# What is Quantum field theory: Definition + 580 Threads

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. ### I The claymath 4-d QFT problem and virtual particles (as an example)

I am trying to understand how would one opt to solve this open problem?, if there are some objects in the non-constructive-axiomatic QFT which mathematically are ill-defined. One such ill defined notion is of virtual particles. I tried to understand what constitutes a virtual particle. For...
2. ### I Will every object in the universe evaporate?

According to a recent paper (https://arxiv.org/abs/2305.18521) (explained here: https://www.ru.nl/en/research/research-news/eventually-everything-will-evaporate-not-only-black-holes) every massive object in the universe will evaporate in a similar way into Black Holes through Hawking radiation...
3. ### I Can there be quantum fluctuations without spacetime?

There is a paper called "On nothing" (https://arxiv.org/abs/1111.0301) which goes on to argue that the universe could not have arisen from a state without spacetime (as some proposals do using quantum fluctuations to explain how the universe was born without spacetime) However, there is a...

20. ### I Are All Photons Truly Virtual?

My understanding is (was) that "virtual particles" is a computational concept used in perturbation calculations in QFT e.g. in Feynman diagrams. This understanding is in conflict with the following note in Quantum Field Theory for the Gifted Amateur by Tom Lancaster and Stephen J. Blundell: and...
21. ### I Exploring Measurements in Quantum Field Theory: From Light Cones to Bell Tests

Hello, I'm interested in how measurement, entanglement, bell test etc are handled in QFT. It seems most QFT texts are being quite light on details on the subject. There would be is a preparation step as the start followed by some interaction and a measurement at the end. Interaction is usually...
22. ### Studying Should I study relativistic QFT to get non-relativistic QFT?

First time in PF, I am sorry if I did not choose the right category. I have been doing theory in condensed matter (mostly numerics) as a PhD but I never got to learn proper quantum field theory (QFT). Aside from a few introductory courses at university, I never learned what is a many-body...
23. ### A Dimensional Regularization

Hi guys! I was wondering if there is any difference choosing between d = 4 -e or d = 4 - 2e. If so, what are the impacts ?
24. ### Is the Lorentz Boost Generator Commutator Zero?

Using above formula, I could calculate the given commutator. $$[\epsilon^{\mu\nu\rho\sigma} M_{\mu \nu}M_{\rho\sigma},M_{\alpha\beta}]=i\epsilon^{\mu\nu\rho\sigma}(M_{\mu \nu}[M_{\rho\sigma},M_{\alpha\beta}]+[M_{\rho\sigma},M_{\alpha\beta}]M_{\mu \nu})$$ (because...
25. ### A Uncovering the Combinatorial Origins of Yang-Mills Theory?

For many years now, the theorist Nima Arkani-Hamed has lent his prestige and energy to a research program that aims to transform our understanding of quantum field theory, by using symmetries in the sums of Feynman diagrams to uncover perspectives on the theory not based in ordinary space-time...
26. ### A The Quantum State as a Function of The Quantum Field

In answering another question, I came across a nice paper by Weinberg: https://www.arxiv-vanity.com/papers/hep-th/9702027/ One thing that struck me was the following comment: 'In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the...
27. ### A The relation between ferromagnets, Phi4 and non-linear sigma model

I'm struggling to understand the relation between phi4 theory,non-linear sigma model and ferromagnets. I've read this in a paper(Phys.Rev.B14(1976)3110):'It is possible to describe the long-distance behavior of the Heisenberg ferromagnets in two different ways:the phi4 theory which corresponds...
28. ### A Understanding Ghost Fields in QED: Eliminating Unphysical Degrees of Freedom"

I have a question about following statement about ghost fields in found here : It states that introducing some ghost field provides one way to remove the two unphysical degrees of freedom of four component vector potential ##A_{\mu}## usually used to describe the photon field, since physically...
29. ### Other What are areas of research that pertain to Grand Unified Theory?

I am planning on pursing a Phd in Theoretical physics or Mathematical Physics in the next several years. My main motivation is doing research when it comes to grand unified theory. What areas of research (within that umbrella, in a theoretical sense) should I start looking into that are at the...
30. ### Noether current in quantum field theory

Hi Have been trying to solve the below question for a while, wondered if anyone could help. Considering the action $$S=\int -\frac{1}{2}\sum^2_{n,m=1} (\partial^{\mu}\phi_{nm}\partial_{\mu}\phi_{mn}+m^2 \phi_{nm} \phi_{mn})dx$$ under the transformation $$\phi'=e^{\alpha}\phi e^{-\alpha}$$...

33. ### 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...

36. ### 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...
37. ### 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...
38. ### 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...
39. ### 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 [1] and later it was generalised to the associahedron [2],the EFT-hedron [3]... I was...
40. ### 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...
41. ### 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)...
42. ### 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...
43. ### 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...
44. ### 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...
45. ### 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?
46. ### 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...
47. ### 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...
48. ### 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 $$f_k=\frac{1}{\sqrt{2L^3\omega}}e^{ik_\mu x^\mu}$$...
49. ### 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
50. ### 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...