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. C

    A QM Interpretations as applied to QFT

    [Moderator's Note: Thread spun off from previous discussion.] MWI and the TSVF are both easily generalized to QFT. One only needs to define the decoherence basis for the fields (see https://arxiv.org/abs/quant-ph/9510021) and then one simply interprets the decoherent histories as ontological...
  2. J

    Quantum Does a draft of Zeidler's missing volumes of his QFT series exist?

    I enjoyed a lot the three first volumes of Zeidler's planned series of 6 books on QFT. Unfortunately, he passed away too soon. However, it is clear from reading the first three books, that an outline of the next books in the series was already planned. Is there a draft, containing the basis of...
  3. TeethWhitener

    A QFT Srednicki Chap 6: Weyl Ordering

    In Srednicki’s QFT Chapter 6 (intro to path integrals), he introduces Weyl ordering of the quantum Hamiltonian: $$H(P,Q)=\int{\frac{dx}{2\pi}\frac{dk}{2\pi} e^{ixP+ikQ}}\int{dp \text{ }dq\text{ }e^{-ixp-ikq}H(p,q)}$$ where ##P,Q## are momentum and position operators and ##H(p,q)## is the...
  4. J

    A Why the probabilistic approach is not more prominent in QFT?

    Of course, there is probability theory in QFT. The partition function can be understood as a characteristic functional. What surprises me is there is little discussion about characteristic functionals, except for some 40 year old papers. It seems surprising to me that physicists, being used to...
  5. J

    I Hamiltonian in QM for QFT forces/fields effects

    In QM. Can you use the Hamiltonian (or kinetic plus potential energy) to describe the forces of nature that should supposedly use QFT or Lagrangian? I mean the fields have kinetic and potential energy components and what are the limitations in description and others if you only use them to...
  6. J

    A Why "Green's function" is used more than "correlations" in QFT?

    Very often, the term "Green's function" is used more than "correlations" in QFT. For example, the notation: $$<\Omega|T\{...\}|\Omega> =: <...>$$ appears in Schwartz's QFT book. And it seems very natural, basically because the path integral definition of those terms "looks like" the...
  7. J

    A What is the relationship between QFT and QM?

    I know this question has been asked, in several ways, many times before. I have read many of the posts. And still I do not fully understand the situation: is QM in any way a subset of QFT? Apparently no: QM uses position variables, while QFT does not. QM has the Born rule and a wave function...
  8. J

    A Is there a principle of stationary action for QFT?

    Classical mechanics (and classical field theory) has the principle of stationary action (Hamilton's principle) as main principle. The Euler-Lagrange equations are derived from that principle, by using calculus of variations, on functionals (functions of functions). Is there an equivalent...
  9. J

    A Which operator corresponds to the Green function in QFT?

    The Feynman propagator: $$D_{F}(x,y) = <0|T\{\phi_{0}(x) \phi_{0}(y)\}|0> $$ is the Green's function of the operator (except maybe for a constant): $$ (\Box + m^2)$$ In other words: $$ (\Box + m^2) D_{F}(x,y) = - i \hbar \delta^{4}(x-y)$$ My question is: Which is the operator that...
  10. W

    Particle Would like some particle physics textbook-reading advice

    Hi all, I am in a bit of a funny situation where I need to pick up at least a cursory knowledge of QFT and particle physics in the space of two weeks. I borrowed "QFT and the Standard Model" by Schwartz but I have no idea how I should approach it. Ideally I'd pour through every page, but I...
  11. Q

    A Functional Derivatives in Q.F.T.

    I'm can't seem to figure out how to functionally differentiate a functional such as Z(J)= e^{\frac{i}{2} \int \mathrm{d}^4y \int \mathrm{d}^4x J(y) G_F (x-y) J(x)} with respect to J(x) . I know the answer is \frac{\delta Z(J)}{\delta J(x)}= -i \int \mathrm{d}^4y J(y) G(x-y) but I'm struggling...
  12. P

    A Relativistic derivation of E=1/2MV^2 from QFT or Diriac or other

    It is easy to derive E=1/2mv^2 from the Schroedinger equation for the nonrelativistic one dimensional case where e^ipx-iEt/\hbar is the free traveling wave function: i\hbar x -iE/\hbar x e^ipx-iEt/\hbar = - - \hbar^2/2m x p^2/2m x e^ipx-iEt/\hbar which reduces to E=1/2mv^2 Where should I start...
  13. DarMM

    Quantum QFT Book Quote: Looking for Source

    This seems like the best place to ask this. There is a famous QFT textbook that contains a line like "in field theory one learns humility". Does anybody happen to know what textbook this is?
  14. hyksos

    B What does QFT really predict about matter/anti-matter interactions?

    In the context of popular science literature, when antimatter comes into contact with regular matter, what happens is described as "annihilation" or "they annihilate". It is also rumored that 100% of the mass in the constituents is converted to energy. The rumor would also suggest that there...
  15. H

    I Question about why QFT in 4D is undefined

    I'm a beginner in QFT and I'm always hearing people say that QFT is undefined in 3+1 dimensions or that the Hamiltonian cannot be rigorously defined, what do these statements mean exactly? In particular I'd like to know what makes the 3+1D case that much worse than non-relativistic QFTs like the...
  16. A

    A Cluster Decomposition.Vanishing of the connected part of the S matrix.

