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. I

    Essential Math for Understanding QFT: A Beginner's Guide

    i know these threads are common in this subforum so i apologize but what math should i know before picking up a qft book?
  2. P

    Interactive fields in QFT - the φ^3 example

    Does anybody knows a textbook, a paper or any lecture notes that discusses the \phi^3 interactive field? I use as main reference Ryder's QFT, which discusses only the \phi^4 interaction. And most similar textbooks (like Peskin's, Brown's etc.) do so. I have derived the point functions and...
  3. P

    Interactive fields in QFT - the φ^3 example

    Does anybody knows a textbook, a paper or any lecture notes that discusses the \phi^3 interactive field? I use as main reference Ryder's QFT, which discusses only the \phi^4 interaction. And most similar textbooks (like Peskin's, Brown's etc.) do so. I have derived the point functions and...
  4. J

    Appropriate maths for QFT, LQG, strings etc.

    Hi all, I asked about this on the academic and career guidance forum but didn't get any useful replies. Which of these maths subjects (all at fourth year level) would you recommend for someone interested in the subjects listed in the title? What would you say is missing from this list...
  5. S

    Euler-Lagrange equations in QFT?

    Euler-Lagrange equations in QFT?? Hi, I have a problem with a Wikipedia entry::bugeye: http://en.wikipedia.org/wiki/Euler-Lagrange_equation The equations of motion in your quantized theory (2nd quantization) are d/dtF^=[F^,H^] i.e the quantized version of d/dtF={F,H}. My notation: F^ is the...
  6. S

    A few questions about QM and QFT.

    I'm only going to be a junior next year in high school so bear with me but I've been "studying" quantum mechanics and quantum field theory for a while now. I understand most of what I've read very well but there are a few things that have been bothering me. *How does QFT explain how two...
  7. A

    How is the conjugate momentum defined in the Schrödinger picture of QFT?

    Hi, I have been wondering why we can consider d(phi)/dt when we are in Schrödinger picture (phi is just the usual scalar field here). Isn't this 0 as operators do not depend on time in this picture? However then how does it make sense to talk about the conjugate momentum in this picture which...
  8. B

    Understanding the Trace Theorem in Calculating S-Matrix | QFT Explained

    Hi guys, Everyone knows that one can calculate the S-Matrix with various tricks. One of them is to use traces to simplify the matrices. Can someone tell me or point me to a place where I can find an explanation why I can do this? I think I vaguely remember that I have seen once an...
  9. N

    How can the Cauchy integral and Fourier integral produce the same result?

    I have some extremely basic questions in QFT. First, P&S discuss causality in QFT in the first chapter of the book and, after showing that <0| \phi(x)\phi(y)|0> does not vanish for spacelike intervals, they say "to really discuss causality, however, we should ask not whether particles can...
  10. L

    Handling Static Fields in QFT: Exploring Limitations and Solutions

    Hello, I just realized that I could not figure out how static fields can be handled in QFT. Although I realize that really static fields don't really need QFT, I nevertheless would like to see how QFT covers this extreme case. Maybe a limit for low frequencies would be useful. Have you...
  11. N

    How Can I Access ASTI Video Lectures During Server Issues?

    Here's a blog entry from "An American Physics Student in England" http://fliptomato.wordpress.com/2006/12/30/from-griffiths-to-peskin-a-lit-review-for-beginners/
  12. R

    The Best QFT Books for Learning Quantum Field Theory

    hi everyone, There are so many books about QFT, but what is in your oppinion the best book to learn quantum field theory?
  13. Q

    Relation between condensed matter physics and QFT

    I am confused about the relation between condensed matter physics and Quantum field theory (QFT). Here are my "naive" questions. 1. The condensed matter physics deals with the macroscopic physical properties of matter. The number of atoms of the system is as large as Avogadro's number. But in...
  14. W

    Local QM? MWI, RQM, QFT, LQM, + ?

    I'm interested in studying LOCAL theories within QM. I have the impression that the following theories claim to be such: MWI (Everett) RQM (Rovelli's Relational QM?) QFT (Originated by ?) LQM (There's a book titled ''Local QM'' as I recall.) + Questions: 1. Are there any other LOCAL...
  15. A

    Understanding QFT Notation: Delta Function and Statistical View

    \delta^{\left(d\right)}\left(\b{q}-\b{q}\prime \right) from Quantum Field theory and Critical Phenomena by Justin.. (the text covers QFT from a statistical view) Question: what does the d in brackets mean/do ? Thanks =)
  16. B

    What's the Best Introductory Book on Quantum Field Theory?

    hi, actually i am searching a good introduction into quantum field theory. the book should be like the lectures of feynman (The Feynman Lectures on Physics), i mean, not so mathematically as usually. thx for answering
  17. J

    Homotopy classes appendix in Weinberg's QFT book, Part I

    Hi, I'm trying to teach myself QFT, and I'm stuck with one formula in Part I of Weinberg's trilogy. I think I managed to understand how one gets Formula 2.B.7 in the appendix of Chapter 2, thanks to the information provided by Weinberg, but don't get 2.B.10, page 97. Could anyone one give me a...
  18. W

    What is the physical meaning of the position operator in QFT?

