Qft Definition and 956 Threads

I think I already know the answer to this, but I'm looking for a source: Can the Lamb shift be explained entirely in terms of radiative corrections due to the self-interaction of the hydrogen's electron with its own EM field? That is, is it necessary to reference vacuum polarization or related...

So according to classical electrodynamics, an electron would produce an electric field that is a physical entity in and of itself. This field has momentum so when a test charge is placed within this vicinity, it would be affected by the field itself, not the electron. But what about the QFT way...

I'm slowly working through Srednicki's QFT book and I had a question about section 3 (canonical quantization of scalar fields). At one point, he shows that the creation and annihilation operators ##a(\mathbf{k})## and ##a(\mathbf{k}')## are time-independent via the equation: $$a(\mathbf{k})...

Forgetting for the moment about curved spacetime, does the relativistic QFT in use today by experimental physicists live in Euclidean spacetime or Minkowski spacetime. Thanks in advance.

I have read many textbooks and googled google times for a clear explanation, but I could not find one. How does raising and lowering -annihilation/ creation-(is that energy or particle number?) translate to transition probabilities of path integral.

I was looking through some problems on QFT, and I found these exercises: http://www.damtp.cam.ac.uk/user/tong/qft/oh4.pdf I was wondering about questions 9 and 10... Q9 : speaking I guess aftermatch ,why was there a factor of 2 wrong in the published result? To be honest I don't quiet understand...

I've been reading through a derivation of the LSZ reduction formula and I'm slightly confused about the arguments made about the assumptions: $$\langle\Omega\vert\phi(x)\vert\Omega\rangle =0\\ \langle\mathbf{k}\vert\phi(x)\vert\Omega\rangle =e^{ik\cdot x}$$ For both assumptions the author first...

Hello, I'm trying to understand how the superfluidity is connected with the Lagrangian of the system: in some textbooks (e.g. Antony Zee qft in nutshell) it is stated, that in case, when the excitations in the fluid have energy spectrum linear with momentum , there is a critical velocity, which...

I'm currently studying Quantum Field Theory and I have a confusion about some mathematics in page 30 of Mandl's Quantum Field Theory (Wiley 2010). Here is a screenshot of the relevant part: https://www.dropbox.com/s/fsjnb3kmvmgc9p2/Screenshot%202017-01-24%2018.10.10.png?dl=0 My issue is in...

Evidence for vacuum birefringence from the rst optical polarimetry measurement of the isolated neutron star RX J1856.5−3754...

I have some difficulty understanding how to go about with this problem: I came up with several graphs, you can see them in the attached picture (they are up to ~g^4 order). I am not sure about the self-interaction diagrams, but I think they are considered in the connected graphs (they are not...

Last year I finished the undergraduate course in Mathematical Physics. This year, more precisely in March, I'm going to start the graduate course to acquire a master's degree in Physics. Now, for this course I must choose a research topic and find an advisor. This is being a little bit...

Hi all, I was reading Arnold Neumaier's excellent article on the Vacuum Fluctuation Myth, and ran upon one part I have a question about: he notes that "in bare quantum field theory with a cutoff, the vacuum is a complicated multiparticle state depending on the cutoff – though in a way that it...

Hi, I had a quick question about something from Section 3 of Srednicki's QFT book. In it, he's discussing the solution to the Klein-Gordon equation for classical real scalar fields. He gives the general solution as: $$\int_{-\infty}^{+\infty} \frac{d^3 k}{f(k)}...

Can it be either?

Homework Statement I am a rookie to the QFT extension in Mathematica called FeynCalc, and tried to use that into solving some quiz. Soon I met a problem upon some condition presented in a problem which declares an relation of two same tensor with different indices results in some value when...

Hello, I want to learn QFT but I feel that my understanding of Special Relativity is not good enough. Could you please recommend to me any good relativity books to fill my gaps? My gaps are mostly conceptual. Thanks in advance!

I need to take a look at some references about QFT at finite density but I can't find anything, or at least I don't know where to look. I should emphasize that what I need is QFT at zero temperature and finite density so it seems to me QFT in finite temperature books may not be what I need or...

At the moment I'm working with the https://en.wikipedia.org/wiki/Schwinger's_quantum_action_principle']quantum[/PLAIN] action principle of J. Schwinger. For this I read several paper and books (like: Quantum kinematics and dynamics by J. Schwinger, Schwinger's Quantum action principle by K.A...

