What is Qft: Definition and 978 Discussions

In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1940s and 1950s, and led to the introduction of renormalized quantum electrodynamics (QED). QED was so successful and accurately predictive that efforts were made to apply the same basic concepts for the other forces of nature. By the late 1970s, these efforts successfully utilized gauge theory in the strong nuclear force and weak nuclear force, producing the modern standard model of particle physics.
Efforts to describe gravity using the same techniques have, to date, failed. The study of quantum field theory is still flourishing, as are applications of its methods to many physical problems. It remains one of the most vital areas of theoretical physics today, providing a common language to several different branches of physics.

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  1. S

    B Electron gyromagnetic ratio & lattice qft

    The electron gyromagnetic ratio of 1.0011596522 is computed using perturbation method and Feynman diagrams that is said to produce a value to better than one part in 10^10, or about three parts in 100 billion. Does the nonperturbative lattice QFT also able to compute it? What is the counterpart...
  2. S

    B Exploring the Relationship between QFT, GR, and Backreaction in Curved Spacetime

    I know we do not have a version of QFT (?) in which we can dynamically solve for the QFT and the background spacetime at once. What we can do is where if we come up with a QFT whose expectation value of the stress-energy tensor doesn't match the fixed background spacetime geometry via the...
  3. Megaton

    B Can General Relativity and Quantum Field Theory Be Reconciled?

    Please don't kill me here...I am really just a curious creature...QFT and GR are mutually incapabatable ergo they cannot both be correct...so best is that one is used for low energy large scale predictions (as per theory) and small scale high energies ( as part theory) ...(BTW I know what the...
  4. davidge

    I What order should we take when calculating QFT amplitudes?

    I have been reading about QFT amplitudes. It seems that difficulty increases as we consider more and more terms in the Dyson's expansion for the Scattering operator, and we need to normalize each of them if we want to get a sensible result. My question is, nature usually uses what order? I...
  5. Moayd Shagaf

    Unlocking the Power of Quantum Field Theory: Tips for Studying at 15

    I'm 15 years old boy, and I have pure interest in physics , and I really love to study things like Quantum Field Theory, but my dad won't let me! so how I deal with him?
  6. F

    B Is there a tension between QM and QFT?

    There seems to be some -at least- conceptual difference between particles in QFT which is just a point -eventually- in the field AND the particle in QM which is described by a wavefunction which is extended in space. As if QFT somehow "collapses" the wavefunction.
  7. davidge

    Best book on relativistic QM and QFT

    I loved Modern Quantum Mechanics by Sakurai, where Quantum Mechanics is presented and worked out. Now I would like to proceed further, and learn about Relativistic Quantum Mechanics and Quantum Field Theory. I started by reading Sakurai's Advanced Quantum Mechanics, but later I found that the...
  8. P

    I Does QFT explain macroscopic objects?

    Is it correct to consider a given macroscopic object as a continuum arrangement of harmonic oscillators, each composed of a point mass? Would the error in such a consideration be too large?
  9. T

    I Time in QFT vs. QM: Exploring Differences in Treatment

    I'm starting this thread because @PeterDonis suggested in the other thread that time is treated diferently in quantum field theory and relativistic quantum mechanics/ ordinary quantum mechanics. I'd like to know specifically how is it treated in QFT and in relativistic Quantum Mechanics. Of...
  10. F

    A Can zero dimensional QFT be real?

    I've seen that we can create a toy model of QFT in zero dimensions. Everything occurs at a point. I wonder if this could possibly be real. It seems unlikely that we could ever prove that it is real because it would not propagate in our 3D world, so we could never observe it. Or maybe it can have...
  11. 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}...
  12. Ken Gallock

    I Wick's theorem and Nucleon scattering

    Hi. My question is about nucleon-nucleon scattering. In David Tong's lecture note, he discusses Wick's theorem and nucleon scattering (page 58-60). My problem is that I don't know how to calculate the second line of eq(3.48): \begin{equation} <p'_1, p'_2|:\psi^\dagger (x_1) \psi (x_1)...
  13. B

    B What is the physical interpretation of n-particle correlation function in QFT?

    Hi I would be happy if anyone helped me understand what the physical meaning of n-particle correlation function in QFT is ?
  14. J

    Quantum Resources for studying classical and quantum Yang-Mills(non-abelian QFT)

    Hello! I would like to know what are some good resources for studying classical and quantum Yang-Mills(non-abelian QFT) such as textbooks, lecture notes etc. Thanks in advance!
  15. I

    Quantum QFT: groups, effective action, fiber bundles, anomalies, EFT

    Hi, I am looking for textbooks in QFT. I studied QFT using Peskin And Schroeder + two year master's degree QFT programme. I want to know about the next items: 1) Lorentz group and Lie group (precise adjectives, group representation and connection between fields and spins from the standpoint of...
  16. 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!
  17. 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!
  18. S

    A QCD as a classical field theory?

