What is Quantum-field-theory: Definition and 14 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. G

    Showing that a certain summation is equal to a Dirac delta?

    I'm studying Quantum Field Theory for the Gifted Amateur and feel like my math background for it is a bit shaky. This was my attempt at a derivation of the above. I know it's not rigorous, but is it at least conceptually right? I'll only show it for bosons since it's pretty much the same for...
  2. Riotto

    A Canonical momentum ##\pi^\rho## of the electromagnetic field

    In David Tong's QFT notes (see http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf , page 131, Eq. 6.38) the expression for canonical momentum ##\pi^0## is given by ##\pi^0=-\partial_\rho A^\rho## while my calculation gives ##\pi^\rho=-\partial_0 A^\rho## so that ##\pi^0=-\partial_0 A^0##. Is it...
  3. S

    Studying Minimal preliminary knowledge for a PhD in particle physics?

    Currently, I am doing a master in mathematical physics. I am interested in particles& field theory and want to apply a PhD in this field. But I am not sure whether I can... I just learned a little high energy physics from Griffth and Peskin' book on elementary particles and QFT. Recently, I...
  4. CharlieCW

    Coherent states for Klein-Gordon field

    Homework Statement Show that the coherent state ##|c\rangle=exp(\int \frac{d^3p}{(2\pi)^3}c(\vec{p})a^{\dagger}_{\vec{p}})|0\rangle## is an eigenstate of the anhiquilation operator ##a_{\vec{p}}##. Express it in terms of the states of type ##|\vec{p}_1...\vec{p}_N\rangle## Homework Equations...
  5. N

    Quantizing the complex Klein-Gordon field

    I'm self-studying QFT and attempting exercise 2.2 on Peskin & Schroeder. First off, I'm a bit confused on the logic the authors use in the quantization process. They first expand the fields in terms of these ##a_{\vec{p}},a_{\vec{p}}^\dagger## operators which, if I understand correctly, is...
  6. N

    On deriving the standard form of the Klein-Gordon propagator

    I'm trying to make sense of the derivation of the Klein-Gordon propagator in Peskin and Schroeder using contour integration. It seems the main step in the argument is that ## e^{-i p^0(x^0-y^0)} ## tends to zero (in the ##r\rightarrow\infty## limit) along a semicircular contour below (resp...
  7. bananabandana

    I Negative and Positive energy modes of KG equation

    If we have the normal KG scalar field expansion: $$ \hat{\phi}(x^{\mu}) = \int \frac{d^{3}p}{(2\pi)^{3}\omega(\mathbf{p})} \big( \hat{a}(p)e^{-ip_{\mu}x^{\mu}}+\hat{a}^{\dagger}(p)e^{ip_{\mu}x^{\mu}} \big) $$ With ## \omega(\mathbf{p}) = \sqrt{|\mathbf{p}^{2}|+m^{2}}## Then why do we associate...
  8. L

    A How the g factor comes from QFT?

    I'm reading the book Quantum Field Theory and the Standard Model by Matthew Schwartz and currently I'm studying the chapter 17 titled "The anomalous magnetic moment" which is devoted to computing the corrections due to QFT to the g factor. My main issue is in the beginning of the chapter, where...
  9. L

    Show that the vacuum polarization is transverse

    Homework Statement Show that the vacuum polarization \Pi^{\mu\nu}_2(p) in 1-loop is transverse. Decide whether you want to use Ward's identity and prove this to be true in all orders or only prove for 1-loop. Homework Equations Ward's identity q_\mu \mathcal{M}^{\mu}=0 which must hold where...
  10. L

    Ward-Takahashi identities at tree level in scalar QED

    Homework Statement Let \Gamma^\mu be the three-point vertex in scalar QED and \Gamma^{\mu\nu} be the four-point vertex. Use Feynman's rule at tree level and verify that the Ward-Takahashi identities are satisfied: q^\mu \Gamma_\mu(p_1,p_2)=e[D_F^{-1}(p_1)-D_F^{-1}(p_2)],\\...
  11. L

    A How does one find the Feynman diagrams?

    I'm studying Quantum Field Theory and the main books I'm reading (Peskin and Schwartz) present Feynman diagrams something like this: one first derive how to express with perturbation theory the n-point correlation functions, and then represent each term by a diagram. It is then derived the...
  12. L

    Computing the scattering amplitude from the S-matrix

    Homework Statement Consider two real scalar fields \phi,\psi with masses m and \mu respectively interacting via the Hamiltonian \mathcal{H}_{\mathrm{int}}(x)=\dfrac{\lambda}{4}\phi^2(x)\psi^2(x). Using the definition of the S-matrix and Wick's contraction find the O(\lambda) contribution to...
  13. L

    I How to understand the derivation for this process in QFT?

    I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short - two pages - so I find it instructive to post the pages here: The point is that the author is doing this derivation...
  14. 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...