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. M

    Feynman Diagrams for Interacting Scalar Fields

    Homework Statement Consider four real massive scalar fields, \phi_1,\phi_2,\phi_3, and \phi_4, with masses M_1,M_2,M_3,M_4. Let these fields be coupled by the interaction lagrangian \mathcal{L}_{int}=\frac{-M_3}{2}\phi_1\phi_{3}^{2}-\frac{M_4}{2}\phi_2\phi_{4}^{2}. Find the scattering amplitude...
  2. rocdoc

    I Path Integrals in Quantum Theory

    I have found a general result for certain exponential integrals that may be of interest to those involved with using path integrals. I am not certain that I am applying it correctly but it appears to work, and I can reproduce results quoted in various textbooks , using it. This may however be...
  3. rocdoc

    I Quantum Field Configurations and Wavefunctions

    Could anyone explain what a quantum field configuration is, and any relation this concept may have to the idea of a wavefunction? Perhaps for a scalar, quantum field?
  4. S

    A Information encoding in the Holographic principle

    Can whatever type of information be encoded in a boundary in holographic principle? in a question some years ago regarding holography (https://physics.stackexchange.com/questions/75436/are-stokes-theorem-and-gausss-theorem-examples-of-the-holographic-principle) It is said that AdS/CFT is the...
  5. Demystifier

    A Quantum field theory, spacetime, and coordinates

    [Moderator's note: This thread is spun off from another thread since it was dealing with a more technical point that is out of scope for the previous thread. The quote that starts this post is from the previous thread.] I feel the same about transformations of Dirac matrices and Dirac field...
  6. C

    Field transformation under Conformal transformation

    I am confused about the field transformation under conformal transformation. Consider the scale transformation of field ##\phi## (not necessarily scalar) In CFT of Francesco et al, formula (2.121), the transformation is $$ \vec{x}\rightarrow \vec{x}'=\lambda x,\,\,\,\phi(\vec{x}) \rightarrow...
  7. S

    A Transformation of a scalar field

    I read somewhere that, suppose a scalar field Σ transforms as doublet under both SU(2)L and SU(2)R, its general rotation is δΣ = iεaRTaΣ - iεaLΣTa. where εaR and εaL are infinitesimal parameters, and Ta are SU(2) generators. I don't quite understand this. First, why does the first term have...
  8. L

    A Can disjoint states be relevant for the same quantum system?

    In the algebraic approach, a quantum system has associated to it one ##\ast##-algebra ##\mathscr{A}## generated by its observables and a state is a positive and normalized linear functional ##\omega : \mathscr{A}\to \mathbb{C}##. Given the state ##\omega## we can consider the GNS construction...
  9. F

    I Two questions about "The Physics of Virtual Particles"

    Arnold Neumaier, I have 2 elementary questions about your article “The Physics of Virtual Particles”. 1. In the paragraph headed “States.” on p. 4, of 13, you talk about states of a physical system, with a mixed state specified by a Hermitian operator ρ of trace 1 acting on the Hilbert...
  10. L

    A States in usual QM/QFT and in the algebraic approach

    Studying QFT on curved spacetimes I've found the algebraic approach, based on ##\ast##-algebras. In that setting, a quantum system has one associated ##\ast##-algebra ##\mathscr{A}## generated by its observables. Here we have the algebraic states. These are defined as linear functionals...
  11. VIctor Medvil

    A SR/GRs Views on QM/QFT | Physics Forums

    This ties into this thread https://www.physicsforums.com/threads/i-want-to-know-the-exact-problems-of-merging-gr-and-qm.939509/ , I would like to know SR/GR's opinion of QM/QFT. I need both sides of the story.
  12. VIctor Medvil

    A I want to know the exact problems of Merging GR and QM

    This thread is I want a set of experts in the subject to show me the exact math of why Einstein's field Equations along with Special Relativity and Schrodinger's Equation along with deeper QM like QFT cannot be fused with GR. I want to see the exact anomalies in the equations myself from the...
  13. Quantum Fields: The Real Building Blocks of the Universe - with David Tong

    Quantum Fields: The Real Building Blocks of the Universe - with David Tong

    According to our best theories of physics, the fundamental building blocks of matter are not particles, but continuous fluid-like substances known as 'quantum fields'. David Tong explains what we know about these fields, and how they fit into our understanding of the Universe.
    • Wrichik Basu
    • Media item
    • quantum quantum field theory
    • Comments: 0
    • Category: Quantum
  14. Quantum Fields with David Tong - Questions and Answers

