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.

View More On Wikipedia.org
Recent contents Top users
  1. L

    How Should Spinors Be Applied in Physics Homework Involving Fermions?

    Homework Statement Homework EquationsThe Attempt at a Solution I've started from writing out the amplitude. Here I know that fermion has definite helicity so I can't sum over spins but I should input explicit forms of spinors. Am I correct? How to do this? I would be grateful for helping me...
  2. H

    Feynman rules for nonlinear sigma models

    Nonlinear sigma models are particular field theories in which the fields take values in some nontrivial manifold. In the simplest cases this is equivalent to saying that the fields appearing in the lagrangian are subject to a number of constraints. Since the lagrangian fields are not independent...
  3. L

    Interpretation of a before $\gamma^{5}$ in J$_{\alpha}$

    Could you explain what's the interpretation of a before \gamma^{5} in this current: J_{\alpha}=\bar{\psi_{e}}\gamma^{\alpha}\left(1-a\gamma^{5}\right)\psi_{\nu_{e}} +\bar{\psi_{\mu}}\gamma^{\alpha}\left(1-a\gamma^{5}\right)\psi_{\nu_{\mu}}? And will this factor complicate calculations of decay...
  4. L

    Feynman rules for Yukawa theory

    Hi. Do you know any book/paper/lecture notes where I can find complete derivation of Feynman rules for both scalar and pseudo-scalar Yukawa theory, and maybe an example of application to decay of fermion?
  5. E

    How Does the Higgs Field Influence the Standard Model and Particle Masses?

    Problem I have a project for my university class on the Higgs fields and how it impacts the standard model, and how the Higgs particle is formed and decays into particles with the probability of decay based on the mass of the particles it will decay into. I need resources that I can cite like...
  6. B

    What is the concept of scale invariance in quantum field theory?

    Hey guys! I was reading the following paper http://arxiv.org/abs/hep-ph/0703260 for Georgi and I have a conceptual question about it. Howard Georgi was talking about this Unparticle Physics theory and at the base of his analysis is the principle of scale invariance. So Georgi is saying what if...
  7. I

    Expectation value of a real scalar field in p state

    Hello, I've been trying to find <p'|φ(x)|p> for a free scalar field. and integral of <p'|φ(x)φ(x)|p> over 3d in doing the space In writing φ(x) as In doing the first, I get the creation and annihilation operators acting on |p> giving |p+1> and |p-1> which are different from the bra state |p>...
  8. craigi

    David Tong: Lectures on Quantum Field Theory

    I created this thread to notify people about to the online resources for Tong's QFT course. Lecture videos: Blackboard screens and Videos: http://pirsa.org/C09033 Lecture notes: http://www.damtp.cam.ac.uk/user/tong/qft.html Course text: Peskin and Schroeder (search for it)
  9. X

    Studying Quantum Field Theory without taking graduate QM?

    Hello over the summer I would like to study quantum field theory. I took two semesters of undergraduate quantum mechanics using Griffith's textbook. We covered the entire book in those two semesters. I also know my special relativity pretty well. Is that enough to self study quantum field theory...
  10. bhobba

    Many Worlds and Quantum Field Theory

    I have been meaning to ask this one for a while - but never seem to get around to it. In MW its sometimes said it's simply the working out of the universal wave-function via Schroedinger's Equation. Of course Schroedinger's Equation is only valid non-relativistically. Wallace doesn't really...
  11. S

    Prerequisites for Quantum Field Theory (QFT)

    Hi! I'm desperately trying to develop a list of prerequisites that will enable me to work on topics like quantum gravity, advanced QFT (on curved spacetime etc.) etc. I am currently in the second year of an undergrad theoretical physics degree in the UK, and am heavily unsatisfied with the way...
  12. S

