What is Quantum field theory: Definition and 567 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. Urs Schreiber

    Mathematical Quantum Field Theory - Geometry - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Geometry Continue reading the Original PF Insights Post.
  2. R

    Quantum Good book for quantum field theory?

    Looking for a good quantum field theory book. Any suggestions?
  3. Urs Schreiber

    Insights A First Idea of Quantum Field Theory - 20 Part Series - Comments

    Greg Bernhardt submitted a new PF Insights post A First Idea of Quantum Field Theory - 20 Part Series Continue reading the Original PF Insights Post.
  4. Turbotanten

    A What does it mean for the Hamiltonian to not be bounded?

    If we were to quantize the Dirac field using commutation relations instead of anticommutation relations we would end up with the Hamiltonian, see Peskin and Schroeder $$ H = \int\frac{d^3p}{(2\pi)^3}E_p \sum_{s=1}^2 \Big( a^{s\dagger}_\textbf{p}a^s_\textbf{p}...
  5. TAKEDA Hiroki

    I Double sided arrow notation in Dirac Field Lagrangian

    In a thesis, I found double sided arrow notation in the lagrangian of a Dirac field (lepton, quark etc) as follows. \begin{equation} L=\frac{1}{2}i\overline{\psi}\gamma^{\mu}\overset{\leftrightarrow}{D_{\mu}}\psi \end{equation} In the thesis, Double sided arrow is defined as follows...
  6. J

    A Is it possible that a particle is much heavier through a loop correction

    Let's assume, we have standard model singlet particle s that mixes after electroweak symmetry breaking with an exotic, vectorlike neutral lepton N The relevant part of the Lagrangian reads $$ L \supset h^c s N + h s N^c + M N N^c, $$ where h is the standard model higgs and M is a superheavy...
  7. T

    I Does Feynman's Work on Gravitons Clarify Quantum Gravity?

    Back in the 1960s, Richard Feynman worked on quantum gravity for a few years, and most of his notes are collected in the 'Feynman Lectures on Gravitation'. His approach was that of a particle physicist applying the principles of QED to GR, notably the concept of gravitons mediating the force of...
  8. J

    A Breaking of a local symmetry is impossible, so what about global symmetry....

    Breaking of a local symmetry is impossible. It is often said that therefore the role of the Higgs mechanism in the standard model is a different one. Namely, Once a gauge is fixed, however, to remove the redundant degrees of freedom, the remaining (discrete!) global symmetry may undergo...
  9. J

    A Do the equations of motion simply tell us which degrees of freedom apply?

    A massless spin 1 particle has 2 degrees of freedom. However, we usually describe it using four-vectors, which have four components. Hence, somehow we must get rid of the superfluous degrees of freedom. This job is done by the Maxwell equations. To quote from Gilmore's "Lie Groups, Physics, and...
  10. bleist88

    A The Lagrangian Density and Equations of Motion

    Can Lagrangian densities be constructed from the physics and then derive equations of motion from them? As it seems now, from my reading and a course I took, that the equations of motion are known (i.e. the Klein-Gordon and Dirac Equation) and then from them the Lagrangian density can be...
  11. A

    A Bound states and the energy-momentum relation....

    Hi all - forgive me, I'd asked a series of questions in a previous post that was deemed to be circular, but I still didn't obtain a satisfactory answer to the question I was asking. In this post, I'm going to try to be very careful to use terms that are at least less 'misplaced', per se...
  12. A

    A Observable particles as asymptotic states....

