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. P

    A What knowledge is needed to understand modern QFT research?

    Hi all, I'm interested in the interplay between condensed matter and high energy theory. I'm a bit more than half-way through peskin and schroeder (done with part II, RG and critical phenomena). What I find out is that I'm still sorely lacking in ability to read any of the current research in...
  2. ergospherical

    Quantum Srednicki QFT draft vs printed versions

    There is a draft of Srednicki's QFT book available for free online (here: https://web.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf). I have a book voucher and, since I couldn't find it in the library, was thinking of buying it so long as the content of the book was sufficiently better (i.e...
  3. T

    A QFT with vanishing vacuum expectation value and perturbation theory

    In This wikipedia article is said: "If the quantum field theory can be accurately described through perturbation theory, then the properties of the vacuum are analogous to the properties of the ground state of a quantum mechanical harmonic oscillator, or more accurately, the ground state of a...
  4. Glenn Rowe

    A Simple S matrix example in Coleman's lectures on QFT

    In Coleman's QFT lectures, I'm confused by equation 7.57. To give the background, Coleman is trying to calculate the scattering matrix (S matrix) for a situation in which the Hamiltonian is given by $$H=H_{0}+f\left(t,T,\Delta\right)H_{I}\left(t\right)$$ where ##H_{0}## is the free Hamiltonian...
  5. A. Neumaier

    A An interesting paper about measurement and locality in QFT

    Bostelmann, H., Fewster, C. J., & Ruep, M. H. (2021). Impossible measurements require impossible apparatus. Physical Review D, 103(2), 025017.
  6. J

    A Connection between QFT renormalization and field regularization?

    While in QFT we remove infinite energy problem with renormalization procedure, asking e.g. "what is mean energy density in given distance from charged particle", electric filed alone would say $$\rho \propto |E|^2 \propto 1/r^4 $$ But such energy density would integrate to infinity due to...
  7. samantha_allen

    Courses Should I take a group theory course before QFT?

    I know that studying QFT requires understanding Lie Groups and infinitesimal generators as they correspond to symmetry transformations. I want to study or take a course (offered by my university) in QFT in the coming academic year and I have the option to take a abstract algebra course offered...
  8. hilbert2

    A Anharmonic oscillators with closed-form solutions

    There are some articles from the 1980s where the authors discuss 1D quantum oscillators where ##V(x)## has higher than quadratic terms in it but an exact solution can still be found. One example is in this link: https://iopscience.iop.org/article/10.1088/0305-4470/14/9/001 Has anyone tried to...
  9. Mirod

    Zee QFT problem I.4.1: inverse square laws in (D+1)-dimensions

    I tried to do it for 2+1 D (3+1 is done in the text, by writing the integral in spherical coordinates and computing it directly). In 2+1 D I wrote it as: E = - \int \frac{d^2 k}{ (2\pi)^2 } \frac{e^{kr cos\theta}}{k^2 + m^2} = - \int_0^{\infty} \int_0^{2\pi} \frac{d k d\theta}{ (2\pi)^2 }...
  10. LCSphysicist

    Understanding Scattering Process in QFT Integral

    I have been studying scattering process in QFT, but i am stuck now because i can't understand how this integral was evaluated: $$\int dp\space \frac{1}{\sqrt{p^2+c²}}\frac{1}{\sqrt{p^2+k²}}\space p² \space d\Omega \space \delta(E_{cm}-E_{1}-E_{2})$$$ Where Ecm = c + k, E1 is the factor in the...
  11. J

    A QM is Feynman path ensemble - is QFT Feynman field ensemble?