Homework Statement This is from Srednicki's QFT book, problem 2.9a: Let ##\Lambda = 1+\delta\omega## in the equation: $$ U(\Lambda)^{-1} \partial^{\mu}\varphi(x) U(\Lambda) = \Lambda^{\mu}{}_{\rho} \overline{\partial^{\rho}}\varphi(\Lambda^{-1}x) $$ where ##\overline{\partial^{\rho}}## denotes...

Hi, I remember seeing a few months ago, at a lecture about statistical signal processing, something which looked similar to commutation relations, only with a gaussian, instead of a delta function. Basically, it looked like this: $$\left[\phi(x),\phi(y)\right] = ie^{-\alpha(x-y)^2}$$ This...

I've been making my way through Matthew Schwartz's QFT book "Quantum Field Theory and the Standard Model". In chapter 6 he derives the differential cross-section for a ##2\rightarrow n## interaction. As part of the derivation, he introduces the Lorentz invariant phase space measure (LIPS), and...

I've recently read (portions of) the paper "QFT as pilot-wave theory of particle creation and destruction," available here: http://xxx.lanl.gov/pdf/0904.2287v5 This paper has been mentioned in a number of other threads, but I have a different question (not as an expert, unfortunately). The...

Homework Statement I am trying to express ##T(\phi(x1)\Phi(x2)\phi(x3)\Phi(x4)\Phi(x5)\Phi(x6))## in terms of the Feynman propagators ##G_F^{\phi}(x-y)## and ##G_F^{\Phi}(x-y)## where ##G_F^{\phi}(x-y) =\int \frac{d^{4}k}{(2\pi)^{4}}e^{ik(x-y)} \frac{ih}{-k.k - m^2 -i\epsilon} ## and...

Homework Statement I'm reading through A. Zee's "Quantum Field Theory in a nutshell" for personal learning and am a bit confused about a passage he goes through when discussing field theory for the electromagnetic field. I am well versed in non relativistic quantum mechanics but have no...

I am wanting to get the expression up to ##O(\epsilon^{2}) ## : To show that ##\frac{1}{2w_{k}} (\frac{1}{w_{k}-k_{0}-i\epsilon} + \frac{1}{w_{k}+k_{0}-i\epsilon})## ##=## ## \frac{1}{k_{v}k^{v} + m^{2} - i\epsilon}##, [2] where ##w_{k}^{2}=k^{2}+m^{2}##, ##k## the variable, and (this seemed...

Sorry, I know this has been talked about many times before but I like to put the question in a direct way so I may understand. Since there are more than 10^80 particles and radiation, how can a single point in space carry the values for all these fields at the SAME time all the time if they are...

In QCD, quark is in fundamental representation of SU(3) and thus it has to have 3 charges (what we came to call "colors"). Gauge bosons are in adjoint representation and there are 8 of them. The choice how to assign color charges to them is not unique, one popular choice is based on Gell-Mann...

I'm taking an introductory course in QFT. During quantization of the Dirac field, my textbook gives a lot of information on how annihilation and creation operators act on vacuum, but nothing about how they act on non-vacuum states. I need these to compute $$ \int \frac{d^3 p}{(2\pi)^3} \sum_s (...

In exercise 17.1 we are asked to show that the propagator: $$G^+_o(p,t_x,q,t_y)=\theta(t_x-t_y)<0|\hat{a}_p(t_x)\hat{a}^\dagger_q(t_y)|0>$$ is the same as $$\theta(t_x-t_y)e^{-i(E_pt_x-E_qt_y)}\delta^{(3)}(p-q)$$ so we can take the time dependence out of the creation and annihilation...

As I understand it, the need for quantum field theory (QFT) arises due to the incompatibility between special relativity (SR) and "ordinary" quantum mechanics (QM). By this, I mean that "ordinary" QM has no mechanism to handle systems of varying number of particles, however, special relativity...

Please give me one or some names of QFT topics to make PhD thesis.I am prepairing to make a thesis but I don't know how to choose a topic which is new in QFT and possibly to resolve.

Hello, Reading Richard Feynman’s book “Quantum Electrodynamics” (Edited by Advanced Book Classics), I read that the electron’s self-energy is infinite and that has been a trouble for QED during 20 years. Feynman proposed a solution based on a cut-off, but that’s not fully satisfactory and I...

