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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Gromov-Witten invariants

I'm a mathematician studying Schubert calculus, and I'm out to compute the Gromov-Witten invariants of the complete flag manifold. Well, I actually already know how to compute them, but only in a way ...
2
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1answer
59 views

Different OPE channels in bootstrap

Can someone quickly explain what exactly are those different channels (namely s,t,u) in OPE expansions frequently used in conformal bootstrap. Explanation with a simple example will be really helpful. ...
3
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1answer
162 views

How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?

I came across the S. Coleman's seminal papers 'Fate of the false vacuum' (http://dx.doi.org/10.1103/PhysRevD.15.2929, http://dx.doi.org/10.1103/PhysRevD.16.1762) where he describes the tunneling ...
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0answers
39 views

What are the definitions and the differences between string “background” and string “vacuum”?

In cosmology one studies perturbations around FRW metric classically (pure GR, we say that we perturbe the FWR "background"). In QFT we have perturbation theory quantistically (we expand around a ...
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101 views

What do quantum theory and general relativity have in common? [closed]

What areas of commonality are there between quantum theory and general relativity? Is it even possible to use the the two when calculating the same physical behaviour? Is there a correlation between ...
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48 views

What is the relationship between the “mass” of QFT and that of Newtonian mechanics?

In QFT we work with Lagrangians which contain terms $m$ such that the relativistic relation $E^2 = p^2 + m^2$ is satisfied. By classical analogy $m$ is called the 'mass'. We note that due to the ...
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1answer
55 views

Wightman function for massless vector fields in Coulomb gauge

I've been looking for quite some time an expression for the Wightman functions for a massless vector field in the Coulomb gauge $\nabla\cdot\mathbf{A}=0$ (I think it is equivalent to the Feynman gauge ...
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0answers
35 views

Can the Higgs mechanism provide complex masses for quarks and neutrinos?

Can the Higgs mechanism give complex masses to quarks and neutrinos, or is only real mass generation possible? There exist complex phases in the CKM and PMNS matrices, can they be explained through ...
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38 views

QFT decay rates in lower dimensions

My starting point is the decay of a Higgs particle into two fermions, with decay rate proportional to \begin{equation} \Gamma \propto g_\psi^2 N m, \end{equation} where $g_\psi$ is the coupling, $N$ ...
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17 views

Directional propagator for Gaussian single photon emitters

I am generating photons along a vertical line in 2D space (say along the x=0 line) at spatial coordinates $x = (x_1, x_2, ..., x_n)$ by the following means $\hat{a}^\dagger(x_1)\hat{a}^\dagger(x_2) ...
2
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0answers
99 views

Number of distinct Feynman Diagrams for different orders of $\phi^4$ theory for 2 point function

There is 1 distinct Feynman diagram for zeroth order and 2 distinct diagrams for first order in $\phi^4$ theory for two point function. I want to know is there a way to predict the number of distinct ...
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0answers
79 views

How to calculate scattering amplitude from lagrangian? (quantum field theory)

I'm doing a question in Mark Srednicki's Quantum Field Theory. (Question 10.5) Which says that, when one changes a free field $\phi$ to $\phi + \lambda\phi^2$, the Lagrangian density would include an ...
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0answers
32 views

Cyclicity of trace with fermionic arguments

I think this is a non-question, but it has me considerably worried. Consider the piece of a Lagrangian density given by, $$\mathcal{L} = ...
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0answers
16 views

How to obtain the quantum field-theoretic Hamilton equations

I'm trying to prove the following equation: [$H$, $\Phi (t,\textbf{x})$]=-$i \frac{\partial \Phi(t,\textbf{x})}{\partial t}$ with $\textit{H}$ the complex Klein-Gordon Hamiltionian: ...
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0answers
62 views

How to Fourier transform creation/annihilation operators?

Zee's QFT in a Nutshell pages 65-66. For a complex scalar QFT $$ \varphi(\vec{x},t) = \int\frac{d^Dk}{\sqrt{(2\pi)^D2\omega_k}}\left[a(\vec{k})\mathrm{e}^{-i(\omega_kt-\vec{k}\cdot\vec{x})} + ...
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0answers
78 views

Is this an error in A.Zee's 《Quantum Field Theory in a Nutshell》?

I am reading A.Zee's 《Quantum Field Theory in a Nutshell》 page 44. He is trying to evaluate $Z(J)=\int_{-\infty}^{+\infty}dq e^{-\frac{1}{2m^{2}}q^{2}-\frac{\lambda}{4!}q^{4}+Jq}$ Of the term ...
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1answer
56 views

Momentum operator derivation in QFT from QM

In David Tong`s QFT notes there is a chapter about the derivation of the momentum operator from quantum mechanics (page 44) where he is showing that the momentum operator can be expressed by the ...
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1answer
76 views

$SO(N)$ symmetric theory of $N$ real scalar fields, why do charges have correct commutation relations of generators?

