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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Grassmann numbers in the dual space

I'm reading the section on Grassmann numbers in QFT for the Gifted Amateur and I'm confused by something said therein: First, they define a coherent state for fermions $\rvert \eta \rangle$ as ...
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38 views

What is the simplest chiral $U(1)$ theory that satistifies both gauge and gravity anomalies?

I've learned the chiral $U(1)$ theory that satisfies either gauge anomalies or gravity anomalies. But what's the theory satisfies both of them?
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53 views

$S$-matrix expansion and Feynman graphs for toy model

I have a toy model with three interacting particles $A$, $B$ and $C$ and $A$ can decay to $B$ and $C$. Looking at the process $AB\to BBC$ I just want to know which orders of the $S$-matrix expansion ...
3
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0answers
56 views

Would quantum fluctuations cause problems for scalar-field inflation?

Wheeler once said that spacetime would be highly curved at very small scales because of the uncertainty principle for energy-momentum. In which case the spacetime becomes very bumpy and not smooth ...
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0answers
68 views

Why are coherent states necessary for defining the fermionic path integral?

I am following the discussion of fermionic path integrals and Grassmann variables in QFT for the Gifted Amateur (ch. 28). It defines a coherent state for fermions $\rvert \eta \rangle$ as ...
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1answer
35 views

Interaction Hamiltonian and shifts

When we quantize a free field theory, we set $\phi(x)$ to be the operators and we take the Fourier transform to determine the creation and annihilation operators $a_\omega,a^\dagger_\omega$ such that ...
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0answers
40 views

Calculate 1-point function from generating functional

I have a generating functional: $<exp[i \sum_k c_k x(t_k)]> = exp[-1/2 \sum_{k,k'} c_k c_{k'} G(t_k, t_{k'})]$ and I need to calculate the 1-point and the 2-point function. Does anyone ...
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54 views

Solving Weyl Equations

In my second taking of QFT we just finished the Dirac equation. As an exercise I tried applying what I have (re-) learned to the Weyl equations. I'd like someone to check if my work is correct. For ...
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0answers
30 views

Canonical definition of the integrand in planar $\mathcal{N}=4 \ \mathrm{SYM}$ theory

According to page 101 of Scattering Amplitudes (Elvang, Huang), one can use the zone variables $y$ to define a unique integrand, in the planar case. This is done by saying that the momenta associated ...
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1answer
56 views

How to impose canonical commutation relations when quantising a field

I believe this is a simple question, however I cannot find it explained anywhere what the term: "Impose canonical commutation relations" means. If I have a classical equation, and I wish to quantise ...
0
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0answers
47 views

Definition of the charge conjugation operator

My question will be a bit provocative, I hope it will attract more interest (and hopefully no downvoting). I introduce the following notation: $u(p)\exp(-ipx)$ positive energy solution ...
1
vote
1answer
55 views

Seiberg duality and IR fixed point

This question is related with Seiberg duality for $SU(N)$ gauge theory which states a duality between electric theory, $SU(N_c)$ gauge theory with $N_f$ flavors is dual to its magnetic theory, ...
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31 views

Quantum Fluctuations [duplicate]

Energy is converted to mass and mass to energy. But during quantum fluctuations energy is created without mass, does this not violate the law of conservation of mass and energy?
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0answers
48 views

Why is the D0 oscillation so different from the K0 and B0?

I have looked for this answer into many articles and books but I am not able to figure out why $D^0\to\bar{D}^0$ is so highly suppressed if compared to the $B^0 \to \bar{B}^0$ and $K^0 \to \bar{K}^0$ ...
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0answers
41 views

Books on path integral methods [duplicate]

Are there advanced books on applications to physics of the method of path integral? I am aware of some of the standard textbooks on QFT, but looking for more advanced applications of the method.
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votes
2answers
182 views

Yukawa interaction between Dirac particles is universally attractive?

Can anyone provide me a specific reference to (or supply themselves) the derivation of the fact that the Yukawa interaction$$\mathcal{L}_{\text{int}} = -g\overline{\psi} \psi \phi$$between Dirac ...
2
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0answers
103 views

Goldstone's theorem. What's the catch?

A theory of scalar field with SO(3) symmetry and Higg's potential is presented by Lagrangian $$ ...
25
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4answers
2k views

Why do many people say that virtual particles do not conserve energy?

