian given by $$ L_{XY}[\theta] = \int d^2 x \frac{\chi}{2}\big{(}\dot{\theta}^2 - (\partial_x \theta)^2\big{)} $$ Fourier expanding $\theta$ as $$ \...
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58 views

Suppression of $W$ boson propagator by its mass

In my experimental particle physics introductory class it was often said that quantum electrodynamics (QED) is very predictive for sufficiently small center of mass energys since the $W^\pm$-...
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In general, do critical points of continuous phase transitions have $\beta =0$?

Consider a phenomenological modelling of a continuous phase transition, where the Lagrangian of the system is given by $$L=\frac{a}{2}\phi^2+\frac{\lambda}{4}\phi^4-h\phi.$$ Here $\phi$ is the order ...
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What is a fracton? [closed]

Recent, in articles on QFT and condensed matter new objects appear -- fractons. As I understand now, fracton is a particle with restricted motion: for example, such excitations can move only along ...
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Non-supersymmetric CFT in $d=4, 5, 6$

There's no known interacting CFT in $d>6$, see Interacting CFT in $d>6$ Also we know a lot CFT in $d=2$ (minimal models for example) and in $d=3$ (WF fixed points in $4-\epsilon$ approach to ...
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Mass in Wilsonian RG (vs. mass in ordinary RG)

The essence of Wilson RG can be described in tree steps: Initially we have some theory on scale $\Lambda$. Lower cut-off $\Lambda^\prime =\zeta^{-1}\Lambda<\Lambda$ and integrate out d.o.f. with $\...
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1answer
43 views

How to measure gauge boson?

note that it's taught that in standard model particles that mediated weak interaction force are gauge bosons: vector particles, spin 1, take one charge. I'm wondering how to prove these properties in ...
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56 views

Mass terms for scalar lagrangians?

First off, a pre-question: if I got this wrong, then probably the whole reasoning is wrong as well. Studying the lagrangian for a two-particle scalar field with a quartic interaction in the context of ...
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Emergent supersymmetry in tricritical Ising model

In TASI Lectures on Emergence of Supersymmetry, Gauge Theory and String in Condensed Matter Systems there is a statement that 2d supersymmetry can can emerge from the dilute Ising model: $$ \beta H = ...
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Does Goldstone theorem have anything to do with Cosmic string

Cosmic strings are formed due to topological defects during symmetry breaking phase transition in early universe. While Goldstone theorem states whenever we have continuous symmetry and it is ...
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25 views

Confusion among channel $u$ and channel $t$ in exclusive reactions

In the this paper (https://arxiv.org/abs/1203.4392), on page 2 it is said that Since DVCS amplitude is symmetric under $s \leftrightarrow u$ channel crossing, the CFFs and $^{S}C^i_{\cdots}$ ...
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A problem in IR expansion of the effective field theory

On page 43 of Manohar notes on effective field theories, he argues that since all the integrals in EFT are scale less when expanded in terms of the IR parameter, they all vanish. To me it seems ...
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${\rm SU}(5)$ doublet-triplet splitting problem and disagreement with phenomenology

The statement from Wikipedia about ${\rm SU}(5)$ Georgi–Glashow seems very puzzling to me. Here are the text from https://en.wikipedia.org/wiki/Georgi–Glashow_model#Decomposition: It is the Higgs ...
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Does anyone know how the equation was derived from the given conditions?

When the operators are multiplied together, the term f(hw)g(hw)aa or f*(hw)g*(hw)aa will be kept. But why those terms disappear in the Green function given below?
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Interacting CFT in $d>6$

There's an expectation that there aren't interacting CFT in $d>6$. As I understand, main reason for this is due to the scaling dimension of ordinary scalar fields and Dirac fields. This lead to ...
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Summing over disconnected diagrams - Peskin and Schroeder

In Peskin & Schroeder, page 97, the following expression is given as part of the demonstration of how the $n$-point correlation function is calculated using connected diagrams: $$\sum_{\text{...
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Scattering in QM/NRQM vs QFT

As discussed in this question: How does a wave packet get scattered? And shown in, for example, this video: https://www.youtube.com/watch?v=iq4lGVznr_8 In quantum mechanics particles are scattered due ...
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How does the pion decay constant $f_{\pi}$ depend on the number of flavors $N_f$?

I know that for standard QCD with quarks, chiral symmetry breaking occurs for around 4 - 5 light/active quarks - i.e. pions, or generally pseudoscalar goldstone bosons, definitely appear in the ...
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Singularities in gauge-fixing conditions and topological defects

I am studying the 't Hooft's paper "Topology-of-the-gauge-condition-and-new-confinement" https://doi.org/10.1016/0550-3213(81)90442-9 and there are several points which I would like to ...
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${\cal N}=2$ (Poincaré) supergravity in three dimensions

I cannot find any references where the off-shell algebra of ${\cal N}=2$ supergravity in $D=3$ dimensions is given. From the study of the (massless) representations of ${\cal N}=1$ supersymmetry, I ...
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Recombination phenomena in CFT

Now I study very interesting lectures Superconformal symmetry and representations and I face some statements, which are unclear to me. In unitary CFT there are unitary bounds for dimensions of ...
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18 views

What is the lifetime of the deuteron with respect to sphaleron-induced decay

As far as I've understood, instantons like the sphaleron can give rise to processes that violate $B+L$ but conserve $B-L$, where the baryon and lepton number can only change by a multiple of three. ...
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61 views

Correlation length and renormalization group

In Scaling and Renormalization in Statistical Physics there's following block of information: I have some misunderstanding of some ideas. 1) How to define correlation length for arbitrary theory? I ...

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