Qft Definition and 980 Threads

In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1940s and 1950s, and led to the introduction of renormalized quantum electrodynamics (QED). QED was so successful and accurately predictive that efforts were made to apply the same basic concepts for the other forces of nature. By the late 1970s, these efforts successfully utilized gauge theory in the strong nuclear force and weak nuclear force, producing the modern standard model of particle physics.
Efforts to describe gravity using the same techniques have, to date, failed. The study of quantum field theory is still flourishing, as are applications of its methods to many physical problems. It remains one of the most vital areas of theoretical physics today, providing a common language to several different branches of physics.

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  1. Nod

    A Quantized Dirac field calculations

    Hi everyone! I'm having a problem with calculating the fermionic propagator for the quantized Dirac field as in the attached pdf. The step that puzzles me is the one performed at 5.27 to get 5.28. Why can I take outside (iγ⋅∂+m) if the second term in 5.27 has (iγ⋅∂-m)? And why there's a...
  2. A

    I Can the energy of a particle ensemble in QFT be bounded over time?

    Hi all, Question for which .I feel silly asking - but since I'm still learning: A particle state in QFT is considered to be an asymptotic state with a well defined energy. Now, if I take an ensemble of particles after a very large number of interactions (say, e.g., a macroscopic object like a...
  3. A

    I QFT, event amplitudes and reversed time....

    Hi all, I've recently been reading a paper by Richard Muller and Shaun Maguire (which is not the exact topic of this post). In that work, the authors mention: "We note that in quantum field theory, very small, localized and rapid events contain amplitudes that can be interpreted as taking...
  4. MathematicalPhysicist

    How to Derive Lorentz Scalar and 4-Vector Equations in QFT?

    I hope to replicate my previous thread in QFT which was started three years ago from reading Srednicki's textbook and solution manual and also the problem book that I read (by some serbian fellow). This time I am planning to read several books, so the the title of this thread is general...
  5. F

    I Momentum cut-off regularisation & Lorentz invariance

    Why is it that introducing a hard cut-off ##p^{2}=\Lambda^{2}## breaks Lorentz invariance? Is it simply that it introduces an energy scale and energy is not a Lorentz invariant quantity? Sorry if this is a trivial question, but I just want to make sure I understand the reasoning as I've...
  6. A

    I Lamb shift and the QFT vacuum....

    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...
  7. FallenApple

    I Thinking about the static electric field in terms of QFT

    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...
  8. TeethWhitener

    I QFT operators time/space asymmetry?

    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})...
  9. LarryS

    I QFT in Euclidean or Minkowski Spacetime

    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.
  10. A

    Canonical commutation relation, from QM to QFT.

    Homework Statement This is a system of n coupled harmonic oscillators in 1 dimension. [/B] Since the distance between neighboring oscillators is ## \Delta x ## one can characterize the oscillators equally well by ## q(x,t) ## instead of ## q_j(t) ##. Then ## q_{j \pm 1} ## should be replaced...
  11. F

    A On the equivalence of operator vs path integral in QFT

    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.
  12. ChrisVer

    A Some fun (yet nice) questions on QFT

    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...
  13. F

    I A question about assumptions made in derivation of LSZ formula

    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...
  14. A

    I Goldstone bosons in description of superfluidity

    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...
  15. joebentley10

    I Applying Euler-Lagrange to (real) Klein-Gordon Lagrangian

    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...
  16. Mordred

    A Vacuum birefringence QFT treatment

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

    A QFT phi3 Feynman diagrams and correlation function

    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...
  18. L

    Other Graduate Research topic involving QFT and General Relativity

    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...
  19. A

    I Bare QFT theory with cutoff and multi-particle state....

    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...
  20. TeethWhitener

    I Srednicki QFT: Integration measure for KG eqn?

    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)}...
  21. Primroses

    IR divergences and UV divergences in perturbative QFT

    We know the following definitions in calculating amplitude (or a cross section) in momentum space: 1, Ultraviolet divergences are due to the infinity of the integration measure; 2, Infrared divergences are due to the singularity of the integrand; Now suppose we study a Feynman graph by...
  22. N

    A Is loop quantum gravity a non local or local QFT?

    Can it be either?
  23. ShadowMeson

    Declare a Commutation Relationship in FeynCalc

    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...
  24. J

    Relativity Books about Special Relativity for preparation for QFT

    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!
  25. ShayanJ

    A QFT at Finite Density: Refs & Resources for Zero T

    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...
  26. N

    A Variation in Schwinger's quantum action principle

    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...
  27. TeethWhitener

    Problem 2.9a: How to Show the Equation for U(Λ) in Srednicki's QFT Book?

    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...
  28. G

    A Expanding CCRs, and their underlying meaning

    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...
  29. E

    Coulomb scattering of spin-zero particle (QFT)

    I'm looking at Aitchison and Hey's QFT book, trying to verify Eq. 8.27 (which is in fact problem 8.2). It asks us to verify that the matrix element for the scattering of a charged spin zero particle (s^+) is <s^+,p'|j^\mu_{em,s}|s^+,p> = e(p+p')^\mu e^{-i(p-p')\cdot x} where...
  30. D

    I A question about momentum integrals and lengths

    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...
  31. A

    A QFT as pilot-wave theory - one more time....

    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...
  32. binbagsss

    QFT Wicks theorem contraction -- different fields terms of propagation

    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...
  33. G

    Different formulations of the covariant EM Lagrangian

    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...
  34. binbagsss

    I QFT Feynman Propagator Algebra

    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...
  35. F

    I Is the QFT field real or just a mathematical tool?

    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...
  36. N

    I Understanding Weak Isospin in SU(2) Gauge Theory

    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...
  37. J

    A QFT, what are the transformation rules for

    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 (...
  38. 4

    QFT for the Gifted Amateur Exercise 17.1

  39. 4

    I QFT for the Gifted Amateur Question (3)

    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...
  40. Safinaz

    I Why is QCD not perturbative at low energies?

    Hi all , I'm confused about the definition of a perturbative coupling for QFT that it should be less than 4 ## \pi ## , because the higher order corrections comes of order ## \lambda / ( 4 \pi ) ## .. Now why QCD is not perturvative at low energy because the coupling constant approaches just 1...
  41. D

    A Quantum Field Theory - Why quantise fields?

    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...
  42. F

    Studying Please tell me some names of QFT topics.

    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.
  43. USeptim

    A Issue in the electron’s infinite self-energy

    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...
  44. H

    How Is the Hamiltonian Derived from the Proca Lagrangian?

    Homework Statement Starting from the proca lagrangian $$L=-\frac14 F_{uv}F^{uv}+\frac12 m^2 A_uA^u$$ Homework Equations $$H=\sum p_i\dot{q_i}-L$$ The Attempt at a Solution $$L=-\frac14F_{uv}F^{uv}+\frac12m^2A_uA^u\rightarrow\partial_uF^{uv}+m^2A^v=0$$ $$p^i=\frac{\partial L}{\partial...
  45. M

    A Time Independent Form of Klein Gordon Eqn.: How to Reach (gδ3(x))

    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.
  46. 4

    I QFT for the Gifted Amateur Question (2)

    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...
  47. 4

    I QFT for the Gifted Amateur Question?

    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. $$\hat{u}(a)|q>=e^{-i\hat{p}\cdot a} |q> $$...
  48. F

    I Are renormalizable QFT the ''really renormalizable''?

    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...
  49. L

    A Imaginary parts of amplitues (Schwartz QFT text)

    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...
  50. Glenn Rowe

    I Equivalence of SU(2) and O(3) in Ryder's QFT book

    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} &...
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