I've seen this claim made all over the Internet. It's on Wikipedia. It's in John Baez's FAQ on virtual particles, it's in many popular books. I've even seen it mentioned offhand in academic papers. ...
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votes
1answer
55 views

Why the QED coupling constant is a continuous function? [closed]

In page 316 of 'Student friendly quantum field theory', when discussing Figure 12-4, it says that the QED coupling constant is a continuous function of $\ln(p)$. But I think it's disconnected at ...
3
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2answers
90 views

Why does number of photons fluctuate?

When counting photons (with, e.g., a CCD), there is the so-called ''photon noise'' (important at low photon numbers). What is the explanation in the framework of QED, QFT? Is it the Heisenberg ...
5
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0answers
82 views

Scalar QED, are there any scalar-fermion vertices in this theory?

Consider QED with an additional charged (complex) scalar field, $\phi$:$$\require{cancel} \mathcal{L} = -{1\over4} F^{\mu\nu} F_{\mu\nu} + (D^\mu \phi)^*(D_\mu \phi) - \mu^2 \phi^* \phi - ...
3
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0answers
71 views

Improper integral of the product of exponential function and Laguerre polynomial

I saw this integral in the book [Gerry C.C.,Knight P.L.] Introductory quantum optics: ...
3
votes
1answer
344 views

Why do we need virtual particles?

I understand the $\Delta t \cdot \Delta E \geq \hbar / 2$ relationship and the idea behind them. However, I don't understand why do we need them at all. I'm a physics undergraduate. As far as I know, ...
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1answer
50 views

What's the bubble's wall made up of in false vacuum decay? [closed]

It is well known that for some kind of double well potentials, there are two minima with one is unstable called the false vacuum while the other stable one called the true vacuum. The tunneling is ...
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0answers
25 views

How can we affect the degree of quantum vacuum entanglement?

Susskind and van Raamsdonk have recently described various states of entanglement of the quantum vacuum. As a practical proposition, how can one affect the degree of quantum vacuum entanglement, and ...
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2answers
177 views

Doppler effect of matter waves

We all know that the relativistic mass of a moving object in Special relativity increases for an observer who is measuring it for a moving object. We also know the the concept of particle-wave ...
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0answers
51 views

How to understand particle decoupling in the early universe?

We often say that when the rate of some interactions, say the beta decay and electron capture, are slower that the rate of universe's expansion, then the corresponding particles, say neutrinos, ...
4
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2answers
119 views

Determinant of a propagator

Say I have a path integral $\int D \phi \exp(i S_0)$. $S_0$ is the usual free action $$S_0=\frac{1}{2}\int\phi (-\Box-m^2) \phi=\frac{1}{2}\int \phi G^{-1} \phi,$$ and at the moment I'm not ...
5
votes
1answer
210 views

Is a $SU(2)$ supergauge theory really a $SU(2)$ gauge theory?

Consider $SU(2)$ supergauge theory with $A$, a doublet of two chiral superfields in the fundamental representation. $$A= \begin{pmatrix} \Phi_1\\ \Phi_2 \end{pmatrix}$$ where $\Phi_1$ and $\Phi_2$ ...
1
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1answer
66 views

Criticality in BCS Theory

Can someone provide me with a pedagogical introduction into the role of criticality in BCS theory? The QCD condensate is due to strong coupling. The BCS condensation involves only weak coupling - ...
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0answers
48 views

Difference between the propagators and vertex function [closed]

I am confused between Green's function and vertex function in field theory. Can someone please explain the difference between the two in context ${\lambda} {\phi}^4$ theory?
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0answers
43 views

Measuring expectation value in quantum field theory and in quantum mechanics

There is a way of calculating the vacuum expectation value $\langle 0|\hat\phi|0\rangle$ theoretically in a quantum field theory like there is a rule to compute expectation value of any operator A ...
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0answers
43 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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0answers
37 views

Non-zero gravitational anomaly

Analogous to the Adler-Jackiw-Bell anomaly of QCD, we have an anomaly in gravity when we consider gravity to be coupled to chiral fermions: \begin{equation} \partial_\nu J^\nu_5\propto R\tilde{R}, ...
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0answers
10 views

Can i extend the non-linear realization of the chiral group to $U$ with complex pions?

In chiral perturbation theory we build a Lagrangian invariant under $SU(2)_L\times{}SU(2)_R$ which acts on the matrix $U$ that accommodates the pion degrees of freedom in the following way ...
3
votes
1answer
103 views

Doubts about spontaneous symmetry breaking

I have been exposed to the usual treatment about spontaneous symmetry breaking in the standard model but it shames me to admit that there are some loose ends I still have to tie up. For simplicity, ...
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0answers
33 views

Massless scalar $\phi^3$ tree-level scattering amplitudes?

