What is Quantum field theory: Definition and 571 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. A

    I Frank Wilczek on Virtual Particles and Summing diagrams....

    Hi all, - an initial apology - there are a large number of threads on virtual particles on the site, and I apologize for adding another one. I had two questions - on a related note, the guidance provided by @A. Neumaier's FAW on virtual particles has been highly valuable for a novice . 1) Upon...
  2. A

    I 'Off-shell' particle in an external field....

    Silly question but could someone explain why a real, 'observable' particle is said to be 'off-shell' in an external field? @A. Neumaier 's excellent FAQ notes that the mass shell constraints ceases to have meaning in this case. I'm just not fully clear on why (probably obvious) given that energy...
  3. 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...
  4. John Greger

    A Understanding Hermiticity of Actions in QFT for Checking and Confirming

    Hi! In QFT we are usually interested in actions that are hermitian. Say we are looking at scattering of Dirac fermions with a real coupling constant g, whose Lagrangian is given by: $$L= \bar{\psi}(i \gamma_{\mu} \partial^{\mu} -m) \psi - \frac{1}{2} \partial_{\mu} \phi \partial^{\mu} \phi -...
  5. S

    A QFT topics for entanglement entropy

    I want to know what are the QFT topics that I need to understand in order to proceed in reading papers on entanglement entropy such as, Entanglement Entropy and Quantum Field Theory Entanglement entropy in free quantum field theory Entanglement entropy: holography and renormalization group An...
  6. D

    Particle Schwartz and QFT Following Tong's Notes

    Hello, I have been following Tong's notes on QFT and have found them to be a great introduction. I am almost at the end and am trying to figure out how to proceed. I have seen recommendations on David Skinner's notes, but I think I want to use a textbook either with Skinner's notes or maybe...
  7. saadhusayn

    Calculating effective action at two loops

    Does this mean that the expression for the above vertex is $$ -\frac{g}{2}\epsilon^{abx}\epsilon^{cdx}\int d\tau \langle A_{a} (\tau) A_{c} (\tau)\rangle \langle Y^{i}_{b} (\tau)Y^{i}_{d}(\tau) \rangle $$
  8. saadhusayn

    A Calculating the ghost field in the Becker and Becker paper

    This is the paper that I refer to. I'm trying to figure out the ghost action (Equation 2.16) in the background field gauge. I am attempting to use Srednicki's (chapter 78) expression for the ghost field in the background gauge. However, I am missing out on a √g coefficient in front of the term...
  9. Tiptoeingelephants

    I Is a Particle Simply the Manifested Kinetic Energy of Its Quantum Field?

    Trying to better understand quantum field theory, I've read that particles are created when it becomes an exitation of its quantum field. Would it then be right to think of a particle as the manifested kinetic energy of its field?
  10. Quantum Alchemy

    I Questions about QFT and the reality of subatomic particles

    I've been reading about Quantum Field Theory and what it says about subatomic particles. I've read that QFT regards particles as excited states of underlying quantum fields. If this is the case, how can particles be regarded as objective? It seems to me that this also removes some of the...
  11. sakh1012

    A Dirac Field quantization and anti-commutator relation

    Can anyone explain while calculating $$\left \{ \Psi, \Psi^\dagger \right \} $$, set of equation 5.4 in david tong notes lead us to $$Σ_s Σ_r [b_p^s u^s(p)e^{ipx} b_q^r†u^r†(q)e^{-iqy}+ b_q^r †u^r†(q)e^{-iqy} b_p^s u^s(p)e^{ipx}].$$ My question is how the above mentioned terms can be written as...
  12. D

    A Understanding Harmonic oscillator conventions

    I don't quite understand how he got the line below. By using discrete time approximation, we can get the second order time expression. But i don't see how by combining terms he is able to get such expression.
  13. Y

    Primary calculation involving the Dirac gama matrices

    When working on the exercise 3.2 of Peskin's QFT, I find one of the calculating steps confused for me. I read the solution, which is showed in the picture. I just don't understand the boxed part. I know it involved the Dirac equation, and the solution seems to treat the momentum as a operator...
  14. L

