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 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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46 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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88 views

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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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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51 views

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 ^4\left(-E_{\text{CM}}+...
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168 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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66 views

1-Loop Mass Splitting of vector-like Fermions

In this paper the author argues that for a vector-like fermion doublet, with degenerate mass $M$ at tree level, we always have a mass splitting between the charged component of the doublet $L$ and the ...
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92 views

Quantization of free real scalar massless field in 2d

Is there a reference to literature where one explicitly constructs quantization of the free real scalar massless field in the 2-dimensional space-time? In particular, how the propagator looks like? ...
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117 views

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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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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59 views

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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288 views

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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190 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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99 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
62 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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152 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: $$ e^{-...
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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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118 views

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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1answer
59 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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51 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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106 views

S-matrix element

I'm confused with the relation between the fully resummed propagator in a given QFT and the corresponding S-matrix element. According to the LSZ reduction formula ($\phi^4$ theory for definiteness ...
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93 views

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 c^{+}_{\alpha\sigma}c_{\beta\...
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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 on-...
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67 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 0|\psi_\alpha(x)\bar\psi_\beta(...
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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}) \vec{a}^\dagger(\vec{...
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39 views

The scale anomaly and dependence on scale

The scale anomaly states that if we have renormalizable theory without dimensionful function, which is scale invariant, then corresponding quantum theory may lost this symmetry because of ...
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116 views

Hermitian properties of Dirac operator

I am trying to understand the Hermiticity of the (massless) Dirac operator in both (flat) Minkowski space and Euclidean space. Let us define the Dirac operator as $D\!\!\!/=\gamma^\mu D_\mu$, where $...
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70 views

Nambu notation and the Majorana bound state

In celebrated work of Fu and Kane they show appearance of Majorana bound state thanks to presence of superconductor and surface states of topological insulator. They write Hamiltonian $H = \tfrac{1}{...
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40 views

Why do the masses of decay products affect the branching ratio?

Consider a particle $P$ of mass $100m$ (where $m$ is some unit). It can decay into either of two particle-antiparticle pairs: $P\to P_1\bar{P}_1$ with branching ratio $BR_1$, where $P_1$ has mass $...
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I find there are two methods to calculate the amplitude in QFT. Is it equivalent? [duplicate]

I find there are two methods to calculate the amplitude in QFT. First method: Use LSZ reduction formula $$\langle p_1\cdots p_m;out|k_1\cdots k_n;in\rangle=\big(\frac{i}{\sqrt{Z}}\big)^{n+m}\int d^...
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156 views

Why is conformal field theory so important?

I just started escaping the world of quantum mechanics and looking to study quantum field theory. I heard of AdS/CFT and also heard that CFT is of much importance. Now I do not get why having ...
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1answer
74 views

Deriving Schrodinger equation from QFT with the definition $\psi(\textbf{x},t)\equiv \langle 0|\phi_0(\textbf{x},t)|\psi\rangle$

In the book "Quantum Field theory and the Standard Model" by Matthew Schwartz, he uses the equation $$\partial_t^2\phi_0=(\nabla^2-m^2)\phi_0$$ (i.e., the Klein-Gordon equation for the free ...
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1answer
41 views

Some diracology in traces

Suppose I want to evaluate the trace $p_{\alpha} q_{\beta}\text{Tr}(\gamma^{\alpha} \gamma^0 \gamma^{\beta} \gamma^0)$. Using the standard trace formula for four gamma matrices I arrive at $$p_{\...
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75 views

Why do we say that elementary particles are pointlike? [duplicate]

When people discuss quantum field theory in a popular context, they say that fundamental particles, such as quarks and electrons, are pointlike, with zero size. However, I don't think this is what ...
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86 views

Schwartz's book: Spinor-helicity formalism

I'm trying to learn the spinor-helicity formalism from Schwartz's QFT book. His equation 27.44 is describes the annihilation of an electron(1)-positron(2) pair to a muon(3)-antimuon(4) pair. He ...
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72 views

S-duality of Einstein-Maxwell-Dilaton theory

Consider theory with action $$S = \int d^D x \sqrt{-g} (R - \frac{1}{2} \partial_\mu \phi \partial^\mu \phi - \frac{1}{2k!} e^{a \phi} F^2 _{[k]} ) $$ where $\phi$ is dilaton and $F_{[k]}$ is ...
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Correlation functions in a zero dimensional QFT?

I would like to ask about correlation functions in a 0-dimensional matrix model QFT. What information do these correlators give? I know only of correlators between two different spatial positions.
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56 views

Majorana modes in Kitaev chain [duplicate]

I am reading paper about Kitaev chain of electrons, which can exhibit famous Majorana fermions at ends of wire. The Hamiltonian (his Eq. (6)) reads $H = \frac{i}{2} \sum_j - \mu c_{2j-1}c_{2j} +(w+|\...
3
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67 views

Why is quantising gravity so difficult? [duplicate]

Since gravity is so similar with the Yang-Mills theory, the Christoffel connection is the gauge potential, the Riemann curvature is the field strength, then why is quantising gravity so difficult when ...
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1answer
43 views

What is the easiest way to prepare a Glauber coherent state? [closed]

Without using a laser source. Can you, for example, create a coherent state by filtering another light source (incandescent light bulb, LED, etc)?
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25 views

Majorana neutrino masses from left-handed neutrino condensate?

Let us consider a model with only left-handed neutrinos and with a new-physics interaction between these neutrinos, which leads to their condensation below a certain energy scale. Can we in principle ...
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What should I think of a diverging beta function (in Renormalisation Group flow)?

I have written a set of RG flow equations using Functional Renormalisation Group methods. I am looking at the flow of a well known problem with an additional original coupling. I did not do anything ...
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246 views

What would have been the story of the Universe if there was no mechanism to produce massive fundamental baryonic particles? [duplicate]

Thanks for those of you who took their time answering my problem but it seems that there is a misunderstanding between us. Most answers are based on the assumption of Electroweak symmetry breaking ...
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If an anyon picks up a phase upon particle exchange, how can you exchange them twice, isn't that a contradiction if the phase squared is not 1? [duplicate]

I'm trying to understand anyons, as stated on wikipedia, the interchange operator gives a phase https://en.wikipedia.org/wiki/Anyon $|\psi_1\psi_2>=e^{i\theta}|\psi_2\psi_1>$ So when I ...
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69 views

Number operator in interacting quantum field theory

When treating a quantum field, say the real scalar field, it's totally clear to me how to define a (global) number operator: $$\hat N = \intop \text d ^3 \mathbf p \hat a ^\dagger (\mathbf p )a(\...
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82 views

Uses of effective action and effective potential

Effective potential allows us to answer the question that whether there will be spontaneous symmetry breaking induced by quantum corrections. Is there any other information that can be extracted from ...
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59 views

Reference request: QFT and AdS/CFT for information theorists

There is a lot of buzz recently about connections between quantum information theory and quantum field theory/string theory. I would like to understand in particular how quantum information methods ...
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1answer
78 views

Meaning of counterterms and quantum corrections

When one talks about the “classical Lagrangian” of a field, does one mean the tree-level Lagrangian with physical masses and physical couplings? If yes, does it therefore mean that the bare Lagrangian ...
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84 views

Why can you make $V$ stationary with respect to a parameter of the field in Derrick's theorem?

I'm going over Coleman's derivation of Derrick's theorem for real scalar fields in the chapter Classical lumps and their quantum descendants from Aspects of Symmetry (page 194). Theorem: Let $\...