    While classical mechanics uses single action optimizing trajectory, QM can be formulated as Feynman ensemble of trajectories. As in derivation of Brownian motion, mathematically it is convenient to use nonphysical: nowhere differentiable trajectories - should it be so? Can this connection be...
  12. U

    Questions on field operator in QFT and interpretations

    For a real scalar field, I have the following expression for the field operator in momentum space. $$\tilde{\phi}(t,\vec{k})=\frac{1}{\sqrt{2\omega}}\left(a_{\vec{k}}e^{-i\omega t}+a^{\dagger}_{-\vec{k}}e^{i\omega t}\right)$$ Why is it that I can discard the phase factors to produce the time...
  13. U

    Question on discrete commutation relation in QFT

    Given the commutation relation $$\left[\phi\left(t,\vec{x}\right),\pi\left(t,\vec{x}'\right)\right]=i\delta^{n-1}\left(\vec{x}-\vec{x}'\right)$$ and define the Fourier transform as...
  14. DaniV

    Proving modified Maxwell action is gauge invariant

    I want to show that the action staying the same action after taking ##A^\mu \to A^\mu + \partial ^\mu \chi##, for the first term I suceeded in showing the invariance using the fact ##[\partial ^ \mu , \partial ^\nu]=0## but for the second term I'm getting: ##\epsilon^{\alpha\mu\nu}A_\alpha...
  15. quantumdarkmatter

    Self-Study QFT: Prerequisites for Feynman Diagrams, QED & More

    Summary:: I want to study QFT 1 in the upcoming semester, so what are the prerequisites to study it. By QFT 1 I mean Classical field theory, Canonical Quantization, Feynman Diagrams, and QED. I am trying to self study QM from Griffiths' Introduction to Quantum Mechanics book. What are the sub...
  16. AdvaitDhingra

    QFT interpretation of Hawking Radiation

    Hello, So I was reading about Hawking radiation and I read a QFT interpretation of it. It went something like this: A vacuum contains virtual particles (vacuum energy), which in qft can be described as waves that are out of phase and cancel each other out (matter and antimatter). I a black...
  17. Jamister

    A Exploring the Conservation of 4-Momentum in Quantum Field Theory

    why in QFT 4-momentum is conserved? how can it be derived from basic principles of the Hamiltonian formalism? Is it conserved because of the golden rule?
  18. Demystifier

    A Infinities in QFT (and physics in general)

    Moderator's Note: Thread spun off from previous thread due to topic change. I see. Basically you are worried by stuff a mathematical physicist would study with fancy schmancy functional analysis. I'm not worried too much by such stuff because I don't think that actual infinities (actually...
  19. MathematicalPhysicist

    A Understanding Local and Nonlocal Operators in Quantum Field Theory

    I am reading the claymath problem here: http://claymath.org/sites/default/files/yangmills.pdf on page 6, in the comments (section 5), they call a local operator to be an operator that satisifies: ##\mathcal{O}(\vec{x})=e^{-i\vec{P}\cdot \vec{x}}\mathcal{O}e^{i\vec{P}\cdot \vec{x}}## where...
  20. sophiatev

    A Second Quantization in QFT

    In Quantum Field Theory and the Standard Model by Schwartz, he defines the Hamiltonian for the free electromagnetic field as (page 20, here's a link to the book). This follows (in my understanding) from the fact that the amplitude of the field at a given point in space oscillates as a simple...
  21. L

    B Missing mass in atomic systems

    Hi! My name's Logan Knox and I'm aspiring to eventually understand the physics and nature of the quantum world in its totality, and I have a LONG way to go, but I have to get there by asking the right questions, and I think this is the first step to finding the right question to ask for this...
  22. F

    I What stands for probability in QFT?

    When we apply creation operator in vacuum we certainly have one particle,similarly for annihilation operator.Then what is stand for chance(probability) in QFT?
  23. E

    I Classical equivalent of scalar free field in QFT

    Hi there, In QFT, a free scalar field can be represented by the lagrangian density $$\mathcal{L} = \frac{1}{2}\left(\partial\phi\right)^2 - \frac{1}{2}m^2\phi^2$$ I would like to find a classical system that has the same lagrangian. If we consider the transversal motion of an elastic string...
  24. Pouramat

    Weyl Spinors Transformation, QFT1, Peskin, Chapter 3

    \begin{align} \psi_L \rightarrow (1-i \vec{\theta} . \frac{{\vec\sigma}}{2} - \vec\beta . \frac{\vec\sigma}{2}) \psi_L \\ \psi_R \rightarrow (1-i \vec{\theta} . \frac{{\vec\sigma}}{2} + \vec\beta . \frac{\vec\sigma}{2}) \psi_R \end{align} I really cannot evaluate these from boost and rotation...
  25. H

    A Position is no more an operator in QFT

    In quantum mechanics there is no operator for time (problem with unbounded energy). position is no more an operator in field theory. was there still a problem in QM?
  26. LarryS

    A Why is Quantum Field Theory Local?