    Finding Cartan Subalgebras for Matrix Algebras

    This is one problem from Robin Ticciati's Quantum Field Theory for Mathematicians essentially asking us to find Cartan subalgebras for the matrix algebras ##\mathfrak{u}(n), \mathfrak{su}(n),\mathfrak{so}(n)## and ##\mathfrak{so}(1,3)##. The only thing he gives is the definition of a Cartan...
  15. M

    Wick contraction in scalar QED

    While writing out the Dyson series due to the time ordering above I encountered the two expressions $$T(\mathcal{L}_{int}(x))\quad \text{and}\quad T(\mathcal{L}_{int}(x)\mathcal{L}_{int}(y))$$ I was able to write out the first term in terms of contractions using Wick's theorem and then finally...
  16. RicardoMP

    A Vector and Axial vector currents in QFT

    I'm currently working out quantities that include the vector and axialvector currents ##j^\mu_B(x)=\bar{\psi}(x)\Gamma^\mu_{B,0}\psi(x)## where B stands for V (vector) or A (axialvector). The gamma in the middle is a product of gamma matrices and the psi's are dirac spinors. Therefore on the...
  17. M

    Dyson's series and the time derivative

    I'm having a hard time understanding how exactly to evaluate the expression} $$\partial_t \mathcal{T}\exp\left(-i S(t)\right)\quad \text{where}\quad S(t)\equiv\int_{t_0}^tdu \,H(u) .$$ The confusing part for me is that if we can consider the following: $$\partial_t \mathcal{T}\exp\left(-i...
  18. RicardoMP

    Feynman one-loop integral ##I_{21}##

    Starting from the general formula: $$I_{n,m}=\frac{1}{(4\pi)^2}\frac{\Gamma(m+2-\frac{\epsilon}{2})}{\Gamma(2-\frac{\epsilon}{2})\Gamma(n)}\frac{1}{\Delta^{n-m-2}}(\frac{4\pi M^2}{\Delta})^{\frac{\epsilon}{2}}\Gamma(n-m-2+\frac{\epsilon}{2})$$ I arrived to the following...
  19. weningth

    A How to deal with colour indices on spinors

    I want to calculate transition amplitudes in QCD for processes like ##q(k)q^\prime(p)\rightarrow q(k^\prime)q^\prime(p^\prime)##, where ##q,q^\prime## are quarks. However, I am unsure what to do with the colour indices of the quark spinors upon squaring the matrix element. For the sake of...
  20. M

    Nother current of given symmetry

    This is my first time dealing with scaling symmetry, so I'm sorry if the following is fundamental wrong. My approach was the same as if I was trying to show the same for translation or Lorentz symmetry. We have $$\delta\phi(x)= \phi'(x')-\phi(x)=...
  21. M

    Show that the given Green Function is the propagator of a certain Lagrangian

    My fundamental issue with this exercise is that I don't really know what it means to "show that X is a propagator".. Up until know I encountered only propagators of the from ##\langle 0\vert [\phi(x),\phi(y)] \vert 0\rangle##, which in the end is a transition amplitude and can be interpreted as...
  22. RicardoMP

    A What Is the Renormalized Gluon Dressing Function?

    Consider, for example, the gluon propagator $$D^{\mu\nu}(q)=-\frac{i}{q^2+i\epsilon}[D(q^2)T^{\mu\nu}_q+\xi L^{\mu\nu}_q]$$ What exactly is the renormalized gluon dressing function ##D(q^2)## and what is its definition? My interest is in knowing if I can then write the bare version of this...
  23. RicardoMP

    A Trace of a product of Dirac Matrices in a Fermion loop

    I'm working out the quark loop diagram and I've drawn it as follows: where the greek letters are the Lorentz and Dirac indices for the gluon and quark respectively and the other letters are color indices. For this diagram I've written...
  24. G

    A Is renormalization the ideal solution?