    I've read Arnold Neumaier's excellent Insight article on virtual particles, but I'm very confused about one thing: Observable particles are considered to be on-shell, and as 'asymptotic states' at time +- infinity. Now, in a scattering experiment, I may produce a new particle, which will travel...
  13. R

    A Wick contraction for same indices (Zee, "QFT in a Nutshell")

    Hey, I thought I understood Wick contractions but a formula in Zee's "Quantum Field Theory in a Nutshell" disproved me: In the section on Feynman Diagrams it is tried to evaluate the "four-point Green's function" in (I.7.10) by the integral $$ \int_{-\infty}^\infty \left ( \prod_m \mathrm{d}...
  14. Urs Schreiber

    Insights Introduction to Perturbative Quantum Field Theory - Comments

    Urs Schreiber submitted a new PF Insights post Introduction to Perturbative Quantum Field Theory Continue reading the Original PF Insights Post.
  15. A

    Learn What You Need to Know for Cosmology Research

    Hello, I don't know if this is the right place to post this topic, I could not figure out the right one. I have recently finished my Masters in Condensed Matter. Now I want to follow a PhD where I can work/research on the dynamics of the Universe especially on dark energy, modified gravity...
  16. Urs Schreiber

    A Highest loop order of experimental relevance?

    What is the highest loop order in standard model scattering computations that still contributes a measurable effect seen in past and present particle collider experiments? In other words, to which order are loop corrections necessary for accounting for observed high energy physics? I expect it...
  17. T

    I Relativistic Quantum Mechanics vs Quantum Field Theory

    What's the difference between relativistic quantum mechanics and quantum field theory? In principle, my guess is that to do the former, one needs to express the Hamiltonian in a relativistic, Lorentz invariant, form, because it seems to be the only frame-related term in the wave equation. (Is...
  18. U

    Functional Derivative with respect to Dirac Spinors

    Homework Statement I am currently working on an exercise list where I need to calculate the second functional derivative with respect to Grassmann valued fields. $$ \dfrac{\overrightarrow{\delta}}{\delta \psi_{\alpha} (-p)} \left( \int_{x} \widetilde{\bar{\psi}}_{\mu} (x) i \partial_{s}^{\mu...
  19. J

    Quantum QFT book recommendations except Peskin/Schroeder

    Hello! Due to the textbook by Peskin and Schroeder being rather old, I was wondering what are other, more pedagogical textbooks on Quantum Field Theory that you would recommend! Any suggestion is appreciated!
  20. J

    Quantum What are your thoughts on Manoukian's QFT textbooks?

    Hello! Manoukian's two books on Quantum Field Theory seem pretty good to me, but before buying them I would like to know your thoughts about them! Bear in mind that I need a pedagogical textbook(with good exercises if possible). Thanks!
  21. tomdodd4598

    I 'Normalisation' of Fourier Transforms in QFT

    Hi there - just a quick question about Fourier transforms: When learning about quantum mechanics, I found that the Fourier transform and inverse Fourier transform were both defined with constants of ##{ \left( 2\pi \right) }^{ -d/2 }## in front of the integral. This is useful, as...
  22. noir1993

    A Dyson's Formula from Tong's lecture notes

    I am studying quantum field theory from [David Tong's lecture notes][1] and I am stuck at a particular place. In Page 52., under the heading *3.1.1 Dyson's Formula*, Tong introduces an unitary operator U(t, t_0) = T \exp(-i\int_{t_0}^{t}H_I(t') dt') He then introduces the usual definition of...
  23. P

    Dirac Lagrangian invariance under chiral transformation

    Consider the Dirac Lagrangian, L =\overline{\psi}\left(i\gamma^{\mu}\partial_{\mu}-m\right)\psi, where \overline{\psi}=\psi^{\dagger}\gamma^{0} , and show that, for \alpha\in\mathbb{R} and in the limit m\rightarrow0 , it is invariant under the chiral transformation...
  24. ShayanJ

    Insights Entanglement Entropy – Part 2: Quantum Field Theory - Comments

    ShayanJ submitted a new PF Insights post Entanglement Entropy – Part 2: Quantum Field Theory Continue reading the Original PF Insights Post.
  25. J

    A How are renormalizability and locality connected?