    Properties of fields in quantum field theory

    I have been studying quantum field theory and I am currently in the Lagrangian field theory chapter in my book. Now it says that the energy momentum tensor is as follows: Tμν= [∂L/∂(∂μφ) * ∂νφ] - δμνL Note: I am using L to symbolize Lagrangian density and not just Lagrangian since the latex...
  13. N

    Evaluating Time-Ordered Product with Wick's Theorem

    Homework Statement [/B] Consider a real free scalar field Φ with mass m. Evaluate the following time-ordered product of field operators using Wick's theorem: ∫d^4x <0| T(Φ(x1)Φ(x2)Φ(x3)Φ(x4)(Φ(x))^4) |0> (T denotes time ordering) Homework Equations Wick's theorem: T((Φ(x1)...Φ(xn)) = ...
  14. T

    Order in Renormalization Theory

    I am currently studying QFT with 'An Introduction to Quantum Field Theory' by peskin. In part 2 (renormalization) of the book, he introduces counterterms and shows how to compute scattering amplitude with them. Below are counterterms of \phi^4 theory: Then he calculates a 2-2 scattering process...
  15. BiGyElLoWhAt

    Calculating Functional Derivatives: Understanding Notation and Examples

    If I understand what's going on (quite possibly I don't), I think my book is using bad (confusing) notation. Homework Statement As written: "Calculate ##\frac{\delta H[f]}{\delta f(z)} \ \text{where} \ H=\int G(x,y)f(y)dy##" and ##\frac{\delta H[f]}{\delta f(z)}## is the functional derivative...
  16. N

    Quantum field theory questions?

    In QFM, what does it mean to say that an electron is just an excitation of the electron field? Does this apply to all particles? Does it mean to say that an electron is the quanta of the electron field?
  17. J

    Compton scattering differential cross section

    1. The problem statement, all variables and given/known I have to prove an equation for the differential cross section of compton scattering of an electron and a photon (electron (P) + photon(K) ⇒ electron(P') + photon (K') ) where P and so on are the inital and final four momenta. Given is...
  18. A

    Which Beginner Book is Best for Learning Quantum Field Theory?

    Hello, I'm looking for a good beginner book about QFT. Thanks!
  19. arupel

    Does quantum field theory supersede quantum mechanics?

    In discussing the wave/particle duality, a friend stated basically that the discussion in quantum mechanics is not relevant because quantum mechanics is superseded by quantum field theory. 1. I do not know if this statement is relevant with respect to the wave/particle duality. 2. I am not...
  20. Breo

    An Introduction to Quantum Field Theory (Peskin and Schröder) - Page 22

    Hello, Can someone tell me how to derive: $$ grad\hat{\phi} $$ from: $$ \hat{P}= -:\int \mathrm{d³}x [\pi (x) grad\hat{\phi}(x)]: = \int \mathrm{d³}p [p a⁺(p)a(p)] $$ Are all vectors. Note normal ordering ":" is used. I want to understand well QFT and want to learn to do this calcs...
  21. Richa Sharma

    Studying Reading Quantum field theory by Weinberg books?

    Is it a good choice to read these books first or there's a better way. My professor recommended me these books but as I started them they had bulk of maths and really matter was not that understandable on my first try. I am an engineer. I read physics in free time I can get , so shall I go ahead...
  22. M

    Lorentz transformation, quantum field theory

    Hello, I was reading and trying to follow up with Pierre Ramond's "Field theory: A modern primer" and got stuck in his step to step jumping. Kindly, see attachment and note that Eq (1.2.6) = g_{ρσ}=g_{μ\upsilon}\Lambda^{μ}_{ρ}\Lambda^{\upsilon}_{σ}. My question is what do I need from tensor...
  23. C

    Group and Quantum Field Theory

    Good afternoon : I now what I've written here : https://www.physicsforums.com/showthread.php?t=763322 in the first message. I've made the Clebsh Cordon theorem with the components. Which can be represented by the Young tableau. There also the SU(3) and the su(3) representation of dimension...
  24. F

    Basic question about equations of Quantum field theory (QFT)

