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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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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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 ...
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61 views

AQFT: Can test functions obey the Klein-Gordon equation?

In AQFT we can choose test functions with compact support. Can such functions obey a Klein-Gordon equation? I start with a test function $g$ with compact support and I apply the Klein-Gordon ...
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89 views

Renormalization and Conway/Surreal Numbers

In the final chapter of his book "An Interpretive Introduction to Quantum Field Theory", Paul Teller writes about three interpretations of renormalization in quantum field theory. In particular, ...
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137 views

Why, in quantum field theory, is $\hat{a}(p)|0\rangle=0$?

My Quantum Field Theory lecturer just said that $\hat{a}(p)|0\rangle=0$ because the vacuum state contains no particles. Now, according to Wikipedia, "according to quantum mechanics, the vacuum ...
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Book for quantum field theory similar to Ballentine's quantum mechanics book [duplicate]

I have been studying quantum mechanics from Ballentine's book. I enjoy such books. I want somebody here to recommendation a book for qft with similar approach.
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75 views

Non-symmetry of a lagrangian

If a transformation $\Phi \rightarrow \Phi + \alpha \partial \Phi/ \partial \alpha$ is not a symmetry of the Lagrangian, then the Noether current is no longer conserved, but rather ...
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24 views

Writing the Interaction Hamiltonian for pions in a different way

$\pi^+$, $\pi^-$ and $\pi^0$ are scalars particles with masses approximately equals. Their interaction is, approximately, given by $H_{int}(x) = g \epsilon^{abe}\epsilon^{cde}(\phi^a\partial_\mu ...
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143 views

Do the partial derivative and the creation operator commute?

Does the partial derivative operator $\partial^\mu$ commute with the creation operator $\hat{a}^\dagger$? My notation here is \begin{equation} a_{\boldsymbol{p} }^\dagger|0\rangle=| ...
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161 views

How to Calculate Anomalous Dimensions in (Effective) QED

I am following the conventions here. Consider the (effective) QED Lagrangian ...
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25 views

Holographic dualities with a QFT with a mass gap

The original holographic duality AdS/CFT points to a conformal field theory in the boundary. CFTs do not have a mass gap and all mass spectra are allowed Are there any existing examples of ...
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92 views

Undergrad in QFT/GR looking to do string theory Ph.D [closed]

I am currently a third year undergrad in physics who is currently taking QFT and GR. I took these classes just out of pure interest in the subjects but I find that my mind is being blown almost every ...
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43 views

Visualizing Instantons?

Solitons (aka kinks) in quantum field theory, in an approximation where their internal structure can be ignored, can be visualized as particles. Namely their world line in a spacetime diagram will be ...
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25 views

Two point correlator : Dispersion Relation

Does anybody has a reference or an advice on how to derive the following idendity? \begin{equation} \Pi(s) = \frac{1}{\pi} \int_0^\infty \frac{Im \Pi(s')}{s' - s} ds' \end{equation} where $\Pi(s)$ is ...
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41 views

Proof of periodicity of Floquet Green's function

It is claimed in many papers that the two-time Green's function in time periodic Hamiltonian case is periodic in the average time, i.e. \begin{equation} G(t+T,t'+T)=G(t,t') \end{equation} when ...
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1answer
87 views

Resources for 2 Particle Irreducible (2PI) or Cornwall-Jackiw-Tomboulis (CJT) formalism

I'am currently learning the 2 particle irreducible (2PI) or Cornwall-Jackiw-Tomboulis (CJT) formalism. Does anybody know a textbook or a review that treats this subject? As far I only found the ...
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196 views

Bose-Einstein condensation and phase transition

I would like to ask the following question for which I cannot find a definite answer in the literature. Of what ORDER is the phase transition leading to Bose-Einstein condensation for a ideal and ...
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36 views

Solution of Dirichlet problem for scalar field in Ads

I am reading "Anti de Sitter space and holography" by Witten. In this article he derives the two-point function for CFT from theADS/CFT correspondence for a massless scalar field living in the bulk. ...
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149 views

Mathematical proof that $\exp(-1/|g|)$ is always related with formation of bound states through scales?

