What is Qft: Definition and 978 Discussions

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. M

    Math QFT Books: Arnold, Takhtajan & Beyond

    Are there any QFT books written from a mathematical perspective? Something in the same vain as V. Arnolds Mechanics and Takhtajan's QM. Thanks.
  2. G

    What are matrix elements in QFT?

    Suppose you want the 1-particle matrix elements of an operator in QFT, e.g. \langle p' |\phi^4(x)|p\rangle It seems you would calculate this perturbatively by first Fourier transforming the x-variable to q, assuming an incoming particle with momentum p, an outgoing particle with momentum p'...
  3. BiGyElLoWhAt

    Calculating Functional Derivatives: Understanding Notation and Examples

    If I understand what's going on (quite possibly I don't), I think my book is using bad (confusing) notation. Homework Statement As written: "Calculate ##\frac{\delta H[f]}{\delta f(z)} \ \text{where} \ H=\int G(x,y)f(y)dy##" and ##\frac{\delta H[f]}{\delta f(z)}## is the functional derivative...
  4. Abolaban

    Equation Derivation in QFT book by D.MacMahonhow?

    Hello, I have encountered an equation in page 33 in the book of D.MacMahon titled QFT demystefied. It is the third equation from the top...how did the sum appear as a middle step of the equation? best regards. Abolaban
  5. E

    Wick's Theorem for free fields only

    I'm not quite following why Wick's Theorem only applies to free fields. What part of the argument depends on a free field assumption?
  6. N

    Quantum Please give me some advisory about the QFT book of Grensing.

    Please give me some advisory about the book: Structural aspects of QFT and Noncommutative Geometry of Gerhard Grensing. I am reading QFT book of Weinberg and I have no idea to continue to read which book in QFT after finishing the Weinberg's books.
  7. Ace10

    One Loop corrections in ee--->ee scattering in QED

    Homework Statement First of all, Happy New Year! I have to solve the following exercise (xmas gift :P) and some things are a bit vague..Here is it: For the ee--->ee scattering process, draw all amputated and connected graphs that would contribute. The hint is that one should find 10 different...
  8. pellman

    Modern Axiomatic Quantum Field Theory Texts for Beginners

    I have started reading PCT, Spin and Statistics, and All That. Are there any more recent texts that I should be looking at instead?
  9. M

    What are some options for QFT and string theory MSc programs in the UK?

    I'm currently in my final year at TCD and I'm looking at MSc programs in the UK in the areas of QFT, strings, CFT etc. The ones I know about are the obvious ones in London i.e KCL, Imperial, Part III, but they're out since London is so expensive and I'm extremely limited with funds. I've also...
  10. TrickyDicky

    Magnetic moment from neutral particles in QFT

    Could somebody take a stab at explaining how can quantum fluctuations give neutral elementary particles a magnetic moment? (in the usual explanation given by QFT textbooks, I think there are people around here denying the existence of quantum fluctuations, insert the more neutral expression...
  11. nuclearhead

    Is the Hamiltonian for Klein Gordon fields Hermitian?

    I was reading about the Klein Gordon equation of scalar fields. I notice that the hamiltonian is not Hermitian: ∂0(Φ,π)T = matrix((0,1),(-p2,0)) (Φ,π)T The Hamiltonian operator iH = matrix((0,1),(-p2,0)) is not a hermitian matrix. What does this mean? Does this mean Klein Gordon fields don't...
  12. nuclearhead

    Where does the 'i' come from in QFT path integral?

    So I've been thinking about the axioms of quantum field theory. In particular the expression for the particle amplitudes: G(x1,x2,...,xn) = ∫Φ(x1)Φ(x2)...Φ(xn)ei S[Φ]/ħ D[Φ] / ∫Φ(xn)ei S[Φ]/ħ D[Φ] But I've been struggling to explain the existence of the 'i'. It seems like this is a...
  13. Xiaomin Chu

    Is there any learning group for QFT?

