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. S

    Quantum Particles & Quantum Fields - Hagen Kleinert

    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 -...
  2. G

    A Strings vs. point interactions in QFT?

    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...
  3. I

    B Shape of elementary particles in QFT, etc?

    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...
  4. F

    A Physical interpretation of correlator

    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...
  5. D

    A A question about the mode expansion of a free scalar field

    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...
  6. Mr-R

    A Canonical quantisation of the EM field

    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##...
  7. J

    A Srednicki's QFT: Feynman Rules and Feynman Diagrams

    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...
  8. ShayanJ

    A What Are the Different Formulations of Quantum Field Theory?

    As far as I understand now, there are at least three different formulations of QFT: 1) Second Quantization 2) Functional Formulation(where there is wave-functional which is a function of the field configuration and satisfies a functional Schrodinger equation) 3) Path Integral Is there any...
  9. hilbert2

    A Approximating a QF with finite-dimensional Hilbert space

    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}...
  10. F

    I Particle number conservation and motivations for QFT

    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...
  11. hilbert2

    A QFT and transitions between momentum states

    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...
  12. Spinnor

    B Energy density of charged capacitor via QFT

    From the view point of quantum field theory how does one describe the electromagnetic energy density between the plates of a charged capacitor? Thanks!
  13. M

    Zee, Quantum Field Theory in a Nutshell, problem 1.3.1

    Homework Statement I'm working through Zee for some self study and I'm trying to do all the problems, which is understandably challenging. Problem 1.3.1 is where I'm currently stuck: Verify that D(x) decays exponentially for spacelike separation. Homework Equations The propagator in question...
  14. Mr-R

    B QFT for Gifted Amateurs: Preparing for Advanced QFT

    Hi everyone. For anyone who has the book. I am going through Quantum Field Theory for the Gifted by Amateur Tom Lancaster and Stephen J. Blundell. Are the topics enough to prepare me for a course in QFT and then Advanced QFT? Of course I can look for other resources. But I just want to know how...
  15. G

    A Fock space and Poincaré invariance

    Hi all, is Fock space Poincaré invariant? As far as I can see, the scalar product in Fock space involves the scalar products in its N-particle subspaces, which, in turn, are the integrals of the properly (anti-)symmetrized wave functions over space. This works well in a Galilei-invariant...
  16. MichPod

    I QFT vs Wave Function: Understanding Particle States

    My level is not sufficient enough to easily understand QFT yet there is some basic question I need to understand in it - what in QFT corresponds to a wave function in QM, for a single particle case and, say, for a more general case of multiparticle nonseparable state (suppose the particles are...
  17. JeJe

    What is the Connection Between Quantum Field Theory and Cosmology?

    I'm interested in all discussions but particularly those concerning the areas of QFT and cosmology. I've done much studying on the concept of quantum gravity over the past couple years and I want to learn more :)
  18. D

    A Time dependence of field operators

    In field theory we most of deal with theories whose Lagrangian densities are of the form (sticking to scalar fields for simplicity) $$\mathcal{L}= -\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi - \frac{1}{2}m_{\phi}^{2}\phi^{2} + \cdots$$ where ##\partial := \frac{\partial}{\partial x^{\mu}}##...
  19. Safinaz

    A Unitarity and perturbativity constrains on couplings in QFT

    Hi all, I'm little confused about the unitarity and perturbativity constrains which imposed on a potential's parameters, like 2HD potential. Look for example: [arXiv:1507.03618v3 [hep-ph]] First, I'd like to know what is most essential ? I mean if unitarity constraind ## \lambda## to say less...
  20. E

    Schools What school is good for my undergrad?

    I live in Texas, and I'm going on my senior year of high school. I've come to a problem, I don't know what college/university I should continue my education at. I've already decided what I hope to do when I'm older- qft and quantum gravity, but I don't know what place is good to further ones...
  21. F

    I Relation between quantum fluctuations and vacuum energy?

    As far as I understand it, the non-zero vacuum energy attributed to a quantum field (at each point in space-time) is precisely due to the Heisenberg uncertainty principle (and the fact that the energy of the quantum field at each space-time point is quantised). Accordingly (in order to satisfy...
  22. L

    A What Does Zee Mean by the Equation in QFT Nut, III.6, p. 194?

    ..where can be found: What in the whole wide world does Zee mean with ?? Thank you
  23. I

    What Is the Issue with Scalar Loop Corrections in Non-Abelian SU(N) Theories?

