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. 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...
  2. 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
  3. G

    Calculating Probability of Field States in QFT

    Is it actually possible to calculate the probability of field states in QFT? For example the probability of some scalar field being found as some function f(x,t), i find this problem ignored in most texts.
  4. Larry Gopnik

    Pascual Jordan - The Forgotten QFT Physicist?

    Hallo! I know, I know - everywhere it says "NO HOMEWORK", but I am not entirely sure if writing a Historical Paper on Quantum Field Theory is classified as homework so will attempt to post it here - if it is classed, then I'm very sorry (please move this thread to the correct place). So yes...
  5. S

    Which maths should I need for QFT?

    Thanks for all the help on my QFT question I posted earlier. I have a new question I am very much interested in understanding QFT at a much higher level without going back to college and was wondering which mathematics' in particular are needed to really understand QFT. I did attend Ohio State...
  6. K

    Regarding the creation and annhilation operators in QFT

    Hello! I'm trying to understand QFT for the moment and have a question regarding the basic. So we have a vectorspace (Hilbertspace) of our states. The operator \phi(x) measures the amplitude at point x, whereas the operator \pi(x) measures the momentum density.. The ladder operator...
  7. WannabeNewton

    QFT Textbook Reviews: Mandl & Shaw's 2nd Edition

    Hey guys. So I've spent some time with the following book: https://www.amazon.com/dp/0984513922/?tag=pfamazon01-20 (basically halfway through chapter 4 which is on spin 1/2 fields) and as far as pedagogy goes, this book is a godsend. I don't think I've seen a more lucid upper-division physics...
  8. G

    Zee's QFT book: equal time propagator

    The propagator in 4-dimensions for a free scalar field has the form: Δ(x,0)=Θ(t)A(x,t)+Θ(-t)B(x,t) where Θ is the step function (eq 23 of Zee's QFT book, 2nd edition). He then makes the claim that for spacelike x, one can set t=0, and define Θ(0)=1/2. The going through all the math, he...
  9. A

    QFT Time Ordering: Solve Mystery of Operator Rewriting

    I have asked this question once, but no one seemed to notice it, so I'll try again. In my book the time ordering operator is used to rewrite an operator product: U(β,τ)A(τ)U(τ,τ')B(τ')U(τ',0) = T_τ(U(β,0)A(τ)B(τ')) To refresh your memories the time ordering operator T_τ orders operators...
  10. Q

    Haag's Theorem: Importance & Implications in QFT

    So I'm currently studying QFT, and I got to the point where I realized that the S operator, initially assumed to be unitary, is not unitary anymore, since it is assumed to act between t0 = - infinity and tf = infinity. The author of the book I'm using says this is due to Haag's Theorem, so I...
  11. N

    What is the Asymptotic Behavior of the Propagator in QFT?

    Please demonstrate for me that: In any theory,the propagator \Delta_{f}(k) of a field of type f has asymptotic behavior: \Delta_{f}(k)~k^{-2+2sf} where sf is ''spin'' of the field.For massive fields of Lorentz type (A,B) then sf=A+B. (However,dropping terms that because of gauge...
  12. WannabeNewton

    What is the precise mathematical claim in Haag's theorem?

    Hi guys! So this question has been bugging me a bit and I can't seem to find any textbook (at least, restricted to physics textbooks) that talks about it. In QM, the overarching formalism is clear. We have ##L^2(\mathbb{R})## and states are given by ##|\psi\rangle \in L^2(\mathbb{R})## such...
  13. 1

    Photons, QFT and electric generators

    hi, friends. i am 15 and have made a device using electric motors and generators which is able to produce more "electrical output" than the "electrical input". i have won the national science fair with this but the problem is that the judges say i am braking the 2nd law of thermodynamics and...
  14. G

    QFT Nonlinearity: Interactions & Maxwell's Eqns

    Nonlinearlity of QFT produces interactions, or so I was told today. Maxwell's eqns, though, are perfectly linear. Does that mean that Maxwell's eqns don't predict interactions? Thanks
  15. N