    Im following Weinberg's QFT volume I and I am tying to show that the following equation vanishes at large spatial distance of the possible particle clusters (pg 181 eq 4.3.8): S_{x_1'x_2'... , x_1 x_2}^C = \int d^3p_1' d^3p_2'...d^3p_1d^3p_2...S_{p_1'p_2'... , p_1 p_2}^C \times e^{i p_1' ...
  17. H

    I Divergent vacuum uncertainty of fields in QFT, how to resolve?

    If you calculate the uncertainty of a scalar field in the vacuum state, i.e. ##\langle0\left| \phi^2\right|0\rangle##, you get a divergent integral that comes out to something like $$\frac{1}{4\pi^2}\int_0^\Lambda \frac{k^2 dk}{\sqrt{{m^2}+{k^2}}}$$ Where ##\Lambda## is some momentum cutoff...
  18. P

    I Space is discrete or continuous?

    According to QFT or Quantum Gravitation Theory space and time are discrete or continuous?
  19. P

    I Electroweak force and electrons

    If at high energies the electromagnetic and weak force are combined into one electroweak force, then at high energies, the electrons will not create an electrostatic field and will not repel?
  20. A

    A Massive Vector Field: Questions & Answers

    Hello everybody. The Lagrangian for a massive vector field is: $$\mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{m^2}{2}A_\mu A^\mu$$ The equation of motion is ##\partial_\mu F^{\mu\nu}+m^2A^\nu = 0## Expanding the EOM with the definition of ##F^{\mu\nu}## the Klein-Gordon equation for...
  21. tomdodd4598

    I QFT - Confusion about Fermi's Golden Rule & Cross-Sections

    Hey there! I've recently been looking at calculating amplitudes, densities of states and scattering cross sections in QFT, but am having a little bit of trouble with the exact form of the cross section - particularly with factors of ##2E## for the energies of the incoming and outgoing particles...
  22. A

    A Renormalization (Electron self energy)

    Hello everybody! I have a big question about the renormalization: I do not understand why the "renormalization condition" is to impose the tree level result. Now I will explain it better. Let's take, for example, the electron self energy. The tree-level contribution is the simple fermionic...
  23. A

    A The product of a matrix exponential and a vector

    Hello everybody! I was studying the Glashow-Weinberg-Salam theory and I have found this relation: $$e^{\frac{i\beta}{2}}\,e^{\frac{i\alpha_3}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \\ \end{pmatrix}}\, \frac{1}{\sqrt{2}}\begin{pmatrix} 0\\ v \\ \end{pmatrix} =...
  24. P

    I Weak interaction between electrons

    The two electrons will be repelled by electrostatic force, but they interact with weak force, means that in addition to the electrostatic force between the electrons there will be weak force?
  25. A

    A Understanding Goldstone's Theorem Proof: Volume Limit and Commutator

    Hello everybody! I have a question regarding the first step of the quantistic proof of the Goldstone's theorem. Defining $$a(t) = \lim_{V \rightarrow +\infty} {\langle \Omega|[Q_v(\vec{x},t),A(\vec{y})]| \Omega \rangle}$$ where ##|\Omega\rangle## is the vacuum state of the Fock space, ##Q_v##...
  26. P

    I Difference between spin repulsion and electrostatic repulsion of an electron?

    What is the difference between spin repulsion and electrostatic repulsion of an electron? Is this the same mechanism?
  27. P

    I Is it possible to detect an electrostatic field?

    If the electron creates an electric field around itself that can be detected,then the electrostatic field is real? So why was not the "virtual" photon found?
  28. P

    I Exploring Electron Splitting in Materials: Spinons and Orbitons in QFT

    What does it mean that an electron in a material can split into a spinon or an orbiton? Does QFT have a spinon or orbiton field?
  29. L

    A Interpretation of state created by the field in free QFT

    Let us consider QFT in Minkowski spacetime. Let ##\phi## be a Klein-Gordon field with mass ##m##. One way to construct the Hilbert space of this theory is to consider ##L^2(\Omega_m^+,d^3\mathbf{p}/p^0)## where ##\Omega_m^+## is the positive mass shell. This comes from the requirement that there...
  30. D

    I QM limit of QFT in Schwartz

    In Matthew Schwartz's QFT text, he derives the Schrodinger Equation in the low-energy limit. I got lost on one of the steps. First he mentions that $$ \Psi (x) = <x| \Psi>,\tag{2.83}$$ which satisfies $$i\partial _t\Psi(x)=i\partial_t< 0|\phi...
  31. P

    I Electrons and the Pauli exclusion principle

    electrons are repelled using the Pauli exclusion principle?
  32. P

    I Electrostatic repulsion at a distance

    What does it mean ? "the virtual photon's plane wave is seemingly created everywhere in space at once, and destroyed all at once. Therefore, the interaction can happen no matter how far the interacting particles are from each other." As far as I know, the electrostatic force between two...
  33. A

    On-shell renormalization scheme

    Homework Statement Show that, after considering all 1 particle irreducible diagrams, the bare scalar propagator becomes: $$D_F (p)=\frac{i}{p^2-m^2-\Sigma (p^2)}$$ And that the residue of the pole is shifted to a new value, and beomes...
  34. P

    I Electrons in Quantum Field Theory: A Composite Excitation

    In qft electron can be considered as composite excitation in several fields?
  35. P

    I How does an electron interact in QFT?

