What is Quantum fields: Definition and 58 Discussions

In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles.
QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics.

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  1. bhobba

    A The Quantum State as a Function of The Quantum Field

    In answering another question, I came across a nice paper by Weinberg: https://www.arxiv-vanity.com/papers/hep-th/9702027/ One thing that struck me was the following comment: 'In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the...
  2. M

    Non quadratic potentials and quantization in QFT (home exercise)

    I noticed that ##V(\phi)## has nonzero minima, therefore I found the stationary points as ##{{\partial{V}}\over{\partial\phi}}=0##, and found the solutions: $$\phi^0_{1,2}=-{{m}\over{\sqrt{\lambda}}}\quad \phi^0_3={{2m}\over{\sqrt{\lambda}}}$$ of these, only ##\phi^0_3## is a stable minimum...
  3. josephsanders

    High Energy Literature for introduction to O(N) vector model

    TL;DR Summary: Looking for literature on O(N) vector model Hello, We have been going over the O(N) vector model in my QFT class but the notes are not very detailed and we are not using a textbook. Does anyone know of a good QFT book which goes over this material? I have a copy of Shrednicki...
  4. P

    A Global vs. Local (gauge) Symmetry

    Gauge symmetry is highly confusing, partly because many definitions differ in the literature. Strictly speaking gauge symmetry should be called gauge redundancy since you are mapping multiple representations to the same physical state. What is your favourite definition of what "large" gauge...
  5. J

    A Measurement in QFT: Mapping Fields to Theory's Math Formalism

    How do we map experimental measurements of quantum fields, such as those seen in accelerators, to the theory's mathematical formalism? When we see images of particle tracks produced in accelerators such as the LHC, I think it's safe to say a measurement (or series of measurements) has been...
  6. NnnTech

    What Quantum fields are in the intergalactic space ?

    Hello , what quantum fields exist in intergalactic space ? What math describes these fields ?
  7. W

    B Are all quantum fields coherent?

    Is coherence the medium in which quantum waves propagate? Does coherence also exist in the future to flag decoherence events?
  8. Q

    B We can't unite QM with GR because of what the Qfield is capable of

    I think it can do more than the wave only events we know of (superposition, entanglement, and tunneling). If the quantum field doesn't care about spatial distance, does that mean every unobserved quantum wave is already everywhere throughout the quantum field? Does it explain spooky action at a...
  9. The black vegetable

    I Functional Derivatives: Overview & Tips

    Hi In the last sentence I mean you do include constant terms like I have done when taking the product above?
  10. ilper

    A Why are the quantum fields considered ontological?

    Summary: The quantum fields stem from the quantum mechanical wavefunction, which in the standard QM is epistemological (amplitude of probability). How can they be then considered ontological? The quantum fields stem from the quantum mechanical wavefunction, which in the standard QM is...
  11. Peter Morgan

    A The relationship between random fields and quantum fields

    My paper "Classical states, quantum field measurement", arXiv:1709.06711, has been accepted by Physica Scripta, https://doi.org/10.1088/1402-4896/ab0c53. The version as submitted to Physica Scripta on November 4th, 2018 is available as arXiv:1709.06711v5. I believe that anyone who puts some...
  12. Geofleur

    A Is the visualization of quantum fields as harmonic oscillators accurate?

    After learning that QFT describes particles as excitations of underlying fields, I've been trying to gain a more definite understanding of what it means; I came across this paper: https://iopscience.iop.org/article/10.1088/1361-6404/aaa032 Does the author say anything that is misleading? If...
  13. H

    A Quantum fields and the harmonic oscillator

    When defining quantum fields as a sum of creation and annihilation operators for each momenta, we do it in analogy with the simple example of the harmonic oscillator in quantum mechanics. But why do we assume that the coefficients in the expansion can be interpreted in the same way as in the...
  14. J

    A Are quantum fields real objects in space?

    I always had a tough time understanding how QFT relates to reality. Are these quantum fields (electron field, ect) physically real? Are they things that exist in space or are they just mathematical abstractions that help use calculate things?
  15. F

    B Do Quantum Fields Move Relative to Each Other?

    Do quantum fields move with respect to each other? If not, then what establishes the background spacetime for quantum fields? Is there a way in which to say that the particle wave in one field is stationary in another frame and the rest of the particles are moving with respect to it?
  16. H

    A Question about coefficients of massless quantum fields

    From Chapter 5.9 Weinberg's QFT Vol 1, massless fields are defined as: \psi_l(x)=(2\pi)^{-3/2}\int d^{3}p\sum_{\sigma}[k a(p,\sigma)u_l(p,\sigma)e^{ipx}+\lambda a^{c\dagger}(p,\sigma)v_l(p,\sigma)e^{-ipx}] With coefficients defined by the conditions: u_{\bar{l}}(p,\sigma) =\sqrt{|k|/p^0}...
  17. Urs Schreiber

    Mathematical Quantum Field Theory - Interacting Quantum Fields - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Interacting Quantum Fields Continue reading the Original PF Insights Post.
  18. Urs Schreiber

    Mathematical Quantum Field Theory - Free Quantum Fields - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Free Quantum Fields Continue reading the Original PF Insights Post.
  19. bbbl67

    I Does gravity just emerge out of all the quantum fields?