    I'm reading some QFT and have been puzzled by the following question: What's the physical meaning of the position OPERATOR X_\mu in QFT? whose position does it measure?:confused: Thanks for any help.
  19. S

    Algebraic QFT and Quantum Gravity

    Kea posted this on another thread: The Tomita-Takesaki results are and exciting breakthrough in AQFT, by now getting to be pretty well understood. The beginnings of it are in Haag's book Local Quantum Physics. Another line of work in AQFT that approaches the idea of matter in QG is...
  20. S

    Where can I find a good account of functional methods in QFT?

    I'd like to be as familiar with functional methods as with calculus. Otherwise I always fell not to grasp QFT comprehensively. Any help is much appreciated!
  21. S

    Learning QFT from Peskin and Schroeder

    I'm still pretty new to QFT, so forgive me if I have made a ridiculous mistake. I've been learning QFT from Peskin and Schroeder mostly but decided to read Ryder recently and I have just come across an amazing result (in my opinion) in Chapter 3. Ryder basically shows that the electromagnetic...
  22. CarlB

    Poincare Invariance from General QFT

    Derivation of Poincare Invariance from general quantum field theory C.D. Froggatt, H.B. Nielsen Annalen der Physik, Volume 14, Issue 1-3 , Pages 115 - 147 (2005) Special Issue commemorating Albert Einstein Starting from a very general quantum field theory we seek to derive Poincare...
  23. A

    Taking up QFT for the first time

    I'm taking up QFT for the first time. Basic question really. Given the free complex Klein-Gordon field \phi under the global gauge transformation exp(\imath\alpha) where \alpha is some real parameter, the Noether current is given by j^{\mu}=\imath \left( \phi \partial^{\mu} \phi\dagger -...
  24. CarlB

    The vacuum in QFT. What is it. Why have it. Does everyone believe in it?

    Any good references on the meaning of the vacuum in QM? What were you taught in school? What made sense? What did not? What did you discuss with the other graduate students? Any paradoxes regarding the vacuum? Any thoughts on why string theory is inundated with them? Bring em on. I...
  25. W

    Density matrix for QFT from the path integral?

    (1) How does one obtain the density matrix formalism for quantum fields from the path integral? (2) Suppose I have a box containing interacting particles of different kinds. Is it possible to incorporate into the density matrix formalism both a non-zero temperature T as well as a time t...
  26. M

    Higgs field, QFT in curved spacetime, and spinfoams

    How related are the concepts of the Higgs field and QFT in curved spacetime? As I understand it, The Higgs mechanism is derived from a false vacuum where no particles exist yet, but the Higgs field contains potential energy at an unstable equilibrium. This unstable potential is what drives...
  27. S

    QFT Peskin Errata: Pauli Vilars Regularization & Ward Takahashi Identity

    Hi, This is regarding showing, in ch.7, around p.220, that the Pauli Vilars regularization technique is consistent with the ward takahashi identity. I cannot get the following to work: I add eq. 7.31 to eq. 7.32 and do not get zero. I get alpha over 4 pi. (I am left with integral ( 1...
  28. B

    Explanation for term in formula, QFT

    Hi I've got a question about a term in a formula I've found in Mandl&Shaw's QFT book It's about equation 2.18 on page 31 L(t) = {\sum_i \delta \bf{x}_i {\cal L}_i \ ... Why is there a delta x_i when summing over all lagrangians for getting the lagrange-function for the whole...
  29. S

    QFT and unitary Lorent representation

    Hey guys! A question: My QFT Lagrangian, fournishes through Noether's thm plus relativistic invariance a supposedly unitary and a supposed representation of the Lorentz group. These are the operators meant to act on my Hilbert space of possible states. What guarantees that this actually...
  30. J

    How Can I Understand QFT in My Own Way?

    Hello, I am new in this forum. I studied physics up to the equivalent of a MSc. This included mainly QFT and GR. Then, instead of following a PhD, I went to finance. Now, after a few years, I have decided I want to go back and study QFT. Not full time, but part time (in my free time). I already...
  31. H

    Exploring String Theory on Curved Spacetime: How Does it Explain QFT?