    Under the Schrodinger Picture, nonrelativistic Quantum Mechanics for a fixed number of particles is highly nonlocal, e.g. Quantum Entanglement. But Quantum Field Theory is local. Why is that? Is it because QFT was created to accommodate SR, which, as a classical theory, is local? As always...
  27. joneall

    A Symmetry of QED interaction Lagrangian

    I am trying to get a foothold on QFT using several books (Lancaster & Blundell, Klauber, Schwichtenberg, Jeevanjee), but sometimes have trouble seeing the forest for all the trees. My problem concerns the equation of QED in the form $$ \mathcal{L}_{Dirac+Proca+int} = \bar{\Psi} ( i \gamma_{\mu}...
  28. F

    I Why can't we interprete /x> in relativistic QFT as position eigenfunc?

    Why can't we interprete /x> in relativistic QFT as position eigenstate?And by the way what is the difference between /x> and /1x>=Phi(field operator)(x)/0>?
  29. F

    I Why QFT still goes well while it lacks the notion of wave function?

    In QM by virtue of wave function we calculate any things. But in QFT it seems that there is a lacking of notion of wave function.I do not understand why QFT still goes well(it is a good theory to calculate any things)?
  30. D

    A Suggested reading for quantum information applications in QFT

    What would you say is essential reading for those of us who want to understand how exactly is QFT benefiting from QI? Can anyone give a summary of what is happening, and where to start reading? (at postgraduate/entry-research-level).
  31. S

    Courses Statistical Physics vs QFT vs General relativity

    Good day, I'm starting my master in physics, and it's time for me to choose my courses. I will take one or two of the following three courses, which are: Statistical Physics, QFT and General relativity. Now, I'm finding it very hard to decide as on the one hand, I'm interested in QFT and...
  32. W

    I Renormalization of scalar field theory

    I was reading about the renormalization of ##\phi^4## theory and it was mentioned that in order to renormalize the 2-point function ##\Gamma^{(2)}(p)## we add the counterterm : \delta \mathcal{L}_1 = -\dfrac{gm^2}{32\pi \epsilon^2}\phi^2 to the Lagrangian, which should give rise to a...
  33. Haorong Wu

    Courses Looking for advice for learning QFT

    Hello. I am trying to learn quantum field theory. I am crazy about it but I have some problems in my study. I use An Introduction to Quantum Field Theory by Peskin and Schroeder. It is said that the book is easier to learn than other books. However, I have to spend a lot of time in computing...
  34. SEYED2001

    I How to prove that some fields are different aspects of one general field?

    Hi! I know some theorists believe all quantum fields and gravitational field are different aspects of one universal field. What does that formally (e.g. mathematically) mean "to be different aspects of" and how can one prove, let's say, fields A and B are different aspects of C? By the way, I...
  35. Helena Wells

    A Resolving the Paradox: Combining Quantum Mechanics and Special Relativity

    According to Bell's theorem quantum mechanics is not local.How can we combine it with Special Relativity which is local and gives us another successful theory?
  36. J

    I How does contact occur at the atomic level?

    When we touch something, will there always be a layer of air between us?
  37. A

    QFT question about using momentum raising and lowering operators

    How did you find PF?: Google I know how to express Hamiltonian for scalar field written in field operators through the raising and lowering momentum operators, but I can't figure out how to do the same for the number of particles written in field operators: the 1/2E coefficient within the...
  38. Haorong Wu

    Courses I am a graduate student in quantum optics. Should I learn QFT?

