# What is Quantum field theory: Definition and 546 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 Solving renormalization group equation in QFT

I'm learning about the RG equation and Callan-Symanzik equation. In ref.1 they claim to solve the RG equation via the method of characteristics for PDE. Here's a picture of the relevant part: First, the part I don't understand - the one underlined in red. What does "compatible" mean here...

4. ### A Quantization of real Klein-Gordon field (sign issues)

I have a pretty naive question about quantization of real Klein-Gordon (so scalar) field ##\hat{\phi}(x,t)##. The most conventional form (see eg in this one ; but there are myriad scripts) is given by ##\hat{\phi}(x,t)= \int d^3p \dfrac{1}{(2\pi)^3} N_p (a_p \cdot e^{i(\omega_pt - p \cdot...
5. ### A Lagrangian in the Path Integral

Using free scalar field for simplicity. Hi all, I have a question which is pretty simple, we have the path integral in QFT in the presence of a source term: $$Z[J] = \int \mathcal{D}\phi \, e^{i \int d^4x \left( \frac{1}{2} \phi(x) A \phi(x) + J(x) \phi(x) \right)}$$ So far so good. Now...
6. ### This integration appeared in the reconstruction of cross section

I am reading the Horatiu Nastase's Introduction to quantum field theory (https://professores.ift.unesp.br/ricardo.matheus/files/courses/2014tqc1/QFT1notes.pdf ) ( Attached file ) or Peskin, Schroeder's quantum field theory book, p.105, (4.77). Through p.176 ~ p. 177 in the Nastase's Note, he...
7. ### I All possible QFTs from geometry?

Physicist Nima Arkani-Hamed has taken an approach to understand fundamental physics based on geometry (specifically, positive geometry). This started with his work with Jaroslav Trnka in the amplituhedron  and later it was generalised to the associahedron ,the EFT-hedron ... I was...
8. ### Deriving Maxwell's equations from the Lagrangian

This isn't a homework problem (it's an example from David Tong's QFT notes where I didn't understand the steps he took), but I am confused as to how exactly to take the partial derivative of the Lagrangian with respect to ##\partial(\partial_\mu \mathcal{A}_\nu)##. (Note the answer is...
9. ### A What exactly does 'Locality' in Gauge Theory mean?

What means exactly the principle of 'locality' in context of gauge theory? Motivation: David Tong wrote in his notes on Gauge Theory (p 115): "their paper (the 'original' paper by Yang & Mills introducing their theory) suggests that global symmetries of quantum f ield theory– specifically SU(2)...
10. ### A Asymptotic states in the Heisenberg and Schrödinger pictures

In scattering theory, the quantity of interest is the amplitude for the system—initially prepared as a collection of (approximate) momentum eigenstates—to evolve into some other collection of momentum eigenstates. For example, for ##m\to n## scattering, the amplitude we're interested in is...
11. ### I Spontaneous Symmetry Breaking and quantum mechanics

Confronted with my inability to grasp Witten's Susy QM examples of supersymmetry breaking, I concluded that the problem was that I was not understanding spontaneous symmetry breaking in simpler contexts. It seems that SSB is not possible in QM because of tunneling between the different states...
12. ### I Confusion about Scattering in Quantum Electrodynamics

When it comes to scattering in QED it seems only scattering cross sections and decay rates are calculated. Why is that does anyone calculate the actual evolution of the field states or operators themselves like how the particles and fields evolve throughout a scattering process not just...
13. ### Question related to completeness relation for photons

Hi Would you explain to me what is the q^ and how they are related to completeness.How can i solve this exercise?It is from "Quarks and leptons An Introductory course in Modern Particle Physics" of Halzen and Alan D.Martin.Also, can you point me to a useful bibliography?
14. ### Deriving the commutation relations of the Lie algebra of Lorentz group

This is the defining generator of the Lorentz group which is then divided into subgroups for rotations and boosts And I then want to find the commutation relation [J_m, J_n] (and [J_m, K_n] ). I'm following this derivation, but am having a hard time to understand all the steps: especially...
15. ### Expressing Feynman Green's function as a 4-momentum integral

I am a bit confused on how we can just say that (z',p) form a 4-vector. In my head, four vectors are sacred objects that are Lorentz covariant, but now we introduced some new variable and say it forms a 4-vector with momentum. I understand that these are just integration variables but I still do...
16. ### 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 $$f_k=\frac{1}{\sqrt{2L^3\omega}}e^{ik_\mu x^\mu}$$...
17. ### A Schrodinger equation in quantum field theory

What is the Schrodinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more? I have read that the Schrodinger equation describes a QFT in 0 dimensions. I accept every answer
18. ### A Multiparticle Relativistic Quantum Mechanics in an external potential

It is often argued that Dirac Equation is not valid as relativistic quantum mechanics requires the creation of antiparticles. But, there are also some arguments that suggest otherwise. For example, I saw Arnold Neumaier's website on this that there are multiparticle relativistic quantum...
19. ### 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...
20. ### I Uncertainty Principle in QFT & Early Universe Conditions

I have a question related to the uncertainty principle in QFT and if it is related to the early universe conditions. Do we still have four-vector momentum and position uncertainty relation in relativistic quantum theory? I have been following the argument related to the early universe and the...
21. ### I Equation which is related with the Lorentz invariant quantities

Hi every one.How can i prove the below equation? And then that it's Lorentz invariant quantitude ? Thanks for your help
22. ### B Quantum field theory and wave particle duality

I recently watched this lecture "Quantum Fields: The Real Building Blocks of the Universe" by David Tong where the professor provides a succinct explanation of QFT in about 6 minutes around the midway mark. The main point being that there are fields for particles and fields for forces and the...
23. ### A Ensembles in quantum field theory

Then please explain how the transition in conceptual language from a single quantum field (extending all over spacetime, or at least over the lab during a day) to an ensemble of particles can be justified from the QFT formalism.
24. ### 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...
25. ### I Unruh, Haag et al.: No Room for Particles in Quantum Field Theory?

In a paper by Bain (2011), particles are left with little ontological value because of the Reeh-Schlieder theorem, the Unruh effect and Haag's theorem. The author claims (and here I am copying his conclusion): First, the existence of local number operators requires the absolute temporal metric...
26. ### I Has the Unruh Effect ever been observed?

A recent paper (June 2021) claims to have observed the Unruh effect: https://arxiv.org/abs/1903.00043 A more recent article (with links to the papers inside it) talks about a possible way to detect it (Barbara Soda et al., April 2022), while there are still skeptics (Anatoly Svidzinsky). Here is...
27. ### I Haag's Theorem: Explain Free Field Nature

What is the main reason for a free field staying free according to Haag's theorem?
28. ### I Interpreting ##A^{\mu}(x)|0\rangle## and ##\psi (x) |0\rangle##

I can understand how ##\phi (x)|0\rangle## represents the wavefunction of a single boson localised near ##x##.I don't understand how the same logic appies to ##A^{\mu}(x)|0\rangle## and ##\psi |0\rangle##. Both of these operators return a four component wavefunction when operated on the vaccuum...