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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What is a quantum field?

I'm just tasting a bit of QFT and want to get started. I got stuck right at the start: what is a quantum field, and how should I look at it? This question can be a follow up of the What is a field, ...
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Confusion over trying to understand spinor components

I've been reading about the quantisation of the Dirac field $\psi(x)$ and it is stated that the general solution to the Dirac equation $(i\gamma^{\mu}\partial_{\mu}-m)\psi(x)=0$ is given by the ...
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70 views

Tetrad choice for Pauli-Lubanski in the massless case

The Pauli-Lubanski pseudovector coincides with intrinsic spin in the rest frame of the particle. In a more general frame, one defines a tetrad and projects the PL vector on it to define intrinsic spin ...
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effective field theory of the projective semion model

The "projective semion" model was considered in http://arxiv.org/abs/1403.6491 (page 2). It is a symmetry enriched topological (SET) phase. There is one non-trivial anyon, a semion $s$ which induces a ...
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Why is the symmetric phase in a Bose gas not superfluid?

In the theory of superfluidity in weakly interacting Bose gases, one finds that in the symmetric phase the exctitations have the dispersion relation $\omega = \frac{k^2}{2m}-\mu$ with gap ...
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can different force fields interfere (create interference patterns)

Edit: I have rewritten the question for clarity. I know waves of photons can interfere eachother. What about if you mixed waves of photos with w and z bosons? What about gravitons (if they exist) ...
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Obtaining the $s,t,u$ Feynman diagrams by Wick contraction

Consider a real scalar field described through the following lagrangian $$\mathcal L = \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi - \frac{1}{2}m^2 \phi^2 - \frac{g}{3!}\phi^3$$ The second ...
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$\mathcal{N} = 4$ Super-Yang Mills propagators

In $\mathcal{N} = 4$ Super-Yang mills there are only massless particles. If one wishes to obtain a heavy quark one can see the SYM theory as a stack of (N+1)-branes in AdS$_5 \times$S$^5$ where one ...
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33 views

Why is the bosonic Casimir force attractive while the fermionic CF is repulsive?

Why is the bosonic Casimir force (CF) attractive while the fermionic CF is repulsive? I looked up for many papers and books but all are focused on boundary conditions. I didn't find any conceptual ...
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How to find propagator from Lagrangian at a glance?

If I have a Lagrangian in momentum space of the form $$ \mathcal{L} = W_\mu^{ \dagger}(p)f(p)^{\mu \nu}W_\nu(p) $$ how is the propagator for the field related to the function $f(p)$ (e.g. is it ...
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Relation between Borchers class and the LSZ formula on S-matrix equivalence

It seems well known that different quantum fields can give rise to the same $S$-matrix. I know of two ways this is described. The first is through the Borchers class of relatively local fields, i.e. ...
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Why do we need to build photon colliders? Since electron-position colliders are very “clean”

What's the advantage of gamma-gamma colliders? What new physics can be done with it? Reference: http://www.slac.stanford.edu/pubs/beamline/26/1/26-1-kim.pdf
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174 views

Why can we not choose the stress tensor in a CFT to be identically symmetric?

The stress tensor for a conformal field theory (or any quantum field theory) can be derived from the action $S$ by the functional derivative $$T^{\mu \nu} ~=~ -\frac{2}{\sqrt{|g|}}\frac{\delta ...
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179 views

Spin state after boost

I am working through Weinberg's QFT book, and in problem 1 in chapter 2 I ran into copious amounts of algebra, so I am trying to "cheat" a little by using some assumptions, but am unsure of their ...
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Classical field limit of the electron quantum field

In order to recover classical electromagnetic fields from the quantum electromagnetic field, we consider coherent states of the form $$\exp \left(\int d\vec{r}\, \vec{A}(\vec{r}) ...
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366 views

Momentum Space Renormalization of $\phi ^6 $ Model

I'm trying to find the RG flow to lowest order in $\epsilon = 3 -d $ for the energy functional: $$ f=\frac{1}{2} \phi ^2 +u \phi ^6 +\frac{c}{2} (\nabla \phi ) ^2 $$ where $\ d$ is the dimension ...
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What is the relationship between BRST symmetry and gauge symmetry?