If equation of motion(K-G Eqn.,) follows, ∂μ∂μΦ+m2Φ=ρ where 'ρ' is point source at origin. How time independent form of above will become, (∇2-m2)Φ(x)=gδ3(x) where g is the coupling constant, δ3(x) is three dimensional dirac delta function.

In chapter 11, Lancaster takes us through the 5 steps for canonical quantization of fields, and in example 11.3 he derives a mode expansion of the Hamiltonian which ends in this: $$E=\int d^3 p E_p (a _p^{\dagger} a_p + \frac{1}{2} \delta^{(3)}(0)) $$ Which I have no problem with, but then...

In chapter 9 "Quantum Mechanical Transformations", example 9.3, can anyone explain how $$\hat{p}$$ in the exponential converts itself to q? Apologies in advance if this is very basic, but thanks for looking. $$\hat{u}(a)|q>=e^{-i\hat{p}\cdot a} |q> $$...

The renormalizable QFT is the theory with only a finite number of Feynman diagrams superficially diverge(in all order) and the non-renormalizable QFT is the theory with infinite diagrams superficial diverge. Then my question is in all renormalizable theories can we absorb all divergences into...

From Schwartz http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf p. 257 or his qft book p. 455 1. Why and how does the integral in (24.24) go imaginary, when M > 2m? Is it because the logarithms can not take negative real numbers, thus we have to switch to complex...

I've got a question about the identification of SU(2) with O(3) in Ryder's QFT book (2nd edition) pages 34 - 35. The other posts on this topic I could find don't seem to address this question, so here goes. He derives the matrix in eqn 2.47: $$H= \left[\begin{array}{cc} -\xi_{1}\xi_{2} &...

I've discovered a potential treasure horde tucked away in the deep dark folds of the world wide web. A 1625 page mammoth on all aspects of quantum field theory by Prof. Hagen Kleinert. There's a draft ed. for free available here -...

Hi all! I have a question regarding the principal difference between QFT and string theory according to popular accounts. It is said that QFT deals with point particles leading to the well-known infinities in calculating the transition amplitudes whereas in string theory the interaction is...

Hello, I hope this is not a stupid question as I am not a physicist. But I was curious about how contenders for the so-called Theory of Everything view the shape of the elementary particles. I know that the basic idea of string theory is related to the shape of elementary particles as one...

Consider the 2-point correlator of a real scalar field ##\hat{\phi}(t,\mathbf{x})##, $$\langle\hat{\phi}(t,\mathbf{x})\hat{\phi}(t,\mathbf{y})\rangle$$ How does one interpret this quantity physically? Is it quantifying the probability amplitude for a particle to be created at space-time point...

In the canonical quantisation of a free scalar field ##\phi## one typical constructs a mode expansion of the corresponding field operator ##\hat{\phi}## as a solution to the Klein-Gordon equation...

I have just gone through chapter 14 on the QFT for the gifted amateur by Lancaster and Blundell. Quantising the electromagnetic field results in the Hamiltonian: $$\hat{H}=\int d^3p \sum^{2}_{\lambda=1} E_p \hat{a}^\dagger_{p\lambda} \hat{a}_{p\lambda}$$ with ##E_p=|p|##. In this post ##p##...

I'm reading Srednicki's Quantum Field Theory. I 'm trying to read Srednicki's presentation of Feynman Diagrams in the chapter Path Integral for the Interacting Field Theory. Link to the book: The path integral for the phi-cubed theory is equation 9.11 in the book. Please read that. I get the...

Is it possible to approximately calculate the dynamics of a "phi-fourth" interacting Klein-Gordon field by using a finite dimensional Hilbert state space where the possible values of momentum are limited to a discrete set ##-p_{max},-\frac{N-1}{N}p_{max},-\frac{N-2}{N}p_{max}...

I've read that one of the primary motivations for the need for QFT is that quantum mechanics cannot account for particle creation/annihilation, however special relativity "predicts" that such phenomena are possible (clearly they have been observed experimentally, but I'm going for a heuristic...

Hi, I'm trying to learn some QFT at the moment, and I'm trying to understand how interactions/nonlinearities are handled with perturbation theory. I started by constructing a classical mechanical analogue, where I have a set of three coupled oscillators with a small nonlinearity added. The...