    Hi everyone, I have a question that, when came to me, sounded a bit silly to me as well, but then I realized, I myself maybe don't understand the logic behind this 100%, so why not discussing with you about it. So my question is the following. Usually we are used to do quantum field theory...
  19. 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...
  20. F

    I Timelike Killing vectors & defining a vacuum state

    I've read that if a given spacetime possesses a timelike Killing vector, then it is possible to define a unique vacuum state by constructing positive and negative frequency modes with respect to this timelike Killing vector. My question is, what does this mean? Explicitly, how does one use a...
  21. alemsalem

    A Calculating Einstein's coefficients in QFT vs equilibrium

    Einstein predicted constraints on the coefficients of stimulated emission and absorption of radiation by atoms. He did that by assuming that the gas of atoms had to reach thermal equilibrium. For the gas to reach thermal equilibrium the coefficients had to be related in a certain way, otherwise...
  22. smodak

    Quantum Interesting new QFT book by Shankar

    https://www.amazon.com/dp/0521592100/?tag=pfamazon01-20 Yes, this is the same Shankar who wrote the QM book. It is not a pure QFT introduction like his QM book but seems more like QFT's application too Condensed matter.
  23. Ken Gallock

    I Lorentz transformation and its Noether current

    Hi. I'd like to ask about the calculation of Noether current. On page16 of David Tong's lecture note(http://www.damtp.cam.ac.uk/user/tong/qft.html), there is a topic about Noether current and Lorentz transformation. I want to derive ##\delta \mathcal{L}##, but during my calculation, I...
  24. binbagsss

    QFT Klein Gordon Theory, momentum commutator computation

    Homework Statement Homework EquationsThe Attempt at a Solution [/B] I think I understand part b) . The idea is to move the operator that annihilates to the RHS via the commutator relation. However I can't seem to get part a. I have: ## [ P^u, P^v]= \int \int \frac{1}{(2\pi)^6} d^3k d^3 k'...
  25. F

    I Does a field operator always commute with itself?

    In quantum field theory (QFT), the requirement that physics is always causal is implemented by the microcausality condition on commutators of observables ##\mathcal{O}(x)## and ##\mathcal{O}'(y)##, $$\left[\mathcal{O}(x),\mathcal{O}'(y)\right]=0$$ for spacelike separations. Intuitively, I've...
  26. Z

    Studying What path should I take to eventually understand QFT?

    I'm now graduated as a secondary school educator, having studied a physics minor at university. During that time, I didn't go any further than second year physics, studying basic quantum mechanics, thermodynamics, and special relativity. Much of it I've forgotten, however I keep the basics...
  27. L

    A How the g factor comes from QFT?

    I'm reading the book Quantum Field Theory and the Standard Model by Matthew Schwartz and currently I'm studying the chapter 17 titled "The anomalous magnetic moment" which is devoted to computing the corrections due to QFT to the g factor. My main issue is in the beginning of the chapter, where...
  28. Buzz Bloom

    I A new approach: retrocausality in QFT

    I looked at the other threads that have discussed retrocausality, but a scan of the article https://phys.org/news/2017-07-physicists-retrocausal-quantum-theory-future.html?google_editors_picks=true seems to take a new approach. The paper also gives two references. Proceedings of The Royal...
  29. S

    I Klein-Gordon in QFT: Wave Functions & Spins

    Hello! So in the Klein-Gordon equation you have a field ##\phi## which becomes an operator in QFT and when you apply it on the vacuum state ##|0>## you get a particle at position x: ##\hat{\phi}(x)|0>=|x>##. So if you look at this particle (in a non interaction theory) the wave function of this...
  30. D

    Quantum Which QFT textbooks complement Schwartz, Zee, Peskin, and Mandl?

    Hi. I'm self-studying QFT. I already have the books by Schwartz , Zee , Peskin and Mandl. I like to have as many books as possible. Would the book by Itzykson & Zuber be useful as a complement to these books or is it a bit out of date ? Also does anybody have any opinions on the book "From...
  31. S

    I QFT: Exploring the Meaning of ##\phi## and ##\psi##

    Hello! So I understand that in QFT and based on the second quantization, one introduce the hermitian operator ##\hat{\phi}(x)##. So, if we have a state with n particles ##|n>## we can get the configuration space representation as: ##\psi(x_1,..,x_n,t)=<0|\hat{\phi}(x_1)...\hat{\phi}(x_n)|n>##...
  32. M

    B What are the practical applications of QM and QFT?