    Want to learn QFT but often lose courage when seeing such a huge book(M. Srednicki). The author also suggests learn with someone else. Is there any group for this?
  14. B

    Lorentz Transform on Covariant Vector (Lahiri QFT 1.5)

    Homework Statement Given that ##x_\mu x^\mu = y_\mu y^\mu## under a Lorentz transform (##x^\mu \rightarrow y^\mu##, ##x_\mu \rightarrow y_\mu##), and that ##x^\mu \rightarrow y^\mu = \Lambda^\mu{}_\nu x^\nu##, show that ##x_\mu \rightarrow y_\mu = \Lambda_\mu{}^\nu x_\nu##. Homework Equations...
  15. H

    QFT & QM: Spinors, NRQM & Dirac Field Explained

    Often I see QFT texts introduce dirac spinors by comparing them to the two component spin states (which I have come to accept are also spinors) in NRQM. And arguing that since the NRQM spinors transform via SU(2), our desired quantum fields for spin 1/2 particles should be some higher...
  16. J

    Spin parity and attractive/repulsive forces

    In most introductory QFT treatments, it's stated early on (and without proof) that particles with even integral spin are always attractive, while those with odd integral spin can be repulsive; sometimes this is even cited as evidence that the graviton must be spin 2 (I think Feynman's...
  17. B

    Light speed and uncertanty principle

    Is it true that if time stood still it would violate the uncertainty principle. therefor if you traveled at the speed of light time stands still and you would violate the uncertainty principle. if this is true does that sugest that QFT sets a lower max speed that matter can travel at than what...
  18. ChrisVer

    Is Weinberg missing a \gamma_5 in his mass parameter redefinition?

    I'm having problem in deriving 23.6.11 from Weinberg's-Quantum Theory of fields... We have: \psi_f \rightarrow \exp (i a_f \gamma_5) \psi_f, f denoting the flavor. Then for the mass term lagrangian he writes: L_m = - \frac{1}{2} \sum_f M_f \bar{\psi}_f (1+ \gamma_5) \psi_f - \frac{1}{2}...
  19. L

    Questions concerning integrals in Schwartz's QFT text

    Two (supposedly) trival questions in Schwartz's QFT notes. The notes can be found http://isites.harvard.edu/fs/docs/icb.topic521209.files/QFT-Schwartz.pdf. 1. page 155, equation 15.2, how does the integrand reduce to k dk? I would guess that there must be some logarithm, but k dk? 2. page 172...
  20. B

    How Do Particles Interact in Quantum Field Theory?

    I'm an experimentalist, so go easy on me... What does it mean for a particle to either couple or not couple to a field? I haven't taken a class in QFT yet, so please try to explain the general idea without any details or equations!
  21. M

    Lorentz Transformation in Bjorken & Drell QFT

    Homework Statement [/B] I'm trying to derive (14.25) in B&J QFT. This is ##U(\epsilon)A^\mu(x)U^{-1}(\epsilon) = A^\mu(x') - \epsilon^{\mu\nu}A_\nu(x') + \frac{\partial \lambda(x',\epsilon)}{\partial x'_\mu}##, where ##\lambda(x',\epsilon)## is an operator gauge function. This is all being...
  22. L

    Cross Section: Quark-Gluon vs. Quark-Photon

    This isn't a homework problem. I am preparing for a particle physics exam and although I understand the theoretical side of field theory, I have little idea how to approach practical scattering questions like these. THE PROBLEM: Dark matter might be observed at the LHC with monojet and...
  23. K

    Ward Identity in Schwartz's QFT Book: Massless Photon Assumption or Not?