Consider an $SO(N)$ symmetric theory of $N$ real scalar fields,$$\mathcal{L} = {1\over2} \partial_\mu \Phi^a \partial^\mu \Phi^a - {1\over2} m^2 \Phi^a \Phi^a - {1\over4} \lambda(\Phi^a ...
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0answers
61 views

How should the path integral change under a dilation?

Let's say I have a two-point function of a scalar field in flat space: $$ \langle \phi(x)\phi(y)\rangle = \int \mathcal D \phi \, \phi(x)\phi(y)\,e^{iS[\phi]} $$ Then I dilate things: $$ \langle ...
0
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1answer
73 views

Do different creation/annihilation operators always commute?

In a complex (non-hermitian) scalar QFT, is it correct that the creation/annihilation operators $a,a^\dagger$ (particle) and $b,b^\dagger$ (anti-particle) commute, i.e. $[a,b] = [a,b^\dagger] = ...
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20 views

Scalar fields of different masses and Bogoliubov coefficients

Suppose we have scalar field $$ \hat{\theta} = \sum_{k}\left( \varphi^{+}(t)\hat{A}^{\dagger}_{k}e^{ikx} +e^{-ikx}\varphi^{-}\hat{A}_{-k}\right) $$ with time-dependent frequency: $$ ...
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3answers
85 views

Why is this proof that all $\overline{\psi}\psi\overline{\psi}\psi$ interactions are trivial incorrect?

This is a homework question for my quantum field theory class. I haven't been able to figure out the answer, and neither has anybody I asked. The homework was due two days ago. Consider a spinor ...
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92 views

How do I get the amplitude for the one-loop photon self-energy?

I am studying Maggiore's book on QFT and I am stuck in the amplitudes of one-loop corrections in QED. Could someone clearly explain me how do I get the following amplitude from the respective diagram? ...
3
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1answer
52 views

References on Current Algebra

Although current algebra is out of usage from what I hear, I think I see lots of papers (especially dealing with strong interactions) with transition amplitude written with the currents (this is based ...
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1answer
46 views

Is the scalar field operator self-adjoint?

In A. Zee's QFT in a Nutshell, he defines the field for the Klein-Gordon equation as $$ \tag{1}\varphi(\vec x,t) = \int\frac{d^Dk}{\sqrt{(2\pi)^D2\omega_k}}[a(\vec k)e^{-i(\omega_kt-\vec k\cdot\vec ...
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2answers
73 views

Complex scalar field theory

For the complex scalar field theory $$L = -\partial_{\mu}\phi^{*}\partial_{\mu}\phi - m^{2}\phi^{*}\phi + J\phi^{*}+J^{*}\phi,$$ Why is there no factor of 1/2 in the lagrangian like in the real ...
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2answers
233 views

What is meant by fermionic and bosonic “modes”?

The paper The Dirac quantum automaton: a short review (pdf) starts off by stating: The starting point for the construction of space–time and the physical laws therein is an unstructured, countably ...
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2answers
395 views

Is the many-worlds interpretation (MWI) of QM inconsistent with quantum field theory

I had recently posted a question on the Philosophy stack exchange about "true" randomness, and a lot of the discussion centered around Quantum Mechanics. One of the responders claimed: MWI has the ...
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0answers
41 views

Combinatorics of fourth order feynman diagram

I am trying to calculate how many different forth order feynman loop diagrams I can produce. I know that for 2nd order it is 6x3x2 thus 3! since you start with 3 lines coming out of each vertex so 6 ...
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48 views

Why does a Gauge group have to be a compact Lie group? [duplicate]

In Topological Solitons by Nicholas Manton where he considers "compact Lie groups" to be the gauge groups for generalizing gauge theoretic concepts. But, he does not mention why that condition is ...
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3answers
763 views

If an electron is an excitation of the electron field, what causes the excitation to be stable?

I won't pretend I understand even the basics of QFT, but from what I've heard about electrons, there are really two main ways of thinking about them. Quantum Mechanics describes an electron by a wave ...
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0answers
109 views

How are bound states handled in QFT?

