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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 [tag:particle-physics]. Don’t combine with [tag:quantum-mechanics].

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Peskin equation on the treatment of chiral anomaly

In page 666 (it couldn't be other way - bad joke), chapter 19, the Eq. (19.73) claims (see properties of the $\phi_n(x)$ functions in this post: Change of variables in path integral measure): $$ \...
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Gordon decomposition in Cheng and Li p. 422

In the $\mu \rightarrow e+\gamma$ calculation in Cheng and Li "Gauge theory of elementary particle physics" p.422 they have $$ T=A\bar{u}_e(p-q)(1+\gamma_5)i\sigma_{\lambda\nu}q^\nu\epsilon^\lambda ...
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Virtual pair of particle-antiparticles trajectory [duplicate]

Is it possible to do heuristic calculations on virtual pair of particle-antiparticle trajectories that appear in a vacuum? For example, what is the maximum distance between them during virtual process?...
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Change of variables in path integral measure

In fermion's path integral we have a measure that you can write, in terms of the Grassmann variables $\psi, \bar{\psi}$ as $$ D\bar{\psi}D\psi, \quad \psi(x) = \sum_n a_n\phi_n(x), \quad \bar{\psi}(x)...
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135 views

Simplest model in field theory which leads to a pseudo-Goldstone boson

What can be a simple (if not simplest) continuum field theory model that gives rise to a pseudo Goldstone boson (doesn't matter if it is a toy model)? For example, I would be very happy if one can ...
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Derivation of the QFT Propagator

I don't understand how we get from the RHS to the last line. \begin{eqnarray} \left[ \hat{H}_x - i \frac{\partial}{\partial t_x} \right] G^+(x,t_x,y,t_y) &=& -i \delta (t_x - t_y) \sum_n{\...
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70 views

Symmetry and symmetric vacuum in Quantum Field theory

In the start of section 28.2 of Schwartz's Quantum Field theory and the Standard Model, Schwartz states that for a conserved charge, $\hat{Q}$, which generates the corresponding symmetry ...
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References to understand BRST Quantization

I'm looking for good, rigorous references that discuss BRST quantization in relation to how it leads to dealing with anomalies and ghost fields. I'm looking at high level references (i.e., assume ...
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Why a field theory containing only fermions does not show spontaneous symmetry breaking?

For a real scalar field $\phi$, a theory as simple as the $\phi^4$ theory, can exhibit the phenomenon of Spontaneous Symmetry Breaking (SSB). For a complex scalar field $\phi$, a theory as simple as ...
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Why is the approximate $\rm U(2)\times U(2)$ global symmetry of QCD that has a special importance?

I was looking at Peskin and Schroeder (Section 19.3, page $667-668$). They talk about $\rm U(2)\times U(2)$ symmetry for the QCD Lagrangian in the limit of massless $u$ and $d$ quarks. However, this ...
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Corrections from (to?) the Quantum Action Principle

In expositions of the Quantum Action Principle (sometimes the Quantum Dynamical Principle) it is shown that information may be derived from the vacuum transition amplitude. Specifically, $\langle \psi ...
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Gauge and global symmetries in Chern-Simons/WZW correspondence

I am trying to understand how bulk gauge symmetry in 3d Chern-Simons theory becomes a global symmetry in the boundary 2d WZW theory. In particular, I am trying to understand the papers by Elitzur et ...
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Is it true that in practice quantum fields are *always* measured by means of coupling to particle detectors?

I'm watching some lectures on Relativistic Quantum Information and in one of them - available here - the instructor is talking about measuring quantum fields. He then says basically that in real ...
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rigorous definition of coherence length at mean field theory

so as far as I know, when we are doing mean field theory, in qft, we expand a action of a theory around a classical solution. so we find a classical solution, than we add quantum mechanical ...
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Matsubara Sums and Multiple Poles

In Mahan's book, equation (4.127), he claims that \begin{align} &\frac{1}{\beta}\sum_{ik_n} \frac{1}{ik_n-\xi_1}\frac{1}{ik_n-\xi_2}\frac{1}{ik_n-\xi_3} \\ =& \frac{n_F(\xi_1)}{(\xi_1-\xi_2)(\...
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Quantization of complex Klein-Gordon field in curved spacetime

The quantization of a scalar field in curved spacetime usually goes along the following lines. The minimally coupled scalar field lagrangian is $$\mathcal{L}=\nabla_a\phi \nabla^a\phi^\ast - m^2\phi^\...
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A couple of questions about spontaneous symmetry breaking (SSB)

I have a few doubts about my understanding of spontaneous symmetry breaking. To keep it simple, I will take a global U(1) transformation on a complex scalar field as an example. The questions are ...
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How do the creation operators transform under Lorentz transformation?

