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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Derivative coupling of neutrinos to massless Goldstone boson - calculation of decay width

I have a theory with a derivative coupling of neutrinos $\nu_{i,j}$ to a massless Goldstone boson $\phi$: \begin{equation} g_{ij}\partial^\mu \phi_\mu\bar{\nu_i}\nu_j. \end{equation} Now I want to ...
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Quantum Anomalies and Quantum Symmetries

In Quantum Field Theories (QFT) there is a well known phenomenon of anomalies, where a classical symmetry is broken in the quantum theory due to a so called anomaly. This symmetry breaking can be ...
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36 views

Help in writing down Feynman rule? [duplicate]

I have a term in my Lagrangian that looks like: $A^\mu B^{*\nu} \partial_\mu B_\nu - A^\nu B^{* \mu} \partial_\mu B_\nu$ where A is the photon field, and B is a charged, massive spin-1 boson. I am ...
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35 views

Creation of momentum on vertex (quantum field theory)

For a an interaction term like $g(\overline{\psi} \gamma^\mu \psi) \partial_\mu \phi$ in which $\psi$ is a Dirac spinor and $\phi$ a scalar field (d=4), should we expect this vertex to have a momentum ...
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76 views

Beyond usual quantum mechanic description of entanglement, is there any QFT or stringy formalism/explanation of it? [closed]

Currently entanglement is speculated to be one underlying mechanism of emergent spacetime, but what are its foundations?
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77 views

Relationship between locality, causality, and free theories

This text on QFT defines a free theory as that in which dynamics of the field for each degree of freedom evolves independently from all the other. In principle we have an infinite degrees of freedom, ...
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2answers
79 views

Is superposition just quantum field? [closed]

A quantum particle is always in superposition state until it is measured, does it means that until we have a disturbance/excitation in the whatever quantum field by measurement/interaction the quantum ...
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48 views

Operator notation?

I'm starting out with many-body quantum theory, second quantization etc. by reading the book by Bruus and Flensberg. In the first chapter they write; "A given local one-particle operator $T_j$ ... ...
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76 views

Hierarchy problem and quadratic corrections in the Standard Model

In this paper, the third paragraph of the “Introduction” says that the Standard Model by itself is a natural theory. As I understand, they say there is no quadratic divergence in the Standard Model ...
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34 views

Are there instantonic corrections to continuously degenerate vacua?

In the case of discretely degenerate vacua, for example in the double well potential, there are instantonic corrections to the energies. The degeneracy is lifted, and the true vacuum becomes a ...
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49 views

Existence of lagrangians at strong coupling

It is well known that some QFT do not admit a lagrangian formulation (like the $(2,0)$ SCFT in $d=6$). Up to my understanding, all the examples that I know of non lagrangian theories are always ...
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240 views

Can a scalar field transform nontrivially under a local special conformal transformation?

Is there any way to have a scalar field that transforms non-trivially under local special conformal transformations? Just by the index structure, I can see that the possibilities are $$\begin{align} ...
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How should we understand the value of a recent theory published on Phys. Rev. D? [closed]

I would like to know what to make of this paper, published on Phys. Rev. D on the 11$^{th}$ of January: Quantum field theory of gravity with spin and scaling gauge invariance and spacetime ...
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34 views

Asymptotic behaviour of the propagator for a scalar field

When discussing causality in Chapter 2 of Peskin & Schroeder a couple of equations giving the asymptotic behaviour of the propagator for a scalar field appear: $$ \text{If} \,\, x^0-y^0=t, \, \, ...
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1answer
50 views

Lorentz-invariant phase space for 2->2 scattering

In the schwartz's quantum field theory, Lorentz-invariant phase space(LIPS) is defined by $$d\Pi_{LIPS}=\prod\frac{d^3p_j}{(2\pi)^3}\frac{1}{2E_j}(2\pi)^4\delta^4(\Sigma p)$$ For 2->2 scattering in ...
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113 views

Transformation of photons under Lorentz transformation

This question is a continuation of one of my earlier post. In this post,I asked about the transformation of photon fields under rotation. Here I generalize the question to Lorentz transformation, and ...
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99 views

Field strength renormalization: going outside of Fock space? [closed]

When one talks about field strength renormalization, one defines the renormalized field $\psi^R(x)$ in the following way (I'm using the notation from Matthew Schwartz's book): $\psi^R(x) \equiv ...
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55 views

What is the group transformation property of photons under rotation?