    Hello Forum, The electromagnetic field EM must be treated relativistically because it travels at the speed of light in a vacuum. However, the idea of quantization forces us to treat the field as a quantum mechanical field. QFT is the answer to that. QFT is quantum mechanics with...
  25. M

    Understanding Entropy and Gravity in Quantum Field Theory: A Beginner's Guide

    I read a sentence that says if a spherical volume in placed in a quantized space then the maximum entropy of the system can be calculated and it after simple steps found to be: S~V where V is the volume of the spherical volume. "Then the author said: Each local quantum field theory(with UV...
  26. S

    Is Quantum Field Theory Still Relevant in Modern Physics?

    What ever happened with QFT? Heard so much about it years ago now only once in a while will a past Nobel laureate state it is real. I know string is the thing now. Any thoughts? Sussan
  27. C

    Troubles learning Quantum field theory.

    Hi everyone, I'm having a lot of troubles learning QFT, personally I find it very challenging, besides that my professor has a very difficult accent and given that I'm not an English native speaker it is really hard for me to follow him. I would like to hear your experience learning QFT, Was it...
  28. shounakbhatta

    Lagrangian and quantum field theory

    Hello, I understand the classical Lagrangian which follows the Principle of Least Action(A) A=∫L dt But what is Lagrangian density? Is it a new concept? A=∫Lagrangian density dx^4 Here 4 is the four vector? One time-like and 3 space-like co-ordinates? QFT uses Lagrangian to...
  29. TrickyDicky

    Quantum field theory basic concepts

    Would it be right to say that QFT tries to bring together the many-particles(many-body) discrete systems of quantum mechanics and the relativistic fields that are basically continuous systems? Of course the discrete particle of classical mechanics that when found in big numbers must be dealt...
  30. S

    Do we have a quantum field theory of monopoles?

    Recently, I read a review on magnetic monopole published in late 1970s, wherein some conjectures of properties possibly possessed by a longingly desired quantum field theory of monopoles are stated. My question is what our contemporary understanding of the quantum field theory of monopoles...
  31. P

    Proving Det(A) From Quantum Field Theory Problem

    Homework Statement I was following this book "problem book in quantum field theory by voja radovanovic" and I got stuck in the following problem Prove...
  32. Radarithm

    What is quantum field theory trying to explain?

    The title says it all. I'm sorry if you get annoyed because of my "noobishness", but I'm still a physicist in training (taking undergrad Classical Mechs). I'm really interested in Quantum Theory and I keep hearing about Quantum Field Theory, but not a single website accurately explains what it...
  33. sas3

    New geometric version of quantum field theory

    The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe https://www.simonsfoundation.org/quanta/20130917-a-jewel-at-the-heart-of-quantum-physics/ I...
  34. D

    Many-Body Quantum Field Theory

    What kind of background do I need to study many-body quantum field theory?
  35. S

    Unitary in quantum field theory

    In QFT, which have infinite degree of freedom, there exlst infinite unitary nonequvilent representation. Expecially after phase transition, the two representation are unitary nonequvilent. So can we say that unitary are broken in QFT? Or a pure state can evolved to a mixed state which is a...
  36. C

    Why Is a Given State an Eigenstate of Field Operators in Quantum Field Theory?

    Hi, I am studying Peskin's An Introduction To Quantum Field Theory. On the beginning of page 284, the authors say We can turn the field \phi_S(x_1)|\phi_1\rangle=\phi_1(x_1)|\phi_1\rangle. I tried hard to prove this relation but still can't get it right. Could anyone give me some hints? Thanks.
  37. S

    Is Quantum Field Theory currently used in engineering?

