# 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. ### High Energy Possible typo in Peskin & Schroeder's QFT Textbook (p. 666)?

Hi everyone! I'm going through Peskin & Schroeder's Chapter 19 (Perturbation Theory Anomalies) and it seems to be that equation 19.74 in page 666 has a minus sign missing on the RHS. Namely, I think the correct equation should read \begin{align} (i\not\!\! D)^2 = -D^2 -...
2. ### I Feedback on Educational Script: What's a particle in QFT?

I'm trying to create a YouTube educational science video on Quantum Field Theory and the Standard Model. I'm not a physicist (just a hobby), and would love feedback on my explanation below, and help to point out (or rewrite) parts that are scientifically inacurate or misleading. Or just point me...
3. ### I A probability of field amplitude in QFT

Per quantized scalar field (quantized Klein-Gordon equation), suppose we act on a vacuum state |0> with some set of creation operators to have some particles. How then can we calculate a probability density for the field to have a particular value ##\psi_0## (upon measurement) at a specific...

6. ### A Creation and annihilation operator

Hey, I have a short question. The quantized field in Schrödinger picture is given by: \hat{\phi} \left(\textbf{x}\right) =\int \frac{d^{3}p}{\left(2\pi\right)^3} \frac{1}{\sqrt{\omega_{2\textbf{p}}}}\left(\hat{a}_{\textbf{p}}e^{i\textbf{p} \cdot \textbf{x}} +...

8. ### A QFT S-matrix explanations are incomprehensible

The first look at a scattering process is something like this: We define an initial state |\textrm{in}\rangle = \int dp_1dp_2 f_{\textrm{in,1}}(p_1) f_{\textrm{in,2}}(p_2) a_{p_1}^{\dagger} a_{p_2}^{\dagger} |0\rangle Here f_{\textrm{in,1}} and f_{\textrm{in,2}} are wavefunctions that define...
9. ### A QFT for the gifted amateur: translation of prob. density

Dear all, I was reading through the book "QFT for the gifted amateur" because I'm currently working on a popular science book about symmetries. Chapter 9 is about transformations of the wave function. On page 80 the book says It's the second equality that confuses me: doesn't the statement...
10. ### A Anti-symmetric tensor question

The sigma tensor composed of the commutator of gamma matrices is said to be able to represent any anti-symmetric tensor. \sigma_{\mu\nu} = i/2 [\gamma_\mu,\gamma_\nu] However, it is not clear how one can arrive at something like the electromagnetic tensor. F_{\mu\nu} = a \bar{\psi}...

16. ### I Propagator of massless Weyl field

I have this Lagrangian for a free massless left Weyl spinor, so it’s just the kinetic term, that can be written embedding the field into a larger Dirac spinor and then taking the left projector in this way: $$i \bar{\psi} \cancel{\partial} P_L \psi$$ Srednicki says that the momentum space...
17. ### I Why is there an additional prefactor in equation (12.52) of Peskin's QFT book?

Hey all, I am currently having trouble understanding equation (12.52) in Peskin's QFT book. Specifically the term for external leg corrections, in which they tack on an additional prefactor of ##(-ig)##. Normally with external leg prefactors, we don't see the coupling constant multiplied onto...
18. ### I Finding ##\partial^\mu\phi## for a squeezed state in QFT

I'm trying to apply an operator to a massless and minimally coupled squeezed state. I have defined my state as $$\phi=\sum_k\left(a_kf_k+a^\dagger_kf^*_k\right)$$, where the ak operators are ladder operators and fk is the mode function $$f_k=\frac{1}{\sqrt{2L^3\omega}}e^{ik_\mu x^\mu}$$...
19. ### I Exploring the Big Picture of QFT

What is the big picture of QFT? I have studied quantum mechanics from: -Griffiths -the first few chapters of Sakurai -Ballentine I have studied electrodynamics from Griffiths and General Relativity from Carroll I have assigned level I to the question, but any answer is welcome
20. ### I QFT vs GR Cosmological Constant

I am sorry but I can't seem to find the actual estimated value of the cosmological constant that is predicted by quantum field theory. Can anyone help me and tell me the approximation of that value and/or the value of the approximate observed cosmological constant that physicists today think...
21. ### 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...

44. ### A Noether and the derivative of the Action

I know that the Action has units Energy·time or Momentum·position. A second fact is that the derivative of the action with respect to time is Energy and similar with momentum-position, consistent with a units ie. dimensions check.Is it a coincidence that both are Noether conserved quantities...
45. ### A Generalized Forces and QED/QCD

In Lagrangian mechanics we learn about generalized forces. However, I haven't seen these explicitly mentioned in books on QFT. Can the Lagrangians of QED or QCD be expressed in terms of generalized forces or is there some connection there, in particular to the Nielsen form.
46. ### I When to use Feynman or Schwinger Parametrization

I had been doing some calculations involving propagators with both a quadratic and a linear power of loop momentum in the denominator. In the context of HQET and QCD with strategy of regions. The texts which I am following sometimes tend to straightaway use Schwinger and I am just wondering if...
47. ### A QED Formulation with Massive Photon Fields

I was reading Diagrammatica by Veltman and he treats the photon field as a massive vector boson in which gauge invariance is disappeared and the propagator has a different expression than in massless photon. After some googling, I found that this is one way to formulate QED which has the...
48. ### B Unitarity in GR+QFT: Obeying Full QG Model?

Does unitarity have to be obeyed in a full quantum gravity model?
49. ### A In QFT, what is the momentum of a created particle?

This seems important to me, since in some interactions, particles are produced by pairs of opposite momentum in the rest frame of the interaction.
50. ### 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...