    In his paper Quantum Field Theory: renormalization and the renormalization group Zinn-Justin states: Low energy physics does not depend on all the details of the microscopic model because some RG has an IR fixed point or at least a low dimension fixed surface. Of course at this stage the next...
  26. J

    A Why do we need to renormalize in QFT, really?

    There are several reasons given in the literature, why UV infinities arise in QFT in the first place. My problem is putting them together, i.e. understand how they are related to each other. So... UV divergences arise and thus we need to renormalize, because: We have infinite number of...
  27. G

    A What does a CPT transformation do to particle properties?

    If I have a particle with: Momentum: p Spin: s Energy: E Position: x Time coordinate: t Charge: q And I preform a CPT transformation on said particle, what will these variables become? Can you show me mathematically? Also, could you show me how this effects the wavefunction/quantum state of...
  28. L

    Other Quantum Information and General Relativity

    Last year I've finished the undergraduate course in Mathematical-Physics and Mathematics and this year I've started on graduate school on Physics in order to obtain a master's degree. What I'm really interested are two main topics: general relativity and quantum field theory. I also like...
  29. M

    B How does string theory fit with QFT?

    In string theory, particles is vibrating strings. However, QFT treats particles as excitations in a quantum field. Can both of these theories be correct? If so, how does them fit together?
  30. A

    I Quantum "tunneling" of sorts and QFT....

    Hi all, Another naive question related a previous post (where the topic diverged somewhat). I'm wondering about the following thought experiment: Consider the field associated with a single electron. Now, confine the field to a region (volume) of radius R - that is, field values outside of R...
  31. binbagsss

    Strings, Virasoro Operators&constraints, commutator algrebra

    Homework Statement [/B] Question: (With the following definitions here: ) - Consider ##L_0|x>=0## to show that ##m^2=\frac{1}{\alpha'}## - Consider ##L_1|x>=0 ## to conclude that ## 1+A-2B=0## - where ##d## is the dimension of the space ##d=\eta^{uv}\eta_{uv}## For the L1 operator I am...
  32. A

    I Change in electron energy level and photon emission....

    Hi all, This is likely a naive question, following up on something @vanhees71 posted some time ago in another thread: My question is the following - if we take an electron that has, for example, absorbed a photon, is the portion of the wavefunction representing the electron in a lower energy...
  33. L

    Decay rate of a particle into three particles

    Homework Statement Consider the process of decay of a muon into one electron, one electron antineutrino and one muon neutrino using the Fermi theory. Assume the matrix element is, ignoring the electron's and the two neturino's masses, |\mathcal{M}|^2 = 32G_F^2(m^2-2mE)mE being E the electron...
  34. I

    B What exists between Strings in String Theory?

    Hello, I am new to this. As I understand it, the difference between the quantum field theory and string theory is that in the former, physical field is considered as the fundamental reality, while in the latter it is believed that everything comes out of strings. My question is, by everything do...
  35. binbagsss

    Complex scalar field -- Quantum Field Theory -- Ladder operators

    Homework Statement STATEMENT ##\hat{H}=\int \frac{d^3k}{(2\pi)^2}w_k(\hat{a^+(k)}\hat{a(k)} + \hat{b^{+}(k)}\hat{b(k)})## where ##w_k=\sqrt{{k}.{k}+m^2}## The only non vanishing commutation relations of the creation and annihilation operators are: ## [\alpha(k),\alpha^{+}(p)] =(2\pi)^3...
  36. A

    I Momentum and energy in QM and QFT

    Hi all - apologies, I'm starting a new thread here for something buried at the end of another thread - but I think the topic of that thread had changed sufficiently to warrant a more succinct top-level post. Thanks very much to PeterDonis for his very useful answers in the previous thread...
  37. N

    I Common interaction vacuum for QED + QCD?