In Weinberg's QFT book In chapter 4, the change of creation operator under Lorentz transformation is describe by (4.2.12), $$\begin{aligned} U_{0}(\Lambda, \alpha) a^{\dagger}(\mathbf{p} \sigma n) ...
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Is there any Feynman diagram for Baryon/Hyperon decay with missing energy?

I am reading the hyperon decays with missing energy this paper tells for the prospects of baryon decays with missing energy I want to know some of the Feynman diagrams for hyperon decays. Can anyone ...
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Tensor decomposition v.s helicity amplitude

It is common to write e.g photon two point function in terms of manifest transverse and longitudinal form factors with lorentz structure factored out, e.g via explicit tensor decomposition $$\Pi^{\mu \...
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35 views

Anomalous magnetic moment of the electron - integration problem

In Schwartz's QFT book (eqn 17.31), to find the anomalous magnetic moment of the electron from the form factors, near the end of the calculation the following integral needs to be evaluated: $$ F_{2}(...
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Why does the renormalizable theory have only those particles with helicity less than or equal to 1?

Let the helicity operator be $\frac{P \cdot J}{P^0}$ with an eigenvalue $\lambda$. Then why do renormalizable theories have $|\lambda| \le 1?$ (in general dimensions or in 4ds?) Also, what is the ...
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Doubts about the use of tensor product In quantum mechanics

I'm studying quantum mechanic in particular tensor product and Hilbert space (for the first time). I have some doubts and I would like to check if I have understood correctly. Factorization The ...
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What's the difference, if any, between Soft Hair & Quantum Hair

In the early 90s, John Preskill, Sidney Coleman, Frank Wilzcek and Lawrence Krauss presented a series of papers [1][2][3] on Quantum Hair on Black Holes due to Cosmic strings in a number of ways ...
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Feynman-Wheeler absorber theory

Firstly, I’m sorry if this is not a question that should be here. I would like to ask if anyone could link or guide me to where I could find resources (articles, books, etc.), about Feynman-wheeler ...
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How to prove that the scattering amlitude of bi-adjoint scalar field theory admits a Cachazo-He-Yuan (CHY) representation?

How to prove that the scattering amlitude of bi-adjoint scalar field theory admits a Cachazo-He-Yuan (CHY) representation?
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IR divergence Feynman diagram topology query

I am trying to calculate the superficial degree of Infrared divergence. To do this I am reading section 12 of this source. It seems you can calculate it by a method involving the 'shrinking' of ...
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Two photon vertex from tensor fermion bilinear

The fermion bilinears are $\bar{\Psi}\Psi$, $\bar{\Psi}\gamma⁵\Psi$, $\bar{\Psi}\gamma^\mu\Psi$, $\bar{\Psi}\gamma^\mu\gamma^5\Psi$ and $\bar{\Psi}\sigma^{\mu\nu}\Psi$, where $\sigma^{\mu\nu} = (i/2)[\...
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67 views

Does the Uehling potential have any observable effect?

Uehling potential is the correction made to the coulomb potential due to vacuum polarization (electron-positron pair creation and annihilation). How big is this correction compared to the coulomb ...
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Tunneling in quantum mechanics and domain wall in 1d Ising model

I am following David Tong's lecture notes on Statistical Field Theory. You can find it here. In page 51-52, he said the domain wall in 1d Ising model is the same as quantum tunnelling in quantum ...
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Strong empirical falsification of quantum mechanics based on vacuum energy density

It is well known that the observed energy density of the vacuum is many orders of magnitude less than the value calculated by quantum field theory. Published values range between 60 and 120 orders of ...
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Bogoliubov transformation for fermionic Hamiltonian

I have the Hamiltonian $H=\sum\limits_k [Ab^{\dagger}_{k}b_{k} + B(b^{\dagger}_kb^{\dagger}_{-k}+b_{k}b_{-k})]$, where $b^{\dagger}_k$ and $b_k$ are fermionic creation and annihilation operators. ...
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QCD flavor gauging?