QFT seems very well suited to handle scattering amplitudes between particles represented by the fields in the Lagrangian. But what if you want to know something about a bound state without including ...
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0answers
56 views

Propagator for fermion fields and Feynman diagrams

I need some help concerning the interpretation of propagators and Feynman diagrams. The free fermion propagator is given by the contraction of two fields $\psi(x),\bar\psi(y)$: ...
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218 views

Peskin-Schroeder Problem 3.5, supersymmetric theories regarded as field theories on parameter space w/commuting & anticommuting coordinates?

I know how to do Problem 3.5 of Peskin-Schroeder. Let us organize the fields $\phi$, $\chi_\alpha$, $F$ of Problem 3.5 into a superfield$$\Phi(x + i\theta\sigma\overline{\theta}, \theta) = \phi(x) ...
8
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1answer
365 views

Renormalization group resummation

I'm having trouble in understeanding a mathematical feature of RG, namely how it provides a way to resum the perturbation series and how that's defined mathematically. From a conceptual point of view ...
0
votes
3answers
74 views

In, QFT, do the excitations in the quantum fields exist physically? [closed]

In QFT, all particles are really just excitations in their quantum fields, and we know that these fields are just mathematical.For example, an electron is an excitation of the electron field. But my ...
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2answers
92 views

How does quantum mechanics and quantum field theory explains discrete energy levels of particles?

Please give me a brief explanation as to how qm and qft describe and explain the energy level that exist in an atom. I understand that in QM energy state is quantized but does not offer an ...
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0answers
35 views
0
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0answers
92 views

u-Channel Matrix element for electron-positron annihilation

This one is a quantum related question. The calculation relates to the Matrix element for the annhilation of a electron-positron into two photons: $$ e^-e^+\rightarrow\gamma\gamma $$ I've recently ...
2
votes
1answer
65 views

How can parity be meaningful in an affine space?

I've recently begun a course in QFT (within a Physics Master's), and despite (admittedly limited) reading I can't get my head round the idea of parity. Here's what I think I understand: the Minkowski ...
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vote
1answer
84 views

Does “sum over all paths” in the path integral imply “sum over all paths” in momentum space when one Fourier-transforms?

How is the Fourier-transformed-field path integral interpreted? Is it still a "sum of all paths" in momentum space? Just that with another action? Consider for instance the (Euclidean) partition ...
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0answers
36 views

QFT with fixed boundary conditions

I am looking for references on the formulation of QFTs with fixed boundary conditions for the fields (typically $\phi(0)=\phi(L)=0$), and especially how to construct the corresponding perturbative ...
0
votes
3answers
170 views

How can quantum wavefunctions be smooth/continuous when particles are created/destroyed/changed?

My (admittedly limited) understanding of the Schrodinger equation tells me that the vector differential operators are only meaningful over a differentiable phase space. For example, if the dimensions ...
0
votes
1answer
225 views

Simple QFT simulation - how to do it

I would like to write a simple QFT simulation for a free scalar field with a cubic interaction term. However, I got stuck a bit. I will try to describe what I think I understand. I want to have a ...
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1answer
89 views

Is a Feynman diagram depicting a vacuum bubble “that gets real” valid?

In exercise I.7.3 of A. Zee's QFT in a Nutshell, we have to draw all the Feynman diagrams of the scalar theory $$ Z(J) = \int D\varphi e^{i\int d^4x\{\frac ...
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1answer
74 views

A question on using Fourier decomposition to solve the Klein Gordon equation

Given the Klein Gordon equation $$\left(\Box +m^{2}\right)\phi(t,\mathbf{x})=0$$ it is possible to find a solution $\phi(t,\mathbf{x})$ by carrying out a Fourier decomposition of the scalar field ...
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0answers
82 views

Topology and Quantum Field Theory

I am interested in finding any one particle state $\left| \Psi \right>$, mostly possibly topological in nature like a kink, such that $$ \left< VAC | R \widetilde{R} | \Psi \right> \neq ...
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1answer
122 views

Propagator and probability amplitude that a particle propagates

My QFT knowledge has very much rusted and i got confused by these few lines from Peskin and Schroeder: p.27: " [..] the amplitude for a particle to propagate from $y$ to $x$ is $\langle 0| \phi(x) ...
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0answers
20 views

FESR: Relation Between Total Cross Section and Spectral Function

In the papers I am reading the total cross section of electrons, positron scattering into hadrons can always be written in terms of an integral of a weight function w(s) and the spectral function ...
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1answer
105 views

Zee's Nutshell: Feynman diagrams “baby problem”: Connected vs. Disconnected

On page 47 of A. Zee's QFT in a Nutshell, he explains how disconnected Feynman diagrams can be built from lower-order connected diagrams: I don't know how to understand formula $(6)$. I understand ...