    Quantum gravity theories and GUTs are nonrenormalizable theories, but does this actually mean that these theories must be flawed, or does it mean that renormalization must be a flawed concept, or is this not actually a problem? If it is impossible to produce a renormalizable quantum gravity...
  25. R

    I Calculating a particular amplitude with Feynman diagrams

    So I’m trying to compute the probability amplitude of an electron with momentum p1 and a positron with momentum p2 annihilating into a photons with momenta q1 and q2. My question is how do you use Feynman diagrams to calculate the first and second order expansions (seen in the third image)? I...
  26. takunitoche

    A Derivation of the Yang-Mills 3 gauge boson vertex

    Hello everyone, I am stuck in the derivation of the three gauge-boson-vertex in Yang-Mills theories. The relevant interaction term in the Lagrangian is$$\mathcal{L}_{YM} \supset g \,f^{ijk}A_{\mu}{}^{(j)} A_{\nu}{}^{(k)} \partial^{\mu} A^{\nu}{}^{(i)} $$ I have rewritten this term using...
  27. takunitoche

    Three gauge boson Yang-Mills vertex

    Hello everyone, I am stuck in deriving the three gauge-boson-vertex in Yang-Mills theories. The relevant interaction term in the Lagrangian is $$\mathcal{L}_{YM} \supset g \,f^{ijk}A_{\mu}{}^{(j)} A_{\nu}{}^{(k)} \partial^{\mu} A^{\nu}{}^{(i)} $$ I have rewritten this term using the...
  28. D

    Calculating Divergent Amplitude in Phi-4 Theory

    For the diagram In scalar field theory, I have obtained an integral which looks like $$\int_{0}^{\Lambda} \frac{d^4 q}{(2\pi)^4} \frac{i}{q^2 - m^2 + i\varepsilon} \frac{i}{(p - q)^2 - m^2 + i\varepsilon}$$ I am required to calculate this and obtain the divergent amplitude $$i\mathcal{M} =...
  29. G

    I Quantum field theory: an informative approach

    I'm looking for a book that describes the quantum field theory without going deeply in the theory with formulas or complex description of the mathematics under the theory. I know that this theory is really complex and it needs a deep knowledge of quantum physics in order to be understood. But...
  30. M

    A Gravitational dressing in quantum field theory

    In quantum field theory, a dressed particle is a particle ("bare particle") considered in combination with certain secondary effects that it produces (e.g. the virtual pair creation involved in vacuum polarization). The dressed states are regarded as more physical, hence closer to reality. Axel...
  31. Sophrosyne

    Is the concept of "wave function collapse" obsolete?

    Summary: In the past, physicists talked of the phenomenon of "wave function collapse" very freely, whereas now there seems to be some reservation about it. Why? In reading older popular physics literature, physicists used to talk about "wave function collapse" freely and more often...
  32. B

    A Are unstable particles ever really external lines in QFT?

    Let's for example consider the Z boson. It can't directly be detected; so is it ever really correct to draw it as an external line on a Feynman diagram? I've seen processes involving it before be written as something -> Z + something, then Z -> ... but since unstable particles aren't really on...
  33. R

    I Young physicist in seek of guidance

    Is there anyone on here who could help me fill in my gaps in quantum field theory up to renormalization? I know how to canonically quantize a theory and how to use scalars (spin 0), vectors (spin 1) and spinors (spin 1/2) but lack more advanced knowledge like renormalization which I could...
  34. SisypheanZealot

    Dirac Delta using periodic functions

    I know it is something simple that I am missing, but for the life of me I am stuck. So, I used the identity ##sin(a)sin(b)+cos(a)cos(b)=cos(a-b)## which gives me $$\int^{\infty}_{-\infty}dx\:f(x)\delta(x-y)=\int^{\infty}_{-\infty}dx\:f(x)\frac{1}{2L}\sum^{\infty}_{n=-\infty}\lbrace...
  35. RicardoMP

    Derivatives on tensor components

    This was my attempt at a solution and was wondering where did I go wrong: -\frac{\partial}{\partial p_\mu}\frac{1}{\not{p}}=-\frac{\partial}{\partial p_\mu}[\gamma^\nu p_\nu]^{-1}=\gamma^\nu\frac{\partial p_\nu}{\partial p_\mu}[\gamma^\sigma...
  36. FourEyedRaven

    Particle Thomson (Modern Particle Physics) & Schwartz (Quantum Field Theory)

    Hi. Are these two books complementary, or do they have too much in common? https://www.amazon.com/dp/1107034264/?tag=pfamazon01-20 www.amazon.com/Quantum-Field-Theory-Standard-Model/dp/1107034736/ My problem is that I still don't quite understand the difference between university courses in...
  37. W