Both the photon and the W boson are spin-1 particles. Under rotation W boson must transform under the 3-dimensional representation of SU(2). However, the photon has two degrees of freedom (or helicity ...
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What prevents this third-order QED scattering from having a non-zero amplitude?

I have learned that in the Dyson-Wick expansion of the QED scattering operator $$ S=e^{-i\int_{t_i}^{t_f}H\mathrm{d}t} $$ with the QED interaction Lagrangian $$ H=e\bar\psi\gamma^\mu A_\mu\psi $$ ...
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1answer
64 views

“Irreversibility” of the RG flow

In his remarkable work, Zamolodchikov proved a theorem regarding two dimensional QFT Renormalization Group (RG) flow, describing a monotonically decreasing function in the flow parameter which is ...
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96 views

Reparametrization invariance in scalar QFT: What does it mean, exactly?

In the Cecotti's book "Supersymmetric Field Theories" he wrote " Physical quantities are independent of the fields we use to parametrize the configuration, that is, observables are invariant under ...
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46 views

Chern Simons Theory over S^3 as integral - what is domain of integration?

I found these nice lecture notes Lectures on localization and matrix models in supersymmetric Chern-Simons-matter theories so I am hoping to understand some parts of the Chern Simons theory better. ...
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28 views

Linear term in six dimensional $\phi^3$-theory

In our current QFT homework we are given the following Lagrangian in six spacetime dimensions. It is $$ \mathcal L = \frac12 [\partial \phi]^2 - c_0 \phi - \frac{m_0^2}2\phi^2 - ...
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30 views

Can virtual particles be thought of as pieces of 'nonregular' waves?

I just came across this blog post, which gives an interpretation of virtual particles I haven't seen before. To rephrase it, consider a 1D system of springs and masses, where the springs are slightly ...
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1answer
37 views

electric field's area [closed]

How much area an electric field surrounds? since we're just able to draw the electric lines of force we sometimes think that the field is though 3d but surrounds a finite area.But is it measurable or ...
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61 views

Does this vertex equal 0?

If I have an interaction term in my Lagrangian that looks like: $\mathcal{L}_{int} = (\partial_\mu B_\nu)(A^\mu B^\nu - A^\nu B^\mu)$ where B is a massive spin-1 field. Am I correct in thinking that ...
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29 views

Doubts about quark confinement, the pole mass and the quark gluon plasma

I have seen written a few times that the notion of a pole mass for a quark contradicts the quark confinement picture and that non-perturbatively it is expected that the quark pole mass be infinite. ...
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50 views

Is there a correlation between Brownian motion and cosmic microwave background radiation?

Is there any correlation between Brownian motion, the phenomenon of osmosis - compared to cosmic microwave background, the Noise we see in analog television? Brownian motion or pedesis (from Greek: ...
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127 views

What are the remaining obstacles to low-energy quantum gravity?

In a 2003 review Burgess outlined how the QFT perturbative methodology is being extended to gravity, and described some effective quantum gravity expansions that reproduce general relativity in the ...
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39 views

Mode expansions of fields

This is a very simple question but would appreciate it if someone could clarify - I've heard different things from different people so I'm a little bit confused yet the question is simple: Given the ...
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67 views

Angular momentum of the vacuum

I'm studying quantum field theory from "An introduction to Quantum field theory" by Peskin and Schroeder and from "A modern introduction to quantum field theory" by Maggiore. I've read from "An ...
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1answer
69 views

Coherent state path integral - derivation

I divided the time interval $[t_0=:t_i,t_f:=t_N]$ into $N$ steps $[t_{k-1},t_{k}],\, k=1,\dots, N$ and applied the resolution of unity for coherent states \begin{equation} ...
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33 views

Why is it legitimate using bispinors in HQET?