The CHY formula for massless scattering at tree-level can compute i.e. scalar, gluon and graviton amplitudes. For gluon scattering there are many other resources available to compute all kinds of ...
1
vote
3answers
91 views

Modern explanation of the Young experiment with Quantum Field Theory?

In the Young double slit experiment it is possible to detect the arrival of individual photons as well as an interference pattern. It doesn't makes much sense to me that something could be either a ...
2
votes
0answers
47 views

What is the relation between dimension and Quantum Field Theory? How does different dimensions change QFT? [closed]

Does the quantisation rules & field operators for scalar or Dirac fields change with dimension? Most books wrote about 3 spatial dimensions, and then upgraded it to 4 spacetime dimensions, keeping ...
3
votes
2answers
108 views

What happens when a field turns on or off?

Short Setup I am curious about the the mechanics of fields, whether electromagnetic, gravitational, etc. So as a specific example in order to simplify (hopefully) how to ask this question, consider ...
3
votes
1answer
103 views

How does order of scalar $\phi$ interaction impact feynman diagrams?

On page 60 of srednicki (72 for online version) for the $\phi^{3}$ interaction for scalar fields he defines $Z_{1}(J) \propto exp\left[\frac{i}{6}Z_{g}g\int d^{4}x(\frac{1}{i}\frac{\delta}{\delta ...
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0answers
45 views

Superpotential Symmetry

Superpotential in general has the form $W=a_n\Phi^n$. If I require that my superpotential should be invariant under the following global transformation, $\delta \Phi=i\epsilon \Phi$ and $\delta ...
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0answers
26 views

Klein Gordon equation of fields via the definition of the time ordered product

My question is as follows: Consider that, $$ (-\partial_1^2+m^2)\langle 0|T(\phi(x_1)\phi(x_2))|0\rangle $$ Due to the definition of the time ordered product one can get: $$ ...
3
votes
1answer
74 views

How to show that $\bar\psi\gamma^\mu\psi$ of a Dirac spinor $\psi$ transforms as a vector?

This is part 2 of exercise II.1.1 of Zee's QFT in a Nutshell (here's part 1). This is what I have got: \begin{align} \bar\psi\gamma^\lambda\psi \mapsto ...
2
votes
1answer
79 views

How to show that $\bar\psi\psi$ of a Dirac spinor $\psi$ transforms as a scalar?

I would like to show that for a Dirac spinor $\psi$, the scalar product $\bar\psi\psi$ transforms as a scalar under a Lorentz transformation $\Lambda$, where $\bar\psi = \psi^\dagger\gamma^0$. This is ...
1
vote
1answer
113 views

Is the Higgs mechanism a gauge transformation or not? ( $U(1)$ context )

I'm trying to understand the way that the Higgs Mechanism is applied in the context of a $U(1)$ symmetry breaking scenario, meaning that I have a Higgs complex field ...
5
votes
2answers
151 views

Derivation of momentum in QFT - from Energy-Momentum Tensor [closed]

The conserved 4-momentum operator for the complex scalar field $\psi = \frac{1}{\sqrt{2}}(\psi_1 + i\psi_2)$ is given in terms of the mode operators in $\psi$ and $\psi^{\dagger}$ as $$P^{\nu} = \int ...
5
votes
1answer
70 views

Nonabelian global symmetries, $SO(N)$ charges in terms of creation and annihilation operators

Consider an $SO(N)$ symmetric theory of $N$ real scalar fields,$$\mathcal{L} = {1\over2} \partial_\mu \Phi^a \partial^\mu \Phi^a - {1\over2} m^2 \Phi^a \Phi^a - {1\over4} \lambda (\Phi^a ...
3
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1answer
111 views

What is the meaning of the UV =? IR statement in String theory

I was looking through these notes http://www.damtp.cam.ac.uk/user/tong/string/six.pdf and on page 146 it says "This corresponds to the fact that any putative UV divergence of string theory can always ...
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0answers
59 views

Why is it that the conformal anomaly has to be scale invariant?

When reading about conformal anomalies, such as in this paper it is often stated that the anomaly (ie. $ \delta W[g]/ \delta \sigma$ where $ W[g]$ is the quantum effective action for gravity) must be ...