I ran across this old post: What the heck is the sigma (f0) 600? The question author is explaining his understanding of the spectrum of QCD in terms of various interesting things like chiral symmetry ...
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Calculation of current from path integral

I would like to calculate $\langle\bar{\psi}\psi\rangle$ in free theory. I start from the following generating functional: $$Z[J]=\int\mathcal{D}[\bar{\psi},\,\psi]\exp\left(i\int d^dx\,[\bar{\psi}(i\...
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Lepton flavor violating process on loop level $\mu \rightarrow e \gamma$ via Higgs, Divergent integral

I am stuck with calculating the proces $\mu \rightarrow e \gamma$ as in this diagram: I wrote down the matrix element like this: $$ \mathcal{M}=\bar{u}(p-q)\left[\int \frac{d^4k}{(2\pi)^4}A\frac{(k+...
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$\tau \rightarrow \nu_{\tau} e^- \bar{\nu}_e$ decay. Where is my mistake?

I want to calculate $\tau \rightarrow \nu_{\tau} e^- \bar{\nu}_e$ decay rate $\Gamma$, with the effective four fermion interaction to leading order. $$\mathcal{L}_{eff} = -\frac{G_F}{\sqrt{2}} [e^+\...
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Problems of Klein Gordon equation

Consider the Klein-Gordon equation $$(\square+m^2)\varphi=0.$$ People usually claim that $\varphi^* \varphi$ cannot be interpreted as a probability density because $\int d^3\vec{x}\varphi(t,\vec{x})^*...
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Computation of Feynman integrals in terms of Chen Iterated integrals

One of the techniques used to compute Feynman integrals in dim-reg is the so-called "differential equations method". Exploiting integration-by-parts identities (linear functional relations between ...
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1answer
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Are there viable alternatives to the no boundary proposal?

As I understand it, quantum field theory can be described as the evolution of a wave function $\psi_t[\phi]$ depending on some fields, $\phi$. But when we include gravity and we admit that time is ...
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Kallen-Lehmann representation and branch cuts at threshold masses

Let us consider the Kallen-Lehmann representation for the two-point function of scalar fields $$ \langle \Omega | T\left\{\phi(x) \phi(y)\right\}|\Omega\rangle = \int \frac{d^4 p}{(2\pi)^4} e^{ip\...
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Why do we need wave packet? [closed]

My question is that why we need wave packet to describe the free particle states? Will this packet decompose after propagating for a period of time?
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QFT - QED total cross sections pair annihilation into photons

Reading on the book "peskin schroeder an introduction to quantum field theory" the cross section for the production of pairs, it is not clear to me why in the calculation of the total cross section it ...
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Cross section for 2 particles that decay independently

This maybe is a naive basic question but I want to be sure. If I want to calculate the cross section of the process $$p\bar{p} \rightarrow W^+HX \rightarrow e^+\nu_e b\bar{b} X$$ ($H$ is a Higgs ...
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How can we have a quark condensate without a quark potential?

The QCD quark Lagrangian in the chiral limit is $$ L_q = i \bar{q}{\not D} q $$ which possesses a global $SU(3)_L \times SU(3)_R$ symmetry. I've read many places that this is symmetry is ...
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The fundamental transition problem [duplicate]

can anyone explain what is mentioned here https://arxiv.org/abs/1405.6091 (page 7 and 8) in simple terms: Finally, Krauss makes the very problematic claim that “the structures we can see, like ...
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Why is a diagonal scattering matrix preferable?

Maybe it is a trivial question, but it is not so clear to me why (if it is so) I would rather want a diagonal S-Matrix. Thanks
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Black hole horizon states in standard derivations of Hawking Radiation

In all standard derivations of Hawking radiation given e.g. by Hawking, Parker and Wald, one has the so-called horizon states. The point is that when one is quantizing a scalar field on a black hole ...
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EW theory vertices

I'm trying to undertand the following vertex: Initial state of up and anti-down quarks with finalk state made of $W^+$ boson. Does it go with left or right projector? I think that from Lagrangian it ...
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Peskin & Schroeder eq. 9.26 and functional methods

I have been reading chapter 9 in Peskin & Schroeder's QFT book and has been stuck in transition from equation 9.26 to 9.27. Equation 9.26 reads: $$\frac{1}{V^2} \Sigma_{m,l} \exp{[-i(k_m.x_1+k_l ....
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Two-point correlation function of a scalar field $\langle 0 | \phi(x) \phi(0)| 0 \rangle$

I'm trying to find the two point correlation function for a massless scalar field obeying $\square \phi = 0$. I can write $$\langle 0 | \phi(x) \phi(0)| 0 \rangle = \int \frac{d^dk}{(2\pi)^d} \delta(...