    Renormalization of QFT - the counterterms

    I would like to ask if anyone can give me a hand with the understanding of the counterterms. I am reading by myself Chapter 10 of Peskin & Shroeder and got stuck in the middle of their example of how to renormalize \phi^{4} theory. What is puzzling me is how to obtain from the new Lagrangian...
  16. Islam Hassan

    QFT: Point-Like Particles vs Wave-Particle Duality

    Is there a (theoretical) partial or total inconsistency in QFT's postulate/premise/description of elementary particles as dimensionless, point-like objects with respect to the wave-particle duality nature of QM? This is in the sense that such description is *only* particle-like. Clearly, even...
  17. N

    Why do fields vanish at infinite time during canonical transformations?

    The footnote at &7.6 page 329 writes: '' Recall that by canonical transformation, we mean a transformation from a set of phase space coordinates \Psi^{a},\Pi_{a} to some other phase space \tilde{\Psi}^{a},\tilde{\Pi}_{a} such that [\tilde{\Psi}^{a},\tilde{\Pi}_{b}]_{P}=\delta^{a}_{b} and...
  18. S

    QFT: Scattering Amplitudes in Yukawa Theory

    Homework Statement I'm working with the Yukawa theory, where the interaction term in the Lagrangian density is g\varphi\overline{\psi}\psi. As an exercise for getting used to using the Feynman rules for the theory, I'm asked to show explicitly (i.e. I'm not allowed to invoke charge...
  19. T

    Particles QFT for condensed matter physicist (should I?)

    Hi, I would like to ask whether if a course in Quantum Field Theory (in particle physics context) would be of any use to future condensed matter physicist. Is it beneficial to be exposed to things like Canonical Quantization, Interacting Fields, Dirac Equation, Quantizing Dirac field and QED? I...
  20. G

    Question about non-relativistic limit of QFT

    In pages 41-42 of these notes: http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf , it is said that |\vec{p}|\ll m implies |\ddot{\tilde{\phi}}|\ll m|\dot{\tilde{\phi}}| Why is this so?
  21. K

    What background one needs to have to study QFT?

    What background one needs to have to study QFT? I have a good background in calculus, linear algebra, PDEs, and quantum mechanics (at Shankar's level). Are these enough?
  22. C

    Proving the Gamma Matrix Identity in QFT: Is There a Mistake in My Attempt?

    Homework Statement Prove that \gamma^{a}\gamma^{b}\gamma^{c}\gamma^{d}\gamma^{e}\gamma_{a} = 2\left(\gamma^{e}\gamma^{b}\gamma^{c}\gamma^{d}+\gamma^{d}\gamma^{c} \gamma^{b}\gamma^{e}\right) Each of the \gamma^{i}s are as used in the Dirac equation. Homework Equations...
  23. I

    On QFT, dimensionality and regularization

    Hello everyone ! First of all, Quantum Field Theory is not my field of research. However, I have to investigate on some problems in QFT and I'm trying to get familiar with it again. I'm basically working with scalar fields and I encounter some problems in dealing with renormalization...
  24. D

    Is Dark Energy Linked to Vacuum Energy in QFT?

    I'm reading a paper by Art Hobson called "There are no particles, there are only fields" and had a question about something in there. (http://arxiv.org/abs/1204.4616) (Page 20-21) He basically says that since the vacuum in QFT has energy and non-vanishing expectation values, it is ultimately...
  25. K

    Is the Field Operator in Quantum Field Theory an Observable or a Creation Tool?

    Hello! I'm finally starting to get a grip around quantum field theory. The last hang up is the following: I've been told that since we are quantizing a field, the field strength is the observable. Now analogous to QM we then define a field of hermitian operators, ##\phi(x)##, which give a...
  26. N

    How to Derive the Number of Components of a Rank-2A Tensor in Four Dimensions?

    In &5.6 writes: "An (A,A) field (A is spin) contains terms with only integer spins 2A,2A-1,...,0, and corresponds to a traceless symmetric tensor of rank 2A.(Note that the number of independent components of a symmetric tensor of rank 2A in four(space-time) dimensions is...
  27. marcus

    QFT and QSM in gen. cov. bndry form: ways it could fail?

