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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Direct vs. indirect CP violation: theoretical foundations

I know very little about the difference between direct and indirect CP violation. I've been studying QFT from Peskin and Schroeder's "An Introduction to QFT", and they don't seem to address this ...
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Special conformal transformation of stress-energy

Consider a 2d CFT, e.g. a single bosonic degree of freedom. The $TT$ OPE is $$ T(w) T(z) = \frac{c/2}{(z-w)^4} + \frac{2 T(w)}{(z-w)^2} + \frac{\partial T(w)}{z-w} + \text{regular terms}. $$ Does ...
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Fermions, different species and (anti-)commutation rules

My question is straightforward: Do fermionic operators associated to different species commute or anticommute? Even if these operators have different quantum numbers? How can one prove this fact in a ...
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34 views

General properties of Matsubara frequency summations

By properties, I mean linearity, shifting, commutativity, etc. I was hoping to evaluate something like $S_\eta = \dfrac{1}{\beta}\displaystyle\sum_{i\omega} g(i\omega)$ where $g(i\omega) = ...
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28 views

Question on in and out states in chapter 10 of Weinberg's QFT volume 1

In chapter 10 section 2 (on pomology) of Weinberg's QFT volume 1, he shows $G$ has a pole when the external line goes on shell. In the proof, he inserted a complete set of single-particle states ...
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24 views

Relation of conformal symmetry and traceless energy momentum tensor

In usual string theory, or conformal field theory textbook, they states traceless energy momentum tensor $T_{a}^{\phantom{a}a}=0$ implies (Here energy momentum tensor is usual one which is symmetric ...
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45 views

Merger of old black holes

On the eve of a possible announcement on the production of gravitational waves via a black hole merger, I think this question is quite aptly timed. I have a few questions regarding the evolution of ...
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Correlation function for ghosts in 2D CFT

In Di Fracenso, page 117, it is explained that the correlation function for two primary fields $\phi_1,\phi_2$ of weights $h_1,h_2$ is constrained to be of the form ...
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57 views

Why doesn't a plane wave solution represent a single photon?

Why doesn't a plane wave solution represent a single photon? And what is meant by the quantum-mean field being zero? EDIT: This post is an extension to a previous post I made asking about the photon ...
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62 views

Quantum State of Photon Question

I need to learn more about quantum field theory for my PhD research and I wont be able to take a class until after the summer. I am reading the QFT book from Landau and Lifshitz. I have some ...
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28 views

Ryder QFT, Is there an errata sheet?

Just spent the last hour trying to find one, but to now avail. Has anyone ever seen such a thing?
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336 views

Why should field operators satisfy the classical equations of motion?

To quantize a scalar field theory with the action: $$S=\int \mathrm d^Dx\mathscr{L}(\phi,\partial_\mu\phi)=\int \mathrm dx^0L(\phi,\partial_0\phi)$$ we promote $\phi(\vec{x})$ and $\pi=\frac{\delta ...
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Understanding the $\phi^4$ phase diagram

I'm having trouble making sense of this phase diagram. The model is a $V(\phi)=g_2 \phi^2+g_4\phi^4$ scalar field theory. Here's what I think I understand: the capital letters represent different ...
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115 views

Quantum field theory's interpretation of double slit experiment

After reading Art Hobson's article titled, "There are no particles, there are only fields" published in The American Journal of Physics in 2013, I'm wondering what other experts think of his main ...
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34 views

Callan-Symanzik equation for the QCD scattering cross section of the $e^{-}e^{+}\to q\bar{q}$ process

In Peskin and Schroeder (Section 17.2) it is stated without derivation that the scattering cross section for the $e^{-}e^{+}\to q\bar{q}$ process obeys the following Callan-Symanzik equation: $$ ...
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Explaining the Atemporal Dimension of Feynman Diagrams

In a Feynman diagram, I understand that one of the dimensions (horizontal, say) represents time. Could someone please rigorously explain why a second dimension (vertical) is necessary? In particular, ...
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29 views

Derived Geometry and Deformation Quantization

Can anyone please explain to me in layman' terms what derived geometry deals with and what deformation Quantization is? I have only a good understanding of Relativity,Classical Mechanics.
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34 views

meson decay in Yukawa theory [on hold]

I want to calculate decay width $\Gamma_{i\rightarrow f}$ (under assumption that we don't measure the polarization of particles in final state) in a decay process $$\phi \rightarrow \psi \bar{\psi}$$ ...
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Would superconducting mirrors in a superposition of spatial states make a difference related to the dynamical Casimir effect?