    I am particularly interesting in QFT, and I am going to be a graduate student in quantum optics and quantum information this autumn. Strangely, I find that there is no courses for QFT. After all, I though QFT are about quantum and field, and quantum optics are about quantum and field, too...
  39. AndreasC

    I Exploring Foundations of Quantum Mechanics & QFT

    Hey, applied maths and physics student here. I started wondering recently what the meaning of measurement was in quantum mechanics, and I remembered that I had once heard of the bohmian interpretation which challenged the impression I had so far (which was that hidden variables had been...
  40. I

    A Zero-point Energy Contribution Below the Planck energy cutoff

    Is it possible to determine the amount of zero-point energy contributed by all fields below the Planck energy cutoff?
  41. abivz

    I Obtaining the Dirac function from field operator commutation

    Hi everyone, I'm new to PF and this is my second post, I'm taking a QFT course this semester and my teacher asked us to obtain: $$[\Phi(x,t), \dot{\Phi}(y,t) = iZ\delta^3(x-y)]$$ We're using the Otto Nachtman: Elementary Particle Physics but I've seen other books use this notation: $$[\Phi(x,t)...
  42. abivz

    I QFT - Field operator commutation

    Hi everyone, I'm taking a QFT course this semester and we're studying from the Otto Nachtman: Texts and Monographs in Physics textbook, today our teacher asked us to get to the equation: [Φ(x,t),∂/∂tΦ(y,t)]=iZ∂3(x-y) But I am unsure of how to get to this, does anyone have any advice or any...
  43. Lynch101

    B Bell's theorem, QFT, and the Relativity of Simultaneity

    I've been slowly grinding away with what I can about quantum mechanics and QFT. I'm not sure how far I've gotten but I've come up against a bit of a roadblock concerning how the relativity of simultaneity applies in QFT with specific reference to the outcome of Bell tests. My misunderstanding...
  44. G

    A Bremsstrahlung single photon or spectrum

    Non-relativistic Bremsstrahlung is discussed classically in Rybicki “Radiative Processes in Astrophysics” where Larmor’s formula is used to find the power radiated in a collision between an electron and a Coulomb field. The Fourier transform of the pulse allows for a description of the pulse in...
  45. weningth

    A Why does this amplitude not vanish by the Ward identity?

    Consider the process e^-\rightarrow e^-\gamma depicted in the following Feynman diagram. The spin-averaged amplitude with linearly polarised photons is \overline{|M|^2}=8\pi\alpha\left(-g^{\mu\nu}+\epsilon^\mu_+\epsilon^\nu_-+\epsilon^\mu_-\epsilon^\nu_+\right)\left(p_\mu p^\prime_\nu+p_\nu...
  46. RicardoMP

    What is the relationship between polarization vectors and spin in QFT?

    I'm looking forward to have a better understanding of the polarization vector in quantum field theory in order to solve a particular problem. In class and in several textbooks I see that ##s^\mu=(0,\vec s)## and ##|\vec s|=1##. Are polarizations vectors defined to have no temporal component in...
  47. JD_PM

    A Commutation relations between HO operators | QFT; free scalar field

    I am getting started in applying the quantization of the harmonic oscillator to the free scalar field. After studying section 2.2. of Tong Lecture notes (I attach the PDF, which comes from 2.Canonical quantization here https://www.damtp.cam.ac.uk/user/tong/qft.html), I went through my notes...
  48. N

    Calculation of g-factor correction in Peskin p. 196

    I'm reading peskin QFT textbook. In page 196 eq. (6.58) it says $$F_2(q^2=0)=\frac{\alpha}{2\pi}\int ^1_0 dx dy dz \delta (x+y+z-1) \frac{2m^2z(1-z)}{m^2(1-z)^2}\\=\frac{\alpha}{\pi}\int ^1_0 dz\int ^{1-z}_0 dy \frac{z}{1-z}=\frac{\alpha}{2\pi}$$ I confirmed the conversion from the first line...
  49. JD_PM

    A Lorentz Transformations and Angular momentum | Tong's QFT notes

    I am reading Tong's lecture notes and I found an example in which there are several aspects I do not understand. This example is aimed at: - Understanding what is the analogy in field theory to the fact that, in classical mechanics, rotational invariance gives rise to conservation of angular...
  50. smodak

    Quantum Is No-Nonsense Quantum Field Theory a Student-Friendly Introduction?

    No-Nonsense Quantum Field Theory: A Student-Friendly Introduction by Schwichtenberg, Will let you know how it is when I read it. More details here
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