    I was reading Schwartz's qft book. I saw the proof of ward identity taking pair annihilation as an example. he claimed he didn't assume that photon is massless in this derivation. but i have confusion with this statement. gauge invariance is a fact related to massless particles. now he has...
  24. S

    QFT, weinberg volume 1 page 66

    hi guys, this is the first time i post a thread. I have an issue on proving the scalar products for arbitrary momenta. Can anyone help me ? I always end up with N(p)N*(p')(D(L^-1(p)L(p'))_rowrow'detla I have been spending hours on proving this..still i can't prove it...
  25. atyy

    QFT & Statistical Physics: Exploring Rough Paths & Constructive CFT

    Because of the Feynman path integral, QFT can be made into a statistical field theory. In rigourous relativistic field theories, this is formalized by the Osterwalder-Schrader conditions. At any rate, there are well established links between quantum field theory and statistical physics. A...
  26. R

    Understanding Traceless Proof for Gamma Matrices

    I'm reading through some lecture notes and there is a proof that the gamma matrices are traceless that I've never seen before (I've seen the "identity 0" on wikipedia proof) and I can't work out some of the steps: \begin{align*} 2\eta_{\mu\nu}Tr(\gamma_\lambda) &=...
  27. MathematicalPhysicist

    Solutions to problems in Weinberg's books on QFT

    Does someone have solutions to Weinberg's books on QFT which he care to share with me?
  28. TrickyDicky

    QFT Corrections to Electron's g-Factor: Implications for Spin Symmetry

    Do the corrections after renormalization to the gyromagnetic ratio of the electrón, more precisely its g-factor, that slightly deviate from the relativistic Dirac equation prediction of g=2 as corresponds to a spin 1/2 fermion, mean that the fermions spin symmetry is only aproximate? i.e. that...
  29. E

    QFT renormalization and Haag's theorem

    Hi all! I'm a beginner in QFT. I've read a lot of posts here about Haag's theorem, but I haven't found one which can answer simply and briefly to my question (if such an answer exists): Do UV divergencies appear because of the Haag's theorem? Thank you
  30. K

    Elementary doubts i i got confronted with while reading qft

    why should Proca eqn be like ∂γ Fγμ + m2 Aμ = 0 but not ∂γ Fμγ + m2 Aμ = 0 ? another doubt is (λ-1 ω λ)μγ = λ-1 ρμ ωρσ λσγ ? why in λ-1 transformation got upper index in the second place but not in the first place? if someone clear my doubts...I would be thanful... regards.. Kau
  31. V

    Statistical Physics vs QFT for quantum information processing

    Good day, I'm starting my master in physics, and it's time for me to choose my courses. I've decided that I probably want to pursue the direction of quantum information processing, and I'm trying to pick my courses with that in mind. For my first semester I'll be taking four courses: Quantum...
  32. D

    QFT & String Theory: "Particle First" vs "Field First

    As Steven Weinberg put it, "the idea of quantum field theory is that quantum fields are the basic ingredients of the universe, and particles are just bundles of energy and momentum of the fields." At least, this is one way to look at QFT. The other approach is to imagine that these particles are...
  33. ShayanJ

    Puzzling thing about QFT in curved space-time

    In the page http://en.wikiped ia.org/wiki/Hamilton%E2%80%93Jacobi%E2%80%93Einstein_equation, under Shortcomings of four-dimensional spacetime", you can see the following line: Is it correct? If it is, how can it be? Because in GR, gravity is space-time curvature!
  34. M

    Solving Schwartz QFT Eqn 5.26 to Get Eqn 5.27

    Hello. From Schwartz QFT BOOK, How could Eqn 5.26 can be Eqn 5.27? d \Pi_{LIPS}=(2 \pi) ^{4} \delta^{4}(\Sigma p) \frac{d^{3} p_{3}}{(2 \pi) ^{3}} \frac{1}{2 E_{3}} \frac{d^{3} p_{4}}{(2 \pi)^{3}} \frac{1}{2 E_{4}} Eqn(5.26) d \Pi_{LIPS}=\frac{1}{16 \pi ^{2}} dΩ ∫ d p_{f}...
  35. K

    Path Integrals in QFT: Beyond Peskin's Reference

    Can anyone suggest me a good reference for path integrals (QFT), apart from peskin.
  36. B

    History and origin of amplitude summation in QFT

    In chapter 2.2 of Feynman's book on QFT, he states that the probability amplitude of a particle going from a to b is the sum of contributions from all paths, and that each path contributes the same amplitude, but with a different phase. My question is, why does Feynman state that this is the...
  37. R