    Most research into quantum-gravity is looking for a specific particle, the graviton, to represent the gravitational force at a quantum level. But they also acknowledge that it might be impossible to find the graviton particle, because gravity is so weak. Now, is it possible that we're looking at...
  20. F

    I Can Quantum Fields be derived from Particles?

    Typically, particles are said to be excitations of quantum fields. My question is whether fields can be derived from particles. Perhaps virtual particles can be summed up in some way to produce a field, for example. Any theories on this? Thanks.
  21. L

    I Understanding the scalar field quantization

    I am getting started with QFT and I'm having a hard time to understand the quantization procedure for the simples field: the scalar, massless and real Klein-Gordon field. The approach I'm currently studying is that by Matthew Schwartz. In his QFT book he first solves the classical KG equation...
  22. M

    B Covariant Quantum Fields

    I just read Carlo Rovelli new book "Reality is Not What It Seems: The Journey to Quantum Gravity" in one sitting. I'd like to know about the following: "Fields that live on themselves, without the need of a spacetime to serve as a substratum, as a support, and which are capable by themselves of...
  23. A

    B Quantum field theory VS Quantum mechanics

    Hello I am little bit confused about one topic on theoretical Physics and that is If we want to describe our Quantum world (example atoms in metal) then should I use Quantum field theory or Quantum mechanics?
  24. D

    B How and why do quantum fields interact with each other?

    Why is it that quantum fields interact? How do they do this? Does every exitation of any field affect all other fields? I'd appreciate an explanation that uses as little math as possible, I don't have a science background.
  25. A. Neumaier

    A States in relativistic quantum field theory

    No. This is a noncovariant, observer-specific view.In the covariant, observer-independent view of fields, states are labeled instead by the causal classical solutions of hyperbolic field equations. On the collection of these the Peierls bracket is defined, which is the covariant version of the...
  26. 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 -...
  27. 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...
  28. guywithdoubts

    Is There One Electromagnetic Field in the Universe or Multiple Fields?

    Most threads discussing this subject have only confused me further, gone offtopic and later been locked. I have a basic yes/no question, which is the following: is there one single electromagnetic field in the universe that is excited locally (creating fields, in apparent plural, although...
  29. Strangelet

    Problem with Maxwell Lagrangian Density

    Homework Statement I have to expand the following term: $$\dfrac{1}{4} F_{\mu\nu}F^{\mu\nu} = \dfrac{1}{4} \left(\partial_{\mu}A_{\nu} - \partial_{\nu}A_{\mu}\right) \left(\partial^{\mu}A^{\nu} - \partial^{\nu}A^{\mu}\right)$$ to get in the end this form...
  30. M

    Imperial QFFF vs Cambridge Part III

    Hi there, this has probably been done to death on countless other threads, but I just thought it would be better to get more personal and actual direct replies by making my own post. I plan to go on and study theoretical physics and I've been accepted into both QFFF and Part III Applied Maths...
  31. K

    Classical and quantum fields

    In QFT, all particles can be interpreted as excitations of some fundamental quantum fields in the vacuum. This is the quantum picture. But in classical world, only photons and gravitons have classical counterparts. How to explain this? The common feature of these two is that they are...
  32. A

    Questions about quantum fields

    Sorry if this is not a very we'll written thread. I have already had to re-write this three times because of computer problems. I have cut out almost all of the text I had previously written and moved straight on to the main questions I have. Please be considerate of my young age, which is...
  33. T

    My understanding of Quantum Fields [Please correct me if I'm wrong]

    I believe I understand the basics of some fields, but I am unsure about the correctness of all of my knowledge. - All particles are excitations of their field (If it's a fermion) and the field they mediate (If it's a boson) - Electron repulsion is created by the exhcnage of virtual photons...
  34. R

    Coherent States (Quantum Fields)

    \HugeHomework Statement Consider a state of the EM field which satisfies \left\langle \textbf{E}_x(\vec{r})\right\rangle =f(\vec{r}) Find a coherent state which satises these expectation values.Homework Equations \textbf{E}(\textbf{r})=\frac{i}{\sqrt{2 V}}\sum _{\textbf{k},\lambda }...
  35. G

    Do quantum fields vanish at infinity?