Related to the dynamical Casimir effect: https://www.technologyreview.com/s/424111/first-observation-of-the-dynamical-casimir-effect/ Related to superposition of macroscopic objects: ...
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67 views

Operators, Distributions and States in QFT

First of all, I will mention what I understand (pls. correct if wrong): States are vectors in the Hilbert space, to include continuous spectrum (and thus distributions), we expand this space to ...
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1answer
57 views

Sign of Wick rotation [closed]

Suppose you have the integral $$i \int^\infty_{-\infty} L_M(t) dt$$ and that $L_M$ contains two poles: when $t>0$ the pole lies above the t-axis and when $t<0$ the poles lies below the t-axis. ...
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32 views

Topological terms VEVs and ghosts

Suppose we have the Standard model, and we want to calculate with VEVs of topological susceptibilities of $SU_{L}(2), U_{Y}(1)$ and $SU_{c}(3)$ fields, which have the form $$ \tag 1 \kappa \equiv ...
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69 views

Is the empty space really empty? [duplicate]

I've come across another article in "list verse" which says that the empty space is not actually empty at least for a while. I've tried to find about this, so I googled it .It also quotes a word ...
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46 views

Atom - light field coupling and emission process

Suppose a "2-state atom" and a light field are quantized with the following Hamiltonians, respectively: $$\hat{H}_A=\hbar\omega_{21}\hat{\sigma}^{\dagger}\hat{\sigma}$$ and ...
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Question about the superconformal index

According to arXiv:1507.08553v1, the superconformal index, defined by $$I(\beta_j) = \mbox{Tr}_{\mathcal{H}}(-1)^F e^{-\gamma\{Q,Q^\dagger\}}e^{-\sum_{j}\beta_j t_j}$$ is independent of the ...
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Fermi's theory of beta decay - Does Fermi's Hamiltonian have the wrong transformation properties?

I'm studying the theory of beta decays as proposed by Fermi in the 30's, and I found an inconsistency between the transformation properties that he claims for his Hamiltonian and the transformation ...
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1answer
29 views

can we quantize a static electron-magnetic vector potential which is time-independent? [closed]

I am thinking since a static vector potential which is time-independent do not have dynamics (such as in Cylindrical coordinate A(ρ, φ, z)=1/ρ) , how can we quantize it? since I know the photons have ...
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1answer
112 views

Quantized light-atom Hamiltonian

Suppose a "2-state atom" and a light field are quantized with the following Hamiltonians, respectively: $$\hat{H}_A=\hbar\omega_{21}\hat{\sigma}^{\dagger}\hat{\sigma}$$ and ...
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1answer
41 views

Fields in the action of the Non-linear Sigma Model (WZW)

I am trying to understand the action of the nonlinear sigma model in the context of understanding WZW-models. On Wikipedia, its action is given as ...
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72 views

Why does analytic continuation as a regularization work at all?

The question is about why analytical continuation as a regularization scheme works at all, and whether there are some physical justifications. However, as this is a relatively general question, I ...
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29 views

QFT: Limits in Time Ordered Correlation Function Derivation

Background In part of the derivation for the time ordered correlation function I have the following equation (This equation I am fine with - it is what follows that I am not), $$ ...
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27 views

Free Complex scalar field and conservation principle

In a free complex scalar field, the difference between the number of Particles and antiparticles is conserved. This constarint can be satisfied with a simultaneous creation of equal number of ...
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135 views

Confusion with Weinberg's QFT book, volume 1, chapter 3: time translation and Heisenberg picture

Sorry if this is a naive question, but I am new to QFT. In the treatment of scattering in section 3.1 of The quantum theory of fields, vol.1, Weinberg first presented the general transformation rule ...
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97 views

Can Quantum Field Theory be right even though it doesn't include gravity? [closed]

Quantum Field Theory doesn't include gravity, so does that mean it can't be right?
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55 views

QFT: Ground State Momentum - Normalisation of States

In my notes I have, $$ \left\langle \mathbf{p} \left| \mathbf{q} \right.\right\rangle = \left\langle 0 \left| {a(\mathbf{p})}\ {a(\mathbf{q})}^{\dagger} \right| 0 \right\rangle $$ I am not sure how ...
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25 views

Is it possible to have transformations that transform the action and the measure while leaving the functional integral invariant?