    Hello all, I hope you can give me a hand with a QFT homework I'm working on. We are to compute the beta equation of a Non-abelian SU(N) theory with: Complex scalars (massless), bosons, ghosts. My question is referring to the Boson self-energy scalar loop correction. 1. Homework Statement We...
  24. A

    I What is the correct explanation of the Casimir force?

    I have been trying to improve my understanding of QFT via reading this forum, Zee's QFT in a Nutshell and Lancaster and Blundell's QFT for the Gifted Amateur. I thought I was making some progress but recent post have left me confused so any pointers would be welcome. As I currently understand...
  25. Fedor Indutny

    Weinberg's QFT -- Two moving observers see a W-boson differently....

    Homework Statement Suppose that observer \cal O sees a W-boson (spin one and mass m \neq 0) with momentum \textbf{p} in the y-direction and spin z-component \sigma. A second observer \cal O' moves relative to the first with velocity \textbf{v} in the z-direction. How does \cal O' describe the...
  26. Adoniram

    QFT - Derivative in Equation of Motion

    Homework Statement As part of a problem, I need to derive the EOM for a generalized Lagrangian. Before I get there, I'm trying to refresh myself on exactly how these derivatives work because the notation is so bizarre. I am trying to follow a simple example I found online: Start with...
  27. carllacan

    I Where exactly does QFT differ from QM? (in their formalisms)

    Hi. First off, I'm not sure if this is the right sub to talk about QFT. Apologies if t isn't. I'm halfway through an introductory QFT course and I still don't get what it is. What is different in its formalism that makes it able to tackle problems that quantum mehanics can't deal with? From...
  28. M

    A Hamiltonian and constant potential

    H=p^2/2m+c What's c? It's of course a shift in energy, but can be thought also as a smoother and smoother real-space local potential that becomes a constant all over the space. On the other hand, why couldn't one think about it as a constant potential in reciprocal space? It's a shift in energy...
  29. M

    Studying Learn QFT: From Sakurai to Group Theory & Beyond

    Hello everyone, First of all, I am a third year undergraduate student. I have just finished studying (on my own) Sakurai' s "Modern Quantum Mechanics" (and I have done almost all exercises). I have taken courses in Complex Analysis (contour integration, residues etc) and in PDE (unfortunately...
  30. Giuseppe Lacagnina

    Lorentz transformations and vector fields

    Hi Everyone. There is an equation which I have known for a long time but quite never used really. Now I have doubts I really understand it. Consider the unitary operator implementing a Lorentz transformation. Many books show the following equation for vector fields: U(\Lambda)^{-1}A^\mu...
  31. diegzumillo

    Is Resurgence Theory and QFT the Next Quantum Mechanics Breakthrough?

    Hey there I'm starting to work on my thesis and this is one possible subject. I'm reading a few papers (pretty much anything that appears on the first google search page) dealing with it from several different angles. From a completely general and mathematical stand to specific examples, like...
  32. F

    I Exploring the Connection Between Quantum Mechanics and Quantum Field Theory

    << Moderator note: Split from https://www.physicsforums.com/threads/why-do-we-need-quantum-mechanics-so-much.859210/ >> What about particle physics? It bases on QFT therefore on QM.Is that right?
  33. O

    Renormalization of Bound States in QFT

    Hi, I am about to work on the problem of trying to find a renormalization program for bound states in QFT. Any suggestions/advice on where to start would be much appreciated.
  34. Giuseppe Lacagnina

    Can a Lagrangian in QFT be Renormalizable?

    Possibly very silly question in QFT. Consider the Lagrangian for a scalar field theory. A term like g/φ^2 should be renormalizable on power counting arguments. The mass dimension of g should be 2 (D-1) where D is the number of space-time dimensions.Does this make sense?
  35. D

    What is a "source term" & what is it physically in QFT?

    Given an inhomogeneous ODE of the form $$a_{n}(x)y^{(n)}(x)+a_{n-1}(x)y^{(n-1)}(x)+\cdots +a_{2}(x)y''(x)+a_{1}(x)y'(x)+a_{0}(x)y(x)=f(x)$$ where ##y^{(n)}(x)\equiv \frac{d^{n}y(x)}{dx^{n}}##, why is the function ##f(x)## on the right hand side referred to as a "source term" ? In what way does...
  36. F

    A Does QFT specify particle propagation?