I know that this function ($g$ means coupling) is non-analytical in $g=0$, so this function is only appreciable under non-perturbative calculations, so is a non-perturbative phenomena. This function ...
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35 views

Supersymmetry breaking and normalizable zero modes

Why does supersymmetry always lead to normalizable zero modes? For example, it is stated in the paper by Michelson and Kaplan (http://arxiv.org/abs/hep-th/9510053) that we can assume, without loss of ...
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395 views

Is there any theorem that suggests that QM+SR has to be an operator theory?

UPDATE To make my question more precise, I'll define what I mean by an operator theory: An operator theory is a theory in which the dynamical objects are operators, i.e., the equations of motion ...
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1answer
78 views

Which definition of a quantum field is right?

In introductory quantum field theory, I was taught that, given a single-particle Hilbert space $\mathcal H$, the quantum field operator for that type of particle was a mapping $\varphi(x)$ from ...
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50 views

Simple question about vacuum fluctuations

Let's say I have an electron traveling alone in the vacuum, when a vacuum disturbance (fluctuation) occurs nearby. If the disturbance has the correct form, say, an electron-position pair, could the ...
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65 views

Distinguishing between left-handed and right-handed weak coupling from electron-neutrino scattering

This question comes from Schwartz's QFT book, exercise 13.6. In it we consider a coupling between fermions (neutrinos and electrons in this particular case) and the Z boson of the form $g_V \bar{\psi} ...
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191 views

Transferring between field and single-particle versions of the Dirac equation

We're covering spinors in QFT class. The Lagrangian (density) $\mathcal{L} = \overline{\psi} (i \gamma^\mu \partial_\mu - m)\psi$ gives the Dirac equation, $(i \gamma^\mu \partial_\mu - m)\psi = 0$. ...
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120 views

Feynman Diagrams Integral Calculation

Are there any easy tricks to calculate integrals of the form: $$\int d^4x \ e^{ikx} \dfrac{1}{x^2} \ \ (\text{ans:} \ i\dfrac{4\pi^4}{k^2}) \ \ \text{and} \ \ \int d^4x \ \mu^2 \dfrac{\ln ...
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54 views

Anti-commutation relation for the dirac field [closed]

The anti-commutation relation for the dirac field is: $$ \{\Psi_a(t,\vec x),\Psi_b^{\dagger}(t,\vec y)\}=\delta (x-y) \delta_{ab} $$ Where: $$ \Psi (x)=\int \frac{dp^3}{(2\pi)^3} ...
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38 views

CFTs in the phase space of QFTs [closed]

In the cases I have encountered a CFT is often realised as a RG fixed POINT of the RG flow. Is it also possible to have a whole family/mine/manifold of CFTs instead?
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65 views

How are tree-level calculations related to the classical theory?

I've read the answers (and linked notes) to another question (Tree level QFT and classical fields/particles) and I understand them. They seem to explain how to organise a perturbative calculation of ...
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1answer
102 views

What is the QFT picture of a static electric field?

Accelerating charge generates electromagnetic waves and loses energy, in QFT terms it emits photons that carry it away. What of a static charge? Moving photons are usually associated with waves, which ...
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1answer
78 views

Explicit derivation of the Feynman amplitude of $e^+e^-\rightarrow\mu^+\mu^-$

I'm trying to compute the Feynman amplitude of the process $$ e^+(p_1,s_1)e^-(p_2,s_2)\rightarrow \mu^+(q_1,r_1)\mu^-(q_2,r_2), $$ considering as interaction Lagrangian $$ ...
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How can we speak use the notion of “particle” in LHC, given that we live in a curved spacetime?

I understood from lectures that the metric of a spacetime was absolute: It does not depend upon the test charge we put inside. Indeed, all the calculation our professor carried out were independent of ...
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35 views

Chiral multiplet : Fundamental and adjoint representation and its Lagrangian

In supersymmetry theory, consider $4d$ $N=1$ theory, we know that chiral superfield (In fundamental representation $\Phi \rightarrow e^{i\alpha} \Phi$) $\Phi$ and its lagrangian is given as ...
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79 views

How do instantons look in real time/spacetime?

Instantons, as I understand it, are mathematical constructions in Eucledean spacetime. Does it imply that instantons do not exist in real spacetime or instanton tunneling effects are does not have ...
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57 views

How do I derive Feynman rules for vectors involving derivatives?