    Quantum Fields with David Tong - Questions and Answers

    According to our best theories of physics, the fundamental building blocks of matter are not particles, but continuous fluid-like substances known as 'quantum fields'. David Tong explains what we know about these fields, and how they fit into our understanding of the Universe.
    • Wrichik Basu
    • Media item
    • quantum quantum field theory
    • Comments: 0
    • Category: Quantum
  15. Urs Schreiber

    Mathematical Quantum Field Theory - Renormalization - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Renormalization Continue reading the Original PF Insights Post.
  16. A

    Quantum Field Theory, Momentum Space Commutation Relations

    Homework Statement Derive, using the canonical commutation relation of the position space representation of the fields φ(x) and π(y), the corresponding commutation relation in momentum space.Homework Equations [φ(x), π(y)] = iδ3(x-y) My Fourier transforms are defined by: $$ φ^*(\vec p)=\int...
  17. F

    I Exploring Oscillations & Interference in Particle Physics

    I will soon start with the course introduction to QFT and are hence an amateur on the subject. However I could not help but wonder, If particles are describes by oschlliations in a field, how can a "bigger body" be made up of several such oscillation? (A bigger particle is made out of several...
  18. Urs Schreiber

    Mathematical Quantum Field Theory - Interacting Quantum Fields - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Interacting Quantum Fields Continue reading the Original PF Insights Post.
  19. J

    I Should the energy density of the vacuum be zero?

    According to [Dark Energy and the Accelerating Universe](https://ned.ipac.caltech.edu/level5/March08/Frieman/Frieman5.html) quantum field theory says that the energy density of the vacuum, ##\rho_{vac}##, should be given by $$\rho_{vac}=\frac{1}{2}\sum_{\rm...
  20. F

    Which courses before GR and QFT?

    Hi! I will soon begin my third year at the theoretical physics program. I have done a bunch of classical & Lagrangian mechanics, SP, atomic physics, electromagnetism, and basic particle physics. Is it a good idea to study general relativity and quantum field theory with this knowledge, what...
  21. Urs Schreiber

    Mathematical Quantum Field Theory - Free Quantum Fields - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Free Quantum Fields Continue reading the Original PF Insights Post.
  22. C

    A Proving Gamma 5 Anticommutes with Gamma Matrices

    "It is easily shown" that the gamma 5 matrix anticommutes with the four gamma matrices. Can someone tell me how or provide a link to such proof?
  23. Urs Schreiber

    Mathematical Quantum Field Theory - Quantization - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Quantization Continue reading the Original PF Insights Post.
  24. DeathbyGreen

    I Loop Integral Form: Finding a Workable Solution without Regularization

    Hi, I'm trying to calculate an integral which looks unfortunately divergent. The structure is similar to a loop integral but the appendix in the Peskin textbook didn't have a useable form. The integral form is (I did a u substitution to make it easier to look at) \int_x^{\infty}du...
  25. John1945

    Mathematical Quantum Field Theory -- Equations? So what?

    << Mentor note -- posts broken off from an Insights comment thread >> Ok, this is where I show my ignorance, but all this is theoretical and why I get lost with these academia discussions. Time is just a mathmatical construct to measure the motion of two or more objects relative to each other...
  26. Urs Schreiber

    Mathematical Quantum Field Theory - Gauge Fixing - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Gauge Fixing Continue reading the Original PF Insights Post.
  27. J

    Quantum What is the level of Klauber's Student Friendly QFT?

    Hi! I have studied about 70% of the textbook QFT for the Gifted Amateur by Lancaster and Blundell and I think that I am now ready to go to more advanced treatments. My thoughts were to go to Klauber's Student Friendly Quantum Field Theory as I have read that it is very pedagogical. Problem is...
  28. Urs Schreiber

    Mathematical Quantum Field Theory - Reduced Phase Space - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Reduced Phase Space Continue reading the Original PF Insights Post.
  29. arupel

    I Quantum field theory and the hydrogen atom

    Quantum mechanics does a good job in describing the hydrogen atom. Are there any views either mathematically or conceptually in describing the hydrogen atom?
  30. A

    I IR divergences and total energies....

    I've done some recent reading on IR divergences (propagators becoming singular, etc.). I believe I understand collinear divergences (to some extent)... but I'm not sure about total energies for (primarily) soft photons. In all scattering experiments, total energy should be conserved - but if...
  31. A. Neumaier

    Insights Interview with Mathematician and Physicist Arnold Neumaier - Comments

    Greg Bernhardt submitted a new PF Insights post Interview with Mathematician and Physicist Arnold Neumaier Continue reading the Original PF Insights Post. Arnold will welcome science questions and comments only.
  32. F

    I A question about Zee's book QFT in a nutshell

    I have read( even Peter Donis mentioned it) that the derivation of the potential between two particles is not a true QFT, why is that? if not, then what is it? Thanks in advance.
  33. I

    Operation with tensor quantities in quantum field theory

    I would like to know where one may operate with tensor quantities in quantum field theory: Minkowski tensors, spinors, effective lagrangians (for example sigma models or models with four quark interaction), gamma matrices, Grassmann algebra, Lie algebra, fermion determinants and et cetera. I...
  34. C

    I In the Casimir effect, can you slide plates unopposed by force?