I am reading about HQET in Grozin's book http://www.amazon.es/Effective-Theory-Springer-Tracts-Physics/dp/3540206922. While constructing the Lagrangian he first consider the usual QCD Lagrangian with ...
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50 views

Green's functions and spectral function

I'm struggling to understand something in the book by Fetter & Walecka, p.295, relating to the causal ($G$), advanced ($G^A$) and retarded ($G^R$) Green's functions, and the spectral function ...
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63 views

Gauging a mixture of internal and spacetime symmetries

Given an internal symmetry, say $U(1)$ or $SU(2)$, I understand how to gauge it, by coupling the conserved current $J_{\mu}$ to a gauge field $A^{\mu}$. Similarly, I understand how to gauge a ...
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45 views

Calculation of divergences of Feynman diagram

In Peskin Schroeder, while considering gluon diagrams for $\beta$-function in QCD, they say that we can calculate the divergent part of loop diagram taking limit of zero external momenta - e.g. for ...
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49 views

Gravitational wave as a consequence of gravity being a field

I was reading an online article about gravitational wave detection and there is a sentence which says: The existence of gravitational wave is simply a consequence of the fact that gravity is a ...
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34 views

S-matrix element for forward scattering and amputed green function

I'm studying dispersion relations applied as alternative method to perturbation theory from Weinberg's book (Vol.1) Let's consider the forward scattering in the lab frame of a massless boson of any ...
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1answer
66 views

Problem arising from quantisation of e.m. field

In my studies on the quantisation of the electromagnetic field I've come across a small calculation that I wasn't able to reproduce. Remember the following: In the Gupta-Bleuler method to quantize ...
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1answer
38 views

Probability of $\alpha$-decay

In standard Gamow model we assume that $\alpha$ particle is already in the nucleus, i.e. four nucleons are "glued" together and this particle is emitted. So, we assume that the probability of the ...
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22 views

What are the actual conventions for the standard model particles' intrinsic parities?

It is known that by fixing the intrinsic parity of three particles with linearly independent quantum numbers B, L and Q, the other particles' parities are fixed by the request that parity be conserved ...
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zee model of radiative neutrino mass

Without computing the expression for radiatively generated neutrino mass matrix $M_{\alpha\beta}$, in Zee model, is it possible to guess that the diagonal elements of the mass matrix vanishes? I ...
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61 views

Making mathematical sense on a Feynman's path integral equation

Usually we find this relation in the context of Feynman's path integral (see, for example, Maggiore's book on QFT, pg 223): $ \int_{q_i}^{q_f}[dq] = \int_{-\infty}^{\infty}d\bar{q}\int_{q_i}^{\bar ...
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21 views

Comoving and physical momentum in a Friedmann universe

It is most probably a very basic question, but I'm a bit stuck with it. Let us consider a spatially flat Friedmann universe with the usual metric ...
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1answer
25 views

Evaluating Compton scattering cross-section

In deriving the cross-section of Compton scattering, we require to perform the polarization sum $$\sum\epsilon_{\mu}\epsilon_{\nu}\sum\epsilon_{\alpha}\epsilon_{\beta}$$ using the identity ...
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30 views

Why doesn't the four-gluon vertex give mass to gluons?

We have a four-gluon vertex and a gluon vacuum condensate. Why doesn't this provide us with gluon masses, as in the NJL model where the condensate gives rise to an effective mass term?
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51 views

How to relate classical field and quantum operator?

Recently I listened to a lecture from perimeter institute. There was an idea which I found interesting. That is, roughly, for a field $\phi(x)$ we can assume the relation with the creation operator ...
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51 views

Decomposing massless N=8 SUGRA multiplet into multiplets of massless N=4

The only massless $N=8$ SUGRA multiplet is given by $(g_{\mu\nu},\psi_\mu^{\Sigma},A_\mu^{[\Sigma\Pi]},\chi_{\alpha}^{[\Sigma\Pi\Lambda]} ,\phi^{[\Sigma\Pi\Lambda\Omega]})$ where the greek upper ...
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60 views

Relation between the reduced Green's function and the full Green's function

Let us assume that we have some Hamiltonian and we know its spectrum $$H_0 \psi_n = E_n \psi_n .$$ We define the Green's function in as $$ G(x,y,E) =\sum_m \frac{\psi_m^*(x)\psi_m(y)}{E-E_m}, $$ and ...
3
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1answer
63 views

Why do the conserved charges in the case of SSB of a global symmetry not exist?

Reading "From Linear SUSY to Constrained Superfields" by Komargodski and Seiberg, I got a bit confused regarding the existence of the conserved charges in a theory with spontaneous symmetry breaking ...