    Hey all, I'm not sure if this belonged in the physics or engineering forum, but here's the question: has quantum field theory been applied to any engineering disciplines yet? I know quantum mechanics has been used extensively in electrical engineering and materials science/engineering. I also...
  38. jtbell

    Quantum Student Friendly Quantum Field Theory by Klauber

    Author: Robert D. Klauber Title: Student Friendly Quantum Field Theory Amazon Link: https://www.amazon.com/dp/0984513922/?tag=pfamazon01-20 (submitted by elfmotat)
  39. Demystifier

    Other Modern Quantum Field Theory: A Concise Introduction

    We usually talk about good books, but we rarely talk about bad books. And that is good. But sometimes, we find that some book is so bad, so really bad, that we strongly want to tell this to the others. So I open this thread to inform others about science books which you find so bad that it...
  40. C

    Physical mass in a quantum field theory

    In special relativity we have the relation that for a free particle E^2 = \vec p^2 + m_0^2 and that also hold in relativistic free field theories (free Klein-Gordon etc) where one can show that we have a completeness relation 1 = \int \frac{d^3 \vec p}{(2\pi)^3} \frac{1}{2E_{\vec...
  41. T

    Quantum Field Theory - Places to study

    Hi! I'm in a master course in theoretical physics and enjoying a lot to learn about Quantum Field Theory (QFT)! So I was thinking doing a PhD related do QFT. What are the best places to work on QFT? Thanks a lot!
  42. Spinnor

    Quantum field theory, photons, and polarization.

    A circularly polarized electromagnetic wave can be thought of proper combinations of orthogonal linear polarized waves, and a linear polarized wave can be thought of proper combinations of left and right circularly polarized waves. It seems one type of wave is no more fundamental then the other...
  43. E

    Quantum mechanics and quantum field theory application ideas?

    First of all sorry for my off-topic question here. I'm a computer science student, who has a high interest in mathematics (especially algebraic geometry), and physics (especially quantum mechanics, quantum field theory). For this semester I'm supposed to create to applications, from which one of...
  44. micromass

    Quantum A Modern Introduction to Quantum Field Theory by Maggiore

    Author: Michele Maggiore Title: A Modern Introduction to Quantum Field Theory Amazon Link: https://www.amazon.com/dp/0198520743/?tag=pfamazon01-20
  45. micromass

    Quantum Quantum Field Theory in a Nutshell by Zee

    Author: A. Zee Title: Quantum Field Theory in a Nutshell Amazon Link: https://www.amazon.com/dp/0691140340/?tag=pfamazon01-20
  46. Greg Bernhardt

    Quantum An Introduction to Quantum Field Theory by Michael E. Peskin

    Author: Michael E. Peskin (Author), Dan V. Schroeder (Author) Title: An Introduction to Quantum Field Theory Amazon Link: https://www.amazon.com/dp/0201503972/?tag=pfamazon01-20 Prerequisities: Contents:
  47. R

    A (apparently?) non-local quantum field theory

    I need to derive the euler-lagrange equations for the following non-local lagrangian density for a complex scalar field ψ \mathcal{L} = \partial_{\mu}\psi^* \partial_{\mu}\psi - \lambda \int dy\, f(x,y) \psi^*(y) \psi(y) where λ is the coupling constant, f is a certain real-positive valued...
  48. H

    Defeated by quantum field theory yet again

    I haven't taken a course in qft yet, just looking ahead to see what's to come, and so far things are not looking good, I read the firet few chapters of qft in a nutshell, and jesus christ what is this stuff, where are the postulates? The equations of motion? How do I even do these crazy path...
  49. A

    Suggestions for sources with detailed calculations in quantum field theory.

    Can you suggest any source available on internet which may be particularly helpful for those studying/brushing up knowledge of classical or quantum field theory without help of any teacher or friend? Some calculations are at first not so straightforward and there are many types of calculations...
  50. C

    Origin of Spin 1/2: Exploring Quantum Field Theory

    Dear Forum, I would like to understand what the origin of spin 1/2 is. I read in Feynman's lectures that the origin is related to quantum field theory. I know nothing about quantum field theory. Is there an easy explanation? Thanks Cabrera
Back
Top