As far as i know the BRST symmetry is an infinitesimal (and expanded) version of gauge symmetry. Recently I read the following: "when QFT was reformulated in fiber bundle language for application to ...
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92 views

Physical Relevance of Classical Limit to QFT's

We know the physical relevance of the classical limit of quantum mechanics quite well. However, if I take the classical limit of a quantum field theory, the answer is not so clear. Suppose I take the ...
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Inverse square law in 2+1 dimensional universe from a Yukawa coupling?

There is a nice result that in 3+1 space time, a Yukawa coupling leads to an inverse square law force as the mass of the scalar field goes to zero. I was wondering what the corresponding force in a ...
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100 views

Why representations instead of just groups?

This question is essentially asking for a clarification on what has already been said in this one. What I don't understand is why it is the representations that are important in Quantum Field Theory ...
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62 views

Few questions regarding String-Net theory and the Standard Model

A friend today showed me this post and after reading Prof. Wen's answer, few questions came to my mind. Prof. Wen says: all fermions (elementary or composite) must carry gauge charges (see ...
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What is the Green's function of the Klein-Gordon equation with a variable mass?

Usually, the Klein-Gordon equation's propagator is calculated with a constant mass. But what if the mass is a variable? That is, $$ (-\partial^2 + m(x)^2)G(x, y) = \delta^4(x-y)$$ where $m(x)$ is a ...
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44 views

Mean free path in QFT

I'm trying to understand the hydrodynamic approximation of a general QFT when the large $k$ and $\omega$ DOF have been integrated out i.e that at highly enough temperature every non-trivial QFT ...
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395 views

Lorentz-invariant phase space of a three-body decay process

I am not following the use of delta function in the 3-body decay process. In $\gamma^* \to gq\bar{q}$ process, with $\gamma^*$ being a virtual photon, we have a phase space factor $$d^9R_3 = ...
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Poincare representations for interacting field theory

I was going through Rudolf Haag's memoir http://link.springer.com/article/10.1140%2Fepjh%2Fe2010-10032-4 and came across these lines: '..in quantum field theory (or for any system of interacting ...
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163 views

What is the problem with quantizing GR in the Effective Field Theory approach?

In the modern view due to Wilson, the cut-off $\Lambda$ is an intrinsic property of a theory and renormalization just means that the theory is invariant under scale transformations below $\Lambda$. ...
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Why is there no fundamental force following from the $SU(4)$ symmetry?

I've understood that the three fundamental interactions described by the Standard Model (the electromagnetic, the weak and the strong force) are thought to correspond (roughly) to gauge invariances ...
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Equation for Electric and Magnetic field from the equation for a “massive photon”

I was reading the Quantum Field Theory book by Maggiore. There he says that in side a superconductor the photon satisfies the equation $$(\Box+m^2)A_\mu=0$$ Then he adds that the electric field and ...
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666 views

What's the deepest reason why QCD bound states have integer charge?

What's the deepest reason why QCD bound states have integer electric charge, i.e. equal to an integer times the electron charge? Given that the quarks have the fractional electric charges they do, ...
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Running coupling, effective potential and the stability of vacuum

Consider the potential $$V(\phi)=\frac{1}{2}\mu^2\phi^2+\lambda\phi^4$$ where $\phi=\phi(t,\textbf{x})$ is a real scalar field. Let, $\mu^2<0$ and $\lambda>0$ then the potential is bounded from ...
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2->2 scattering, Lorentz invariance phase space, Schwartz Eq5.29

In Schwartz Sec. 5.1.2, he explains 2->2 scattering in the center-of-mass frame. In Eq. 5.27 he gives: $$ d\Pi _{\text{LIPS}}=\frac{1}{16 \pi ^2}d\Omega \int dp_f \frac{\delta ...
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How to find the remaining subgroup after some linear combination of Higgs fields gets a VEV?

This is a follow-up question to this question. How can I compute which generators remain unbroken when a linear combination of Higgs fields $a \Phi_1+ b\Phi_2$ get a vev? If I compute the unbroken ...
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Estimate the threshold for $e^+e^-$ production due to the vacuum instability in an atom.