    In Srednicki's textbook (chpt 5) he has an expression: \int d^3k f(k) \int d^4x (\partial^2 e^{ikx}) \phi(x) and he wants to integrate by parts in order put the Laplacian on the field \int d^3k f(k) \int d^4x (e^{ikx})\partial^2 \phi(x) instead of the the exponential. He says that...
  36. E

    Understanding Virtual Particles: Excitations of Quantum Fields

    I did some research on Wikipedia, and I quote from the write up on Real Particles: "The term(Virtual Particles) is somewhat loose and vaguely defined, in that it refers to the view that the world is made up of "real particles": it is not; rather, "real particles" are better understood to be...
  37. M

    Quantum Fields in Curved Space-times

    Hello, people: I've been wondering about the definition of Quantum Fields in Curved Space-times (CS). I know that, in flat space-time (Minkowski), the fields are defined as irreducible representations of the universal covering group SU(2)xSU(2) of SO(4) (which is basically the Lorentz group...
  38. T

    Interpretation of quantum fields and their ground state energies.

    Quantum field theory predicts a value for the cosmological constant that is 123 orders of magnitude larger than the observed value (if one assumes the Standard Model to be correct up to the Planck scale of 10^19 GeV)! To theoretically predict the value of the cosmological constant, one must, I...
  39. L

    What are the eigenstates of quantum fields?

    I believe that in qft the particle states are eigenvectors of the Hamiltonian(which also commutes with the number operator), i.e. H|n> = E|n>. A Fock vector is a product of many particle state vectors. But what are the eigenvectors of psi(x)? thanks
  40. L

    Degrees of freedom of quantum fields and elementary particles

    They say that a photon has two degrees of freedom, its two polarization states. Does that also mean that the electron has only two degrees of freedom, its two spin states? What about the frequency of a photon, is that not a degree of freedom? Or the three space directions that a electron can...
  41. R

    Smeared quantum fields in everyday QFT

    "Smeared" quantum fields in everyday QFT Hello everyone. I have a question regarding algebraic QFT. I read that, in order to avoid ill-defined, divergent expressions like the mode expansions for spacetime-dependent field operators φ(x), one starts from the (Wightman?) axioms, using...
  42. D

    Is the Electromagnetic Field a Classical or Quantum Field?

    how we can differentiate classical and quantum fields?i searched everywher..but i did not get a satisfactory answer
  43. S

    Quantum Fields and Strings: A Course for Mathematicians

    Has anyone here read Quantum Fields and Strings: A Course for Mathematicians vol 1 and/or vol 2? I was thinking about trying to tackle them but I'm unsure of what the mathematical prerequisites for doing so are. My background is in physics, but I have taken courses on differential geometry...
  44. T

    Lie derivatives of Quantum Fields

    Hello, this question will essentially concern quantum field theory in curved spacetime, and it has two parts to it. I have recently acquired DeWitt's treatment of the formalism, which immediately discusses the role of killing vectors in the theory. Specifically, given a killing vector field...
  45. L

    MSc in Quantum Fields and Fundamental Forces at ICL

    Hey guys! I got the offer a few weeks ago and I was wondering if anyone knows what to expect when I go there this October. I am feeling kinda nervous about it since getting the offer seems like a longshot when I applied(didnt get 1st, is currently a 2:1). Any advices, thoughts and comments...
  46. G

    Physics Quantum Fields Theory and Solid State Physics

    Hello! Does any of you know someone in Paris who is working on Solid State Physics using Quantum Field Theory formalism ? Thank you.
  47. Vectronix

    Texts on Quantum Fields without Maxwell's Equations

    Hi I would like to know what your thoughts are on books that make an attempt to discuss quantum electromagnetism without using any of Maxwell's equations. I came across a text written by an author who decided not to use Maxwell's equations because Maxwell and others "didn't have access" to...
  48. M

    ICL MSc in Quantum Fields and Fundamental Forces - how hard?

    Hello, I am thinking of applying for the above course and just trying to gauge how difficult it is really. I have a 2:1 in physics from Cambridge, and although at times I felt like I was knocking my head against a brick wall overall I think I might have pulled to a first if the exams had...
  49. hananeel

    Schools MSc in Quantum Fields and Fundamental Forces at Imperial College London

    I'm an Electronic and communication Engineer, and I'm living in the Caribbean, and i want to study MSc in Quantum Fields and Fundamental Forces Imperial College London, since in its description seems very likely what I'm looking for, which is,... I'm looking a course that can place me in...
  50. R

    Why is this content nonsensical?

    Matter and energy are created from quantum field, but are time and space too created from quantum fields?