    Hello, I know QED and QCD as isolated theories but now I thought about particle interactions with QED and QCD processes (like fpr proton-antiproton scattering). But I'm not sure how to interpret this mathematically. As I understood my Feynman diagrams are nothing more like pictures for the...
  38. L

    Hamiltonian in terms of creation/annihilation operators

    Homework Statement Consider the free real scalar field \phi(x) satisfying the Klein-Gordon equation, write the Hamiltonian in terms of the creation/annihilation operators. Homework Equations Possibly the definition of the free real scalar field in terms of creation/annihilation operators...
  39. S

    Quantum Building a Solid knowledge of Quantum Field Theory

    Hello! I read several books and took courses on quantum mechanics and particle physics and I understood the topics. However I feel that I have only pieces of informations without a global image of what is going on. For example in the particle physics classes we were given Feynman rules without...
  40. L

    I Understanding the scalar field quantization

    I am getting started with QFT and I'm having a hard time to understand the quantization procedure for the simples field: the scalar, massless and real Klein-Gordon field. The approach I'm currently studying is that by Matthew Schwartz. In his QFT book he first solves the classical KG equation...
  41. L

    I Wave equation solution using Fourier Transform

    I'm studying Quantum Field Theory and the first example being given in the textbook is the massless Klein Gordon field whose equation is just the wave equation \Box \ \phi = 0. The only problem is that I'm not being able to get the same solution as the book. In the book the author states that...
  42. nomadreid

    I Cgs or SI in quantum field theory?

    I have an acquaintance who maintains that in quantum field theory, primarily the cgs system is used. OK, I know it's not really important, but I was under the impression that everyone had switched to SI. (My book on quantum field theory has very few actual quantities with units outside of GeV...
  43. redtree

    A Deriving the Lagrangian from the Hamiltonian operator

    In classical mechanics, the Hamiltonian and the Lagrangian are Legendre transforms of each other. By analogy, in quantum mechanics and quantum field theory, the relationship between the Hamiltonian and the Lagrangian seems to be preserved. Where can I find a derivation of the Lagrangian...
  44. S

    Quantum Student Friendly Quantum Field Theory

    The thread https://www.physicsforums.com/threads/qft-operators-time-space-asymmetry.906369/ contains the first recommendation I have seen in these forums for Klauber's book, and instead of hijacking that thread I thought I might ask a question here. I find the book more readable than many for...
  45. K

    A Primaries, descendents and transformation properties in CFT

    I want to clarify the relations between a few different sets of operators in a conformal field theory, namely primaries, descendants and operators that transform with an overall Jacobian factor under a conformal transformation. So let us consider the the following four sets of...
  46. T

    B Why is the Existence of a Quantum Field Questioned?

    Are there thoughts as to why there is a quantum field. Does it arise from something more fundamental? Thanks for considering.
  47. S

    A Bar on a fermion field, arrows on fermion lines and particle-antiparticle nature of a fermion

    This question is about the use of bar on a fermionic field in a Lagrangian, the use of arrows on external fermion lines and the particle-antiparticle nature of a fermion. For illustration of my question, I will use the following the charged-current interaction of the Standard model...
  48. S

    A Deducing decay processes and Feynman diagrams using Lagrangian and conservation laws

    The decay processes of the ##W## bosons are completely governed by the charged current interaction terms of the Standard model: $$\mathcal{L}_{cc} = ie_{W}\big[W_{\mu}^{+}(\bar{\nu}_{m}\gamma^{\mu}(1-\gamma_{5})e_{m} + V_{mn}\bar{u}_{m}\gamma^{\mu}(1-\gamma_{5})d_{n})\\...
  49. F

    A Are there different "types" of renormalization

    I see re normalization being discussed in many situations and it is not very clear what unites them. For example it is talked about during self energy, then when integrals are blown by high energy(in scattering problems I presume), or some problem with IR(the opposite). Then there are these...
  50. F

    A On the equivalence of operator vs path integral in QFT

    I have read many textbooks and googled google times for a clear explanation, but I could not find one. How does raising and lowering -annihilation/ creation-(is that energy or particle number?) translate to transition probabilities of path integral.
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