    How would sliding the plates parallel to each other in order to separate them (they are prevented from contacting to avoid friction) require the same amount of energy as pulling them apart? You're not pushing against the force (the net force at the edges pulling it back is balanced by opposite...
  35. Urs Schreiber

    Mathematical Quantum Field Theory - Gauge symmetries - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Gauge symmetries Continue reading the Original PF Insights Post.
  36. DeathbyGreen

    Trouble with Peskin QFT textbook

    I'm trying to work through a scattering calculation in the Peskin QFT textbook in chapter 5, specifically getting equation 5.10. They take two bracketed terms 4[p'^{\mu}p^{\nu}+p'^{\nu}p^{\mu}-g^{\mu\nu}(p \cdot p'+m_e^2)] and 4[k_{\mu}k'_{\nu}+k_{\nu}k'_{\mu}-g_{\mu\nu}(k \cdot...
  37. V

    I Hidden dimensions and quadratic term of a free field

    Consider a free real scalar field. The quadratic term in field of spacetime implies that a universe of these free particles is created, annihilated, recreated, and so on moment by moment. In this video Susskind explains the quadratic term in the Lagrangian youtu.be/D7yXoNAg3J8 (At minute...
  38. L

    Studying How to learn QFT on curved spacetimes by myself?

    I have a major in mathematical physics and mathematics and currently I'm on a graduate course in Physics working on a master's thesis. When I started the graduate course I was going to work on General Relativity and Quantum Field Theory on Curved Spacetimes (QFTCS). It turns out that by several...
  39. J

    I Schwinger effect verified by Unruh temperature?

    According to https://arxiv.org/abs/1407.4569, equation (2.15), the Schwinger electron-positron pair production rate in Minkowski space, ##N_S##, is given in natural units by $$N_S=\exp(-\frac{m}{2T_U})$$ where the `Unruh temperature for the accelerating charge', ##T_U##, is given by...
  40. A

    A String Vacua and Particle Interactions

    I've been doing a little bit of reading on string theory, and the very large number of string vacua that are possible (i.e., perhaps 10^500 or more). One thing that is not clear to me is exactly what constitutes a 'vacuum' in string theory. In QFT theory, the vacuum is defined as the state with...
  41. Urs Schreiber

    Mathematical Quantum Field Theory - Propagators - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Propagators Continue reading the Original PF Insights Post.
  42. Urs Schreiber

    Mathematical Quantum Field Theory - Phase Space - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Phase Space Continue reading the Original PF Insights Post.
  43. A

    High Energy Recommended books in HEP, QFT, QM, GR

    Hi everyone! I'm trying to make a list of recommended books (introductory and advanced). So far, what I was able to search are the following: Particle Physics: - Griffiths: Introduction to Elementary Particles - Thomson: Modern Particle Physics - Nachtmann: Elementary Particle Physics -...
  44. Urs Schreiber

    Mathematical Quantum Field Theory - Observables - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Observables Continue reading the Original PF Insights Post.
  45. Urs Schreiber

    Mathematical Quantum Field Theory - Symmetries - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Symmetries Continue reading the Original PF Insights Post.
  46. Urs Schreiber

    Mathematical Quantum Field Theory - Lagrangians - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Lagrangians Continue reading the Original PF Insights Post.
  47. Urs Schreiber

    Mathematical Quantum Field Theory - Field Variations - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Field Variations Continue reading the Original PF Insights Post.
  48. Urs Schreiber

    Mathematical Quantum Field Theory - Fields - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Fields Continue reading the Original PF Insights Post.
  49. Urs Schreiber

    Mathematical Quantum Field Theory - Spacetime - Comments

    Greg Bernhardt submitted a new PF Insights post Mathematical Quantum Field Theory - Spacetime Continue reading the Original PF Insights Post.
  50. N

    A Topological Quantum Field Theory: Help reading a paper

    https://www.ma.utexas.edu/users/dafr/OldTQFTLectures.pdf I'm reading the paper linked above (page 10) and have a simple question about notation and another that's more of a sanity check. Given a space ##Y## and a spacetime ##X## the author talks about the associated Quantum Hilbert Spaces...
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