Anomalous symmetries are those for which the Lagrangian stays invariant but the measure of the functional integral does not. I wonder if there are transformations that change both the action and the ...
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1answer
47 views

Normal Ordering in String Theory: Polchinsky vs. all others

Polchinsky defines normal ordering in string theory as: $$:X^\mu(z,\bar z)X^\nu(w,\bar w): = X^\mu(z,\bar z) X^\nu(w, \bar w) + \frac{\alpha'}{2} \eta^{\mu\nu} \log |z-w|^2$$ and for more ...
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NLO compton scattering

I have a question about the NLO processes, that contribute to ${\mid M \mid}^2$ with ${\alpha}^3$ in compton scattering. I can see, that an extra radiative $\gamma$ gives terms $\propto {\alpha}^3$. ...
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53 views

Time ordering of normal ordered product

I would like to calculate $$<0|T(:x^4::y^4:)|0>$$ for scalar fields $x$, $y$ "by hand", but I don't understand yet how. With Wicks theorem I'd say this is strictly 0. Is this correct? By hand I ...
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2answers
92 views

What are non-perturbative effects and how do we handle them?

Schwartz's QFT book contains the following passage. To be precise, total derivatives do not contribute to matrix elements in perturbation theory. The term $$\epsilon^{\mu\nu\alpha\beta} ...
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1answer
51 views

Superficial degree of divergence on Weinberg

Reading volume 1 of Weinberg's QFT book, chapter 12, page 505 he says that if you consider a diagram with degree of divergence $D\geq{}0$, its contribution can written as a polynomial of order $D$ in ...
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42 views

What is a “dynamically generated scale” physically?

A theory like QCD with massless quarks in four dimensions has no explicit mass parameters in its classical Lagrangian. At the quantum level however, instead a mass scale Λ is generated dynamically at ...
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80 views

Classical Fermion and Grassmann number

In the theory of relativistic wave equations, we derive the Dirac equation and Klein-Gordon equation by using representation theory of Poincare algebra. For example, in this paper ...
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53 views

Why do three-scalar correlation functions vanish by parity?

We have the following Lagrangian: $$ \mathcal L = \frac12 (\partial_\mu \phi)^2 - \frac12 m^2 \psi^2 + \bar\psi(\mathrm i \gamma^\mu \partial_\mu -M) \psi - \mathrm i g \bar\psi \gamma^5 \psi \phi \,. ...
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1answer
61 views

Few basic questions about instantons

For the $SU(2)$ Yang-Mill's theory, (1) how can one understand that the finite action solutions of the Euclidean equations of motion (called Instantons) exhibit tunneling effects? (2) Since, this ...
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Electron matrix element in a most simple QFT problem, the e+ e- annihilation

In the beginning of my new QFT book there is this short chapter called Invitation: Pair Production in $e^{+}$ $e^{-}$ Annihilation. An electron and a positron collide and a couple muon & antimuon ...
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Does energy transmission depend on the speed of incoming particle?

Since a few past days , I am struggling with finding an in depth atomic model of force exchange between colliding paricles (originally newtons third law) , because at this point of time i am unable to ...
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1answer
54 views

How to calculate the effective action in general?

Considering the scalar field, we have the effective action $$\tag 1 \Gamma[\phi_{cl}]=\int ...
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Order of the life time of the K± mesons [duplicate]

It is not a homework. I've just wanted to find the order of the life time of the K± mesons. I had some suggestions like Starting from Fermi’s model and dimensional analysis ,Considered decays like K ...
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35 views

How to describe spin-orbital coupling in Weyl semi-metal

In three dimensional Weyl semi-metal, the Hamiltonian that describes low excitation quasi-particle is well-know Weyl Hamiltonian: +/- $k\cdot\sigma$. But if I want to add spin-orbital coupling in that ...