    I need to clear up my (mis)understanding about QFT. Does QFT show how a particle propagates through spacetime? (Or maybe this is the realm of QM) Or does QFT only specify how a particle propagates as a particle through time without reference to where in space it is? But... if QFT specifies how...
  37. FrancescoS

    Performing Wick Rotation to get Euclidean action of scalar f

    I'm working with the signature ##(+,-,-,-)## and with a Minkowski space-stime Lagrangian ## \mathcal{L}_M = \Psi^\dagger\left(i\partial_0 + \frac{\nabla^2}{2m}\right)\Psi ## The Minkowski action is ## S_M = \int dt d^3x \mathcal{L}_M ## I should obtain the Euclidean action by Wick rotation. My...
  38. edguy99

    Quantum Field Theory intro with flying field disturbances

    Great youtube introduction video about Quantum Field Theory (QFT) from a couple of days ago by Dr Don Lincoln @fermilab. The video and description of a particle being a disturbance in a field and flying through the air at 3:25 is especially compelling.
  39. A

    QFT: Understanding Counter-Terms for Renormalization

    Hello, It's been a long time I am trying to accept renormalization in QFT but still I cannot be satisfied. The usual pedagogical way one introduces renormalization is to cure infinities that arise from perturbative expansions. Now, I can accept the statement that we are doing the perturbation...
  40. F

    Is QFT on curved spacetime BtSM

    Is QFT on curved spacetime BtSM
  41. Joshua L

    Schools Best Physics Graduate Schools for QFT, GR, and HEP?

    Hey guys, just curious of your opinions on this matter. Which graduate schools are the best to earn a Ph.D. in physics theory from and research in concerning the theoretical sub-fields Quantum Field Theory, General Relativity, and Elementary Particle Physics (maybe String Theory)? Which has...
  42. B

    Why are particles in QFT assumed to be point-like?

    Why are particles in QFT assumed to be point-like? This assumption is the source of ultraviolet divergences. Does anyone know what is the source of this assumption, and what happens if you assume that particles are not point-like?
  43. P

    How does QFT handle non-locality?

    [Split off from https://www.physicsforums.com/threads/photon-energy-and-light-quantum-hypothesis.847848/#post-5329824] As we know, there is a serious contradiction between nonlocal indeterminacy of quantum theory and local reality of special relativity, specifically reflected in the superluminal...
  44. M

    QFT: Lorentz Trans+ Field infinitesimal variation

    Hello, I do not understand how to compute the infinitesimal variation of the field at fixed coordinates; under lorentz transformation . I am doing something wrong regarding the transformation of the ##x## coordinate. I am looking for: ##\Delta_a=\phi_a'(x)-\phi_a(x)##, variation appearing in...
  45. S

    Standard Model, Mass in QFT - Is There Consensus?

    I realize that Wiki is not the preferred reference source here, but I'll go ahead with this question anyway... In the latest iteration of the article on the Standard Model is the statement, "We see that the mass-generating interaction is achieved by constant flipping of particle chirality." Is...
  46. V

    Recovering QM from QFT: David Tong Notes

    Reading through David Tong lecture notes on QFT.On pages 43-44, he recovers QM from QFT. See below link: [QFT notes by Tong][1] [1]: http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdfFirst the momentum and position operators are defined in terms of "integrals" and after considering states that...
  47. H

    Difference between 2-point and 4-point function in QFT

    As I understand it, the 2-point fnuction is for 1 particle incoming, 1 particle outgoing. The 4-point function is for 2 particles incoming, 2 particles outgoing. Is this correct? So an N-point function describes N/2 incoming particles and N/2 outgoing particles? Thanks!
  48. M

    Quantum QFT books in order of difficulty

    Hi, I'd like to ask you if you could write a list of QFT books in order of increasing difficulty. Thanks!
  49. A

    QFT, excitation of quantum field, physical or mathematical?

    In, QFT, an elementary particles is an excitation of its quantum field. Quantum fields are just mathematical. For example an electron is excitation of the electron field. But is the excitation of the field physically real or just mathematical? What i mean is, is there something physically...
  50. Gvido_Anselmi

    Can Lattice Formulations Accommodate Modern Quantum Field Theories?

    Hello everybody, I have three quite mathematical questions in modern QFT. 1) Why it's supposed that N=2 SUSY Yang-Mills probably cannot be put on a lattice? 2) What is the recent status of lattice approach to conformal quantum field theories? This question is motivated by the following...
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