    This seems to be the most interesting development in QG currently. I want to know what you think might present serious obstacles to completing the program. Where could it go wrong? The idea is that QFT and quantum statistical mechanics (QSM) need to be given a general covariant formulation...
  28. V

    Delta Typo in Photon Propagator?

    The problem is on pages 323 and 324 of the second edition. Homework Statement Given the lagrangian \mathcal{L} = -\frac{1}{4}F_{\mu\nu}(x)F^{\mu\nu}(x) - \frac{1}{2\alpha}(\partial_{\mu}A^{\mu})^2 show that the momentum space photon propoagator is given by D_F^{\mu\nu}(k) =...
  29. L

    Trying to make the connection with QM as a 1 parameter QFT

    I'm seeing lots of underlying connections between the canonical formulism of QFT and QM. But I'm getting a bit confused by their differences. I'll just write down my thought process: QM is a one parameter system (t) in a space with three quantized operators (x,y,z) QFT is a four parameter...
  30. A

    Which online course is the best for learning QFT?

    I'm looking for a good online introductory course in QFT for physiscists (i.e. at university level, for someone who already has the basics of CM, QM and relativity, but for one reason or another worked in completely different fields). I see there are several courses online, but it is not so easy...
  31. T

    Weinberg discussion on induced representations in his QFT Vol.1 Ch. 2

    This is discussed in Weinberg's Quantum Theory of Fields, in the chapter on Relativistic Quantum Mechanics. The point I am somewhat confused about occurs on page 63 - 64, if you have the book. He operates on a single particle state with the unitary homogeneous lorentz transformation...
  32. K

    The variation of a scalar field (from Ryder's QFT book)

    Hello! Im currently reading Ryder's QFT book and am confused with the variation of a scalarfield. He writes that the variation can be done in two ways, \phi(x) \rightarrow \phi'(x) = \phi(x) + \delta \phi(x) and x^\mu \rightarrow x'^\mu = x^\mu + \delta x^\mu. This seems...
  33. R

    QFT newbie-creation of particle and anti-particle

    Hi, I read the following in an online source: In relativistic settings, momentum and energy are equal so the uncertainty principle, for a particle of mass m which is trapped in a box of size L, becomes delta E>= \hbarc/L. If uncertainty exceeds delta E=2mc^2, we get pairs of particles and...
  34. LarryS

    Need QFT Book or Online Course?

    I'm looking for a book on QFT that is both introductory and somewhat rigorous. I have Zee's book but for me it is kind of hard to follow. I would prefer something that is more like a textbook introduction to the subject - not necessarily covering the whole subject but logically rigorous for...
  35. G

    What is the Role of Fine Tuning in the Cosmological Constant Problem?

    The vacuum-vacuum expectation value in the absence of a source is in general not equal to 1, but exp[-iEt], where E is the energy of the vacuum. For some reason in QFT, we say E=0 (i.e., we normalize Z[0]=1, the generating functional), but we don't need to do this and one can in fact calculate E...
  36. G

    Infinities and short distances in QFT

    Infinities in QFT come from high momenta. I sometimes hear that is equivalent to coming from short distances, but I'm not sure I see the connection. The free propagator G(x-y) which I think goes like 1/|x-y|^2 is singular for short distances (when x=y). In momentum space G(x)= ∫d^4k exp[ikx]...
  37. L

    Spacetime displacement operator in QFT

    I'm trying to fit together my understanding of quantum mechanics, quantum field theory, given my lacking maths education. In quantum mechanics we have a time displacement operator and a space displacement operator, which are respectively: \hat{T}(t) = e^{-i\hat{H}t} \hat{D}(\underline{x}) =...
  38. lonewolf219

    REU student working on QFT seeking help

    Hi everybody, I thought I'd give this a shot and see if anyone would like to be a sort of "mentor" for me this summer? I have not taken Quantum mechanics and I am actually working on a QFT-esque REU project for the next 8 weeks (!). Anyone interested in maybe answering (I will definitely...
  39. lonewolf219

    What is the difference between quantum mechanics and QFT?