Suppose I have a term in the Lagrangian: $$\cal{L} \equiv (\partial_\mu B^+_\nu) B^{-\mu} A^\nu $$, where $B^\pm$ are charged massive vector particles and $A$ is photon. Now, how can we derive the ...
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108 views

Does every Hilbert Space carry a representation of Poincare group?

We know all infinite dimensional Hilbert Spaces are unitarily equivalent. It should follow therefore that if I have an unitary representation of say Lorentz or Poincare group on one infinite ...
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31 views

Massless Dirac Field Chirality and CP

I have some very basic questions about Quantum Field Theory. So let's assume we have massless fermions. In 4 spacetime dimensions, due to the Group Structure of $SO(3,1)$ there exists the famous ...
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78 views

Spin and polarization, QM vs QFT

On page 34 of A. Zee's book QFT in a Nutshell, he states: I expect you to remember the concept of polarization from your course on electromagnetism. A massive spin 1 particle has three degrees of ...
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1answer
28 views

Coherent state of charged field

I'm familiar with the idea that coherent states of photons act like the classical electromagnetic field. I've ran across speculation about producing coherent states of other neutral bosonic particles ...
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Kinetic Term Normalization in Quantum FIeld Theory

Say we are given an antisymmetric two-form field: $A_{\mu\nu}$. Its kinetic term in the Lagrangian should be of the form $$ \mathscr{L}_{kin} = a\int d^4x \ ...
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86 views

Gauge group topology

The fundamental difference between spinors and tensors is that spinors are sensitive to the homotopy classes of paths through the rotation group $SO(3)$: \begin{equation} \pi_1(SO(3)) = \mathbb{Z}_2, ...
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46 views

How to separate an exponential with a Hamiltonian with both momentum and position operators?

Statement of exercise On a page 11 of A.Zee's book QFT in a Nutshell, he derives Dirac's formulation of the path integral formulation of QM for a free particle. This starts with the free particle ...
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Quadratic terms in QED lagrangian density

I recently learned that when we speak about a "free lagrangian", this actually means that the lagrangian is quadratic in the fields. When considering the Lagrangian density describing the coupling to ...
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1answer
65 views

can we prove the momentum operator is time inpdependent without using creation and annihilation operator?

in free scalar field, the momentum operator is $$P=-\int d^3 x \pi \nabla \phi$$. If we write it with creation and annihilation operator, then we can get the apparently time independent form,$$P=\int ...
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58 views

$i\epsilon$ versus $2i \epsilon E_k$ in the propagator

The Fourier Transform of the propagator can be written as $$\tilde{\Delta}(k) = \frac{i}{k^2-m^2+i\epsilon} \tag{1} $$ which is then "factored" into $$ = \frac{i}{\left( k^0-E_k ...
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What happens to Goldstone bosons in the Higgs potential after symmetry breaking?

When the gauge symmetry of our Lagrangian breaks spontaneously through the Higgs mechanism, we usually find that $n$ Higgs degrees of freedom become massless through the vacuum expecation value (vev), ...
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Explaining causal completion axiom in Haag-Kastler axioms?

There are several variants of the Haag-Kastler axioms for algebraic quantum field theory. Usually one associates an algebra $\mathcal{A}(O)$ to each open region $O$ of spacetime. An often-suggested ...
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What is Hawking Hartle vacuum state and why does the following Euclidean path integral gives the wave functional of it?

I am studying the wave function of black hole via the paper by Sergey Solodukhkin, Entanglement entropy of black holes,arXiv:hep-th: 1104.3712. In the paper, equation (53) is as follows: ...
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93 views

Relation of field creation operators to path integral?

Applying two field creation operators to a vacuum I get: $$\hat{\psi}^\dagger(x)\hat{\psi}^\dagger(y)|0\rangle = (\hat{\phi}(x)\hat{\phi}(y) - s^{-1}(x-y)) |0\rangle$$ where the quantum field ...
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926 views

Is a single photon always circularly polarized?

While trying to understand polarization in quantum field theory, I wondered how a single photon could go through a linear polarizer. I found a paper which asked "Is a single photon always circularly ...