    Renormalization of a non-local QFT

    Hi guys. I'm working on a model described by a non-local QFT. I think I got the Feynman rules right, but I get divergences from ##\delta(0)##-like factors.Homework Statement It's a QFT for a complex scalar field ##\psi(x)=\psi(\mathbf{x},t)## with action $$S= \int dx...
  38. F

    Basic question about equations of Quantum field theory (QFT)

    Hello Forum, The electromagnetic field EM must be treated relativistically because it travels at the speed of light in a vacuum. However, the idea of quantization forces us to treat the field as a quantum mechanical field. QFT is the answer to that. QFT is quantum mechanics with...
  39. MathematicalPhysicist

    Another question from Srednicki's QFT book

    Sorry for my questions, (it does seem like QFT triggers quite a lot of questions :-D). Anyway, on page 103 (it has a preview in google books), I am not sure how did he get equation (14.40), obviously it should follow from (14.39), but I don't understand where did -ln(m^2) disappear ...
  40. M

    Causality and the Green's Function in Classical EM

    Homework Statement I am not sure about the problem set up. For (a), Using Equation of motion, need to express Lagrangian in terms of only J? I got, L=-\frac{1}{2 \Box^2 }(\partial_\mu J_\nu)^2 - \frac{{J_\mu}^2}{\Box}, using lorentz gauge (b) \partial_\mu J_\mu =0 means k_\mu J_\mu =0 ...
  41. W

    Ward Identity in Srednicki QFT book

    Hello guys, I am working on Ch22 "Continuous symmetries and conserved currents" of Srednicki QFT book. I am trying to understand how to prove the Ward-Takahashi identity using path integral method, done in page 136 of Srednicki. I understood everything up to Equation 22.22, which is 0 =...
  42. D

    QFT - Commutator relations between P,X and the Field operator

    Hi all, I haven't been able to find an answer online but this seems like a pretty basic question to me. What are the commutator relations between the position/momentum operators and the field operator? I'm not even certain what the commutation relations between X/P and a single ladder operator...
  43. diegzumillo

    Peskin QFT - Noether's theorem

    Hi all Maybe you could help me understanding this bit from the beginning of the book (peskin - intro to QFT). Homework Statement In section 2.2, subsection "Noether's theorem" he first wants to show that continuous transformations on the fields that leave the equations of motion...
  44. B

    Exploring the Challenges of Quantizing Gravity and its Integration into QFT

    why are physisist having so much trouble quantising gravity and getting it to fit into QFT?
  45. W

    Things I should look at before I take QFT?

    I think my weakest area is things like integration techniques, complex analysis, and integral transforms, but after a few google searches I can't really find what makes QFT so hard when people see it the first time. I really don't understand how to evaluate path integrals or those...
  46. D

    Understanding S-matrix elements in QFT

    Hi, I was wondering if I could test my understanding on the S-matrix and its role in evolving initial states of systems to final states (after some scattering process has occurred). Would it be correct to say the following: Given a system in an initial state \vert i \rangle, the final...
  47. E

    Need a good Textbook with full solutions QFT and GR

    Hi guys I need a good introductory Textbook with full solutions on Quantum Field Theory and General Relativity I am an upper level undergraduate. Please pick ones that have solution thanks.
  48. D

    How does Weinberg's Quantum Theory of Fields develop QFT in Heisenberg picture?

    Hello, Can anyone recommend me a book that develops QFT in Heisenberg picture? I have found Källen - Quantum Electrodynamics. Thanks in advance for the answers.
  49. H

    General questions on the formalism of QFT

    1. Why are there an unfixed number of particles? Texts usually present some hand-waving argument with bits and pieces of SR and NRQM thrown together. Are there more rigorous explanations? 2. How can the scalar fields suddenly be opeartors? I never understood this step mathematically, one...
  50. A

    QFT (derivative the covariant and contravariant fields)

    Hi, please help me .. How can I derivative covariant and contravariant fields? as in the attached picture Thanks.. http://www.gulfup.com/?tNXcaN w.r.t alpha
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