    Field in the presence of a background electromagnetic field

    Attempt at a solution: $$ -\gamma^{\mu}\gamma^{\nu}D_{\mu} D_{\nu} - im\gamma^{\mu} D_{\mu} + im\gamma^{\nu}D_{\nu} - m^2 =$$ $$ -\gamma^{\mu}\gamma^{\nu}(\partial_{\mu} + ieA_{\mu})(\partial_{\nu}-m) - I am \gamma^{\mu}(\partial_{\mu}+ieA_{\mu})+im\gamma^{\nu}(\partial_{\nu}+ieA_{\nu}) - m^2...
  38. M

    Beta-function for the Gross-Neveu model

    In the Peskin & Schroeder textbook, the ##\beta## function for the Gross-Neveu model is discussed in problem 12.2. After computing it, I have tried checking my results with some solutions found online. My problem is that they all disagree among each other (something quite recurrent for this book...
  39. T

    I Problem of time in quantum field theory?

    Summary: Does the "problem of time in quantum mechanics" go for Lorentz-invariant quantum mechanical theories like QED? Everything I read about "the problem of time in quantum mechanics," i.e. absolute time in QM clashing with relativity's relative time coordinate and relativity of...
  40. Ramil

    Quantum Monte-Carlo calculation of Green's function

    Introducing the spacetime spherical symmetric lattice, I use the following notifications in my program. i - index enumerating the nodes along t-coordinate, j - along the r-coordinate, k - along the theta-coordinate, l - along the phi-coordinate. N_t - the number of nodes along t-coordinate. N_r...
  41. A

    A Do QED effects make a huge change to the position of the electrons?

    In https://en.wikipedia.org/wiki/Lamb_shift about the lamb shift, it's mentioned that the change in the electron's frequency due to QED effects (vacuum polarization and self-energy correction) is about 1 GHz, which would translate to an energy change of hf = 6.63E-25 J. This is 3E-7 times of the...
  42. L

    How to pick a concrete PhD objective in this QFT/Gravity formalism?

    I have a major in Mathematics and Mathematical Physics and I'm finishing a masters in Physics (just finishing to write down the dissertation really). I have also already enrolled the PhD course so that I need now to pick an advisor and a theme before june. My main interest since the early days...
  43. A

    A Do we need stochasticity in a discrete spacetime?

    Suppose that the spacetime is discrete, with only certain positions being possible for any particle. In this case, the probability distributions of particles have nonzero values at the points on which the wavefunction is defined. Do we need randomness in the transitions of particles in such a...
  44. A

    I Does the Compton wavelength put a limitation on position measurements?

    I have read on Wikipedia (https://en.wikipedia.org/wiki/Compton_wavelength) that we cannot measure the position of a particle more precise than half of its Compton wavelength, since the photon we would need will be so energetic to produce electron-positron pairs. How does the creation of...
  45. A

    A Can we create a random variable using QED effects?

    Quantum Electrodynamics (QED) has some observable effects such as the lamb shift, which is mainly caused by the vacuum polarization and the electron self-energy. These effects contribute to the "smearing" of the electron in an unpredictable manner, other than the uncertainty we already have...
  46. A

    A Is there any Bohmian approach to quantum electrodynamics?

    I know that in some Bohmian papers (like https://arxiv.org/pdf/quant-ph/0303156.pdf), electron-positron pair creation and annihilation is modeled by different methods like stochastic jumps in the configuration space. My question is, is there any Bohmian approach to reproduce all of the...
  47. RicardoMP

    How to determine particle energies in center of momentum frame?

    That said, my approach was to determine the energies and 3-momenta at the center of momentum reference frame for each particle, with a fixed s, and check it corresponds to each one of the above, but I'm having some trouble proving that, for example, E_A=\frac{s+m^2_A-m^2_B}{2\sqrt{s}}. I've...
  48. W

    A Path Integral Approach To Derive The KG Propagator

    I'm having trouble understanding a specific line in my lecturers notes about the path integral approach to deriving the Klein Gordon propagator. I've attached the notes as an image to this post. In particular my main issue comes with (6.9). I can see that at some point he integrates over x to...
  49. 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...
  50. 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...
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