    How does the electrons interact in QFT? if they are not localized? For example, when one electron repels another or does an atom repel another atom? How do electrons find each other for interaction?
  36. Geofleur

    I Qualitative description of particles in QFT

    I would like to be able to qualitatively describe what particles are according to quantum field theory without saying anything wrong. Is it correct to say the following things about, say, an electron? (1) Electrons are excitations of an underlying quantum field, the electron field. There is a...
  37. P

    I Electron Repulsion in QFT: How Does It Work in Quantum Field Theory?

    How do electrons repel each other in quantum field theory? Virtual photon - is it just a mathematics?
  38. Z

    Commutation relations in SUSY

    I hope I put this in the correct section of this forum, I apologize if I didn't. Homework Statement :[/B] It is well known that the generators $$ Q_\alpha = \frac{\partial}{\partial \theta^\alpha} - i \sigma^\mu_{\alpha \dot \beta} \bar{\theta}^\dot{\beta} \partial_\mu $$ and $$...
  39. C

    I Visualizing the Attached EM Field for Free Electron in QFT

    My understanding of the QFT model of a free electron is that there is a localized higher energy level in the electron matter field which couples to the EM field in two ways: (1) the coupling allows the electron matter field to 'feel' a force from an outside EM field and accelerate in response...
  40. P

    I Is the electromagnetic field of an electron in QFT a real physical field?

    According to the QFT, each electron creates an electromagnetic field around itself. Is this field real or is it just a virtual mathematical field?
  41. FourEyedRaven

    Quantum Weinberg and his QM and QFT books

    Hi, Two questions. Are Weinberg's "Lectures on Quantum Mechanics" a bridge to his QFT books? I read that his QFT volumes are excellent books, but not for the beginner. So, if I want to begin QFT, can I choose his "Lectures on Quantum Mechanics" for a graduate level QM book, and make the...
  42. P

    I The virtual photon can turn into a virtual electron positron?

    for example, when does an electron repel another electron with an electromagnetic disturbance?
  43. LarryS

    I What makes a field theory relativistic?

    It is my understanding that in both Classical Field Theory and QFT the Lagrangian must be Lorentz invariant in order for the fields to be considered relativistic. Buy what about the field itself (φ or ψ)? As complex-valued functions of space and time do they also have to be Lorentz invariant...
  44. A

    A QFT Causality: Real Scalar Field & Probability

    Hello everyone! I have a question regarding the causality in QFT. If I take into consideration a real scalar field and I calculate: $$[\phi(x),\phi(y)] = 0 \space \space \space \space \space \text{if (x-y)}^2 < 0$$ Thanks to this relation we state that causality in QFT is preserved: a...
  45. C

    I QFT Interpretation of Electron and Attached EM Field

    This is an elementary question on visualizing the interaction of an electron with the surrounding EM field in QFT. I believe in QFT the electron is viewed as an excitation of the Electron matter field with an associated coupling constant between the electron field and EM field (say q) - q...
  46. A

    I Fermionic Field Time Ordering: Understanding the Time Ordered Contraction

    Hello, I am struggling to see why for a fermionic field $\psi$, one has the time ordered contraction $<0|T(\psi(x)\psi(y))|0>$. Could someone offer an outline/hints to see this please? Thanks!
  47. Dewgale

    Anti-commutation of Dirac Spinor and Gamma-5

    Homework Statement Given an interaction Lagrangian $$ \mathcal{L}_{int} = \lambda \phi \bar{\psi} \gamma^5 \psi,$$ where ##\psi## are Dirac spinors, and ##\phi## is a bosonic pseudoscalar, I've been asked to find the second order scattering amplitude for ##\psi\psi \to \psi\psi## scattering...
  48. M

    A Observables in condensed matter (QFT)

    Quantum field theory is a powerful tool to calculate observables given the amplitude of some process. I only know the application to high energy physics: you have a Lagrangian with an interaction term between some fields, and you can calculate the amplitude of some process. Once you have this...
  49. N

    A QFT & Entanglement: NRQT vs. PCT Transform

    Why is it that nonrelativistic quantum theory (NRQT) does not have PCT, whereas QFT does? How would you characterize the collapse of the wave function in terms of PCT? What is its PCT transform? How does QFT address EPR? Many physicists universally accept the Copenhagen interpretation and...
  50. P

    I In QFT people exchange electrons during touching?

    Does in QFT static electricity work classically or is there a more fundamental explanation?
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