    Hi, I'm an undergrad that has not taken quantum mechanics... What exactly is the distinction between quantum mechanics and quantum field theory? Does quantum mechanics describe the interactions of particles? Are Feynman diagrams used in quantum mechanics? I have been doing some...
  40. U

    Spectrum of the Hamiltonian in QFT

    I know in ordinary QM, the spectrum of the Hamiltonian \{ E_{n}\} gives you just about everything you need for the system in question (roughly speaking). So what happens to this spectrum in QFT where |\psi\rangle is now a multiparticle wavefunction in some Fock space? I've been trying to...
  41. J

    Good Books on QFT: Suggestions & Reviews

    Hello. I'd like to know of good suggestions of books on QFT. I have a somewhat firm grasp on non-relativistic Quantum Mechanics, and already know of some good books about it, so I'd like to understand some Quantum Field Theory if at all possible. Thank you in advance for your suggestions :)
  42. U

    The use of different bases in QFT

    In ordinary QFT, everything is formulated in terms of a Fock basis so when we write |\psi\rangle we mean that this is a product of single particle states covering every momentum mode. This leads to a Hamiltonian that's typically of the form \hat H=\int \frac{d^{3}k}{(2\pi)^{3}} [\omega_{k}(\hat...
  43. C

    Antiparticles identical in qft

    Has anyone ever heard of treating a particle and antiparticle as identical based on the formalism of quantum field theory? The argument given is that the creation operator for a particle is the annihilation operator for its antiparticle, but I can't find this idea of treating them as identical...
  44. M

    Fourier Transform on the connected part of QFT transition prob.

    Fourier Transform on the "connected part" of QFT transition prob. Homework Statement Calculate ⟨0|T[ϕ(x₁)ϕ(x₂)ϕ(x₃)ϕ(x₄)]|0⟩ up to order λ from the generating functional Z[J] of λϕ⁴-theory. Using the connected part, derive the T-matrixelement for the reaction a(p₁) + a(p₂) → a(p₃) +...
  45. M

    Explain crossing without invoking QFT?

    Explain "crossing" without invoking QFT? Hi there For someone learning particle physics for the first time (Griffiths' intro book, no knowledge of QFT yet): Why can you "cross" a reaction? Is there an intuitive answer or does one truly need understanding of scattering amplitudes, quantum...
  46. B

    QFT: differential cross section from center of mass to lab frame

    I have the following process: two ingoing particles, a photon hitting a nucleus, and two outgoing particles, the nucleus and a pion. I have computed |M|2 and the differential cross section in the center of mass frame dσ/dΩCM; I now have to go into the lab frame, where the nucleus is initially at...
  47. S

    Does QFT respect conservation of angular momentum?

    Hi there Iive been reading the intro chapter to Peskin and Schroder's 'An intro to QFT' I have a question regarding the conservation of angular momentum during particle collisions/scatterings As an example they talk about e+ e- --> μ+ μ- The take the Centre of Mass (CM) frame...
  48. Y

    State space of QFT, CCR and quantization, and the spectrum of a field?

    State space of QFT,CCR and quantization,spectrum of a field operator? In the canonical quantization of fields, CCR is postulated as (for scalar boson field ): [ϕ(x),π(y)]=iδ(x−y) ------ (1) in analogy with the ordinary QM commutation relation...
  49. Q

    A diff-invariant 1+1d QFT with divergent central charge?

    We know that a free scalar field on a diff-invariant 1+1 dimensional background (i.e. bosonic string theory on the worldsheet) contributes to the central charge of the Virasoro algebra with a constant term. Is there any examples of a 1+1d QFT that has instead a central charge contribution...
  50. S

    QFT Ground State Analysis: Understanding e^(-iHT) |0>

    Hello Everybody, In page 86, in Peskin & Schroeders Introduction to QFT, the following expression is introduced to analyze \left | \Omega \right >; the ground state of the interacting theory: e^{-iHT} \left | 0 \right >. Where |0> is the ground state of the free theory and H is the...
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