When a nucleus with very high $Z$ is created, the binding energy of the innermost electronic orbit becomes sufficient to create $e^+e^-$ pairs. The pair can be created out of the vacuum – the electron ...
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Questions about the beta function in QFT

When someone defines $\beta(g)=\mu\frac{dg}{d\mu},\quad (1)$ he is implicitly assuming that the result of the rhs of this equation can be written only in terms of $g$ instead of $\mu$, which is not ...
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Problem understanding electromagnetic interaction with matter (non-relativistic QED)

I'm having trouble understanding the interaction of radiation with matter in (elementary non-relativistic QED) in Coulomb gauge ($\nabla\cdot\boldsymbol{A}=0$). We saw how to quantize the free ...
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96 views

Srednicki - computing divergent piece of loop integral

I was reading through Srednicki and didn't quite understand one of the paragraphs in Section $51$ on loop corrections in the Yukawa theory on P.$322$. It's the fermion loop correction to the local ...
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1answer
60 views

Probability of finding vacuum?

Consider a real scalar quantum field $\varphi (x)$, interacting with a classical real scalar field $J(x)$ : $$ \mathcal{L} = \frac{1}{2}(\partial \varphi)^2 - \frac{m^2}{2} \varphi^2 + \varphi J$$ ...
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139 views

Degrees of freedom of quantum scalar field

In Srednicki P33, we tried to generalize the time evolution equation in Heisenberg picture: $$ e^{+iHt/\hbar}\varphi(\mathbf x, 0)e^{-iHt/\hbar}=\varphi(\mathbf x, t) $$ into relativistic form: $$ ...
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46 views

Photon one (odd) point function in QED

In Peskin's QFT textbook, when discussing the superficial divergence of loops in QED, the book says (page 317): "To analyse the photon one-point function,note that the external photon must be ...
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A box loop-integral [closed]

I am trying to evaluate the integrate $$ \int\frac{d^Dk}{(2 \pi)^D} \frac{1}{(k^2)^2(k^2-m^2)} $$ using dimensional regularisation ($D=4-2\epsilon$). From various references it appears that it should ...
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202 views

How to deal with boundary conditions for path integrals?

For non-relativistic quantum mechanics, the boundary conditions are rather simple to deal with, they are just \begin{equation} \langle x_1, t_1 \vert x_2, t_2\rangle = \int_{x_1(t_1)}^{x_2(t_2)} ...
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46 views

The energy of dual boundary field in AdS/CFT

In AdS/CFT, when the spacetime is a planar AdS black hole with dimension ($d+1$), the corresponding energy of boundary field theory is proportional to the black hole mass parameter. For example when ...
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How to write the second quantization form of spin-orbit coupling(Dzyaloshinskii-Moriya interaction)?

Spin orbit coupling is the single particle term, so the second quantization form can be written like:$\langle \alpha\sigma|s\cdot(\nabla V\times P)|\beta\sigma'\rangle ...
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Momentum Twistor variables and non-planar theory

I know that the use of twistur-momentum variables makes manifest the arising of certain poles in scattering amplitudes: if the sum of external momenta $P_I = p_i + p_{i+1} + ... + p_j$ is going ...
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Why is the chiral symmetry only $SU(3) \times SU(3)$ and not $SU(6)$?

In the limit where the masses vanish, low energy QCD has a well known chiral symmetry (see http://arxiv.org/abs/hep-ph/0505265 for a very extensive review, and pg 19 for the section relevant for my ...
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251 views

Computing box diagrams with non-vanishing external momenta

I'm trying to explicitly compute the following box diagram in the Feynman-t'Hooft gauge: If I neglect the impulsion of the $s$ quark, then the final amplitude is given by $$\mathcal{A} \propto ...
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70 views

Is there a standard resource that lists all understood particle-particle relationships?

I am just starting to dig a little deeper into particle interactions, and just have an introductory college physics background (no quantum mechanics). But I am interested in the conditions of the ...
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343 views

LSZ reduction vs adiabatic hypothesis in perburbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free ...
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65 views

Vacuum expectation value for 2 point fermionic field

I was trying to compute $\langle 0|T(\psi_\alpha(x)\bar\psi_\beta(y))|0 \rangle$, i.e., the 2-point function for the Dirac field. While, I could easily compute, $\langle ...