    Please list all the practical applications of QM and QFT the way you know from memory.. so far the following is what I know. Practical applications of QM: 1. Understanding the double slit experiment 2. What else? Please enumerate Practical applications of QFT: 1. Solving for the Magnetic...
  33. 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...
  34. S

    I Interpretation of probability density in QFT

    Hello! I am a bit confused about the interpretation of probability density in QFT. Let's say we have the Klein-Gordon equation. I understand that this is the field equation for a spin-0 charged particle. So if we find a solution ##\phi(x)## of the Klein-Gordon equation, as far as I understand...
  35. S

    I Peskin book on QFT question -- 2 integrals for D(x−y)

    Hello! Those who used Peskin's book on qft, in chapter 2, Causality (2.4) there are 2 integrals for ##D(x-y)##. Can someone explain to me how does he solve them, as I tried for a bit and didn't manage to do them (actually to get the behavior as ##t \to \infty##). Thank you!
  36. U

    I Cosmological constant estimation in QFT

    My question is about the interpretation of the large estimated value. In QM we are supposed to think in terms of measurement results and not of ontological properties. So, if QFT predicts a large vacuum energy what is the correct approach? 1. The predicted value is the result you get if you...
  37. 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?
  38. 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...
  39. F

    I How to compute second-order variation of an action?

    Starting with the action for a free scalar field $$S[\phi]=\frac{1}{2}\int\;d^{4}x\left(\partial_{\mu}\phi(x)\partial^{\mu}\phi(x)-m^{2}\phi^{2}(x)\right)=\int\;d^{4}x\mathcal{L}$$ Naively, if I expand this to second-order, I get $$S[\phi+\delta\phi]=S[\phi]+\int\;d^{4}x\frac{\delta...
  40. F

    I Equivalent Klein-Gordon Lagrangians and equations of motion

    Suppose one starts with the standard Klein-Gordon (KG) Lagrangian for a free scalar field: $$\mathcal{L}=\frac{1}{2}\partial_{\mu}\phi\partial^{\mu}\phi-\frac{1}{2}m^{2}\phi^{2}$$ Integrating by parts one can obtain an equivalent (i.e. gives the same equations of motion) Lagrangian...
  41. F

    I Why are free-field Lagrangians quadratic in fields?

    What is the intuitive reasoning for requiring that a Lagrangian describing a free-field contains terms that are at most quadratic in the field? Is it simply because this ensures that the EOM for the field are linear and hence the solutions satisfy the superposition principle implying (at least...
  42. L

    I How to understand the derivation for this process in QFT?

    I'm reading the book "Quantum Field Theory and the Standard Model" by Matthew Schwartz and I'm finding it quite hard to understand one derivation he does. It is actually short - two pages - so I find it instructive to post the pages here: The point is that the author is doing this derivation...
  43. S

    Particle Transition between Quantum Mechanics and QFT

    Hello! I just started reading a book about QFT by Peskin (it was recommended by one of my physics professor and I saw that MIT course on QFT also uses it). However they start right away with Klein-Gordon equation suggesting that I should be familiar with it. I took 2 classes on quantum mechanics...
  44. F

    I Higher order terms in perturbation theory (QFT)

    I'm fairly new to QFT and I'm currently trying to understand perturbation theory on this context. As I understand it, when one does a perturbative expansion of the S-matrix and subsequently calculates the transition amplitude between two asymptotic states, each order in the perturbative...
  45. F

    A Haag's Theorem & Wightman Axioms: Solving Problems in QFT?

    QFT seems to be a bit sick with cluster decomposition assumption ..etc. So here comes Haag's theorem and Wightman axioms to the rescue, or do they? So what do these cures actually say differently than the generic QFT . Do they solve any practical problems, if not why the fuss, millennium prize...
  46. binbagsss

    Generating Functional in Momentum Space -- QFT

    Homework Statement Hi, Question attached: inserting ##\phi (x)= \int \frac{d^4k}{(2\pi)^2}\phi(x)e^{-i k_u x^u}## and similar for ##J(x) ## / ##J(k)## into the action and then integrating over ##k## gives: Solution attached: I AM STUCK on this part, completing the square ; so I see...
  47. M

    A Can classical EM be derived from QFT?

    In QFT, one can derive the equations for particles interacting electromagnetically by demanding phase invariance for the field when writing down the free field lagrangian for the klein-gordon or dirac equation. Question: Does classical EM follow from this method also? (At least theoretically...
  48. 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...
  49. Nod

    A Quantized Dirac field calculations

    Hi everyone! I'm having a problem with calculating the fermionic propagator for the quantized Dirac field as in the attached pdf. The step that puzzles me is the one performed at 5.27 to get 5.28. Why can I take outside (iγ⋅∂+m) if the second term in 5.27 has (iγ⋅∂-m)? And why there's a...
  50. A

    I Can the energy of a particle ensemble in QFT be bounded over time?

    Hi all, Question for which .I feel silly asking - but since I'm still learning: A particle state in QFT is considered to be an asymptotic state with a well defined energy. Now, if I take an ensemble of particles after a very large number of interactions (say, e.g., a macroscopic object like a...
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