    I was reading some of the first chapters of Zwiebach's book. It is explained how quantized relativistic strings turn out to describe an infinite set of possible particles and, therefore, that it is possible to consistently describe the results obtained in the Fock representation in QFT on a flat...
  32. arivero

    Non-Relativistic QFT: Readings & Vacuum Polarization

    Any hints for readings on non relativistic quantum field theory? I guess every NRQFT should be renormalisable, because vacuum polarisation is a relativistic effect. But I would like to read about.
  33. T

    What is the normalization of photon states in QFT?

    If you inspect the QED lagrangian, you'll find that the electromagnetic vector potential must have the units of [1] energy. According to Peskin and Schroder's QFT text, the expansion of the electromagnetic field operator is...
  34. N

    What is the meaning of the quantity c in scalar quantum field theory?

    I know that I have been asking that question before and that people are probably tired of it :redface:. I have done multiloop QFT calculations but when I get back to the fundamentals, something is really bugging me. There are several issues but let m start with a question that would...
  35. R

    Why is Symmetry Postulated in Quantum Field Theory and Particle Physics?

    In Quantum Field Theory and in particles physics, there's a postulate that is SIMMETRY. Why exists this postulate? Best reggards.
  36. J

    QFT: A Modern Intro, by Michio Kaku

    I have obtained a copy of this book and I am having a very difficult time understanding it. My problems start at the bottom of page 38 and continue through the middle of page 41. For instance: The last thing on page 38 is a definition of a scalar field in terms of an equation. The first thing...
  37. S

    Experimental Evidence and QFT.

    After reading one of ZapperZ's posts in the Relativity subforum, I just thought I'd ask the following: What predictions of QED, QCD, Electroweak and the Standard Model still aren't confirmed? I'd be particularly interested in hearing unconfirmed predictions from QED.
  38. S

    Exploring the Development of QFT: Recommended Reads

    I was wondering if anybody could recommend some books which deal with the development of QFT. I'm almost finished Schweber's "QED and the men who made it", which I found excellent, however it only deals with QED. So are there any other good histories of QFT? And is there a "History of QCD"...
  39. B

    Explanation of Eq of Peskin's Intro to QFT Book

    Hi Can someone please explain to me Eq 2.30 in Schroeder's and Peskin's book? (page 21) how does he simplify the long equation of the commutator to this delta distribution? \imath\delta^(^3^)\ (x - x') Thanks
  40. B

    Choosing the Right Quantum Field Theory Book: Peskin or Mandl?

    Hi I'm planning on studying quantum field theory, but I can't choose which book I should buy. I've heard great opinions of both, that's making my decision so hard Peskin's Introduction to Quantum Field Theory https://www.amazon.com/gp/product/0201503972/?tag=pfamazon01-20 or Mandl...
  41. B

    A question from Weinberg's qft book

    can anybody tell me how to induce the quantum field theory as long as you admit the quantum mechanics and the reletivity? it seems that in Weinberg's book ,he shows that,but i can not quite understand:confused: thank you :biggrin:
  42. W

    Question on observables of QFT

    Hi, In Weinberg's QFT book(section 2.2), he said after proved the generator of the symmetry group is Hermitian and can be a candidate for an observable: My questions: 1. Does the observable here mean at least in principle, we can measure it in experment? 2. Does generator of any symmetry...
  43. R

    QFT & Bound States: Is Calculation Possible?

    I read somewhere that quantum field theory does not allow calculations and predictions of bound states in a satisfactory way. Is that true and how much is that a problem given that qft claims to be so fundamental?
  44. marcus

    Can Spinfoam Quantum Gravity Naturally Incorporate Feynman Diagrams?

    This seems to be the goal expressed most clearly at Loops '05. it is a slight redirection or change in emphasis in the common program. Matter should naturally occur in quantum gravity. It's explicit. two leading talks in this regard were by Rovelli and Freidel In the latter's talk, Feynman...
  45. S

    What is the relationship between quantum mechanics and quantum field theory?

    I've read on a few websites, as well as having heard from my professors that the relation between QM and QFT is that QM is the (0+1) approximation of QFT. Does mean that QM ignores the spatial degrees of freedom of field, or is there something else to it, or have I got it all completely...
  46. G

    How do I find the hermitian conjugate of this expression?

    Hi, I'm trying to do problem 3.5 of Peskin & Schroeder and I don't know where to start. First of all, I need to get the hermitian conjugate of the following expression \delta \chi = \epsilon F + \sigma^\mu \partial_\mu \phi \sigma^2 \epsilon^\ast where \epsilon is a 2...
  47. S

    What is the propagation amplitude of a particle in QFT?

    Hola everybody, this is my first visit to PF. Can anyone help me please...my question is from QFT textbook phi(x)|0> is creation of particle at position x, being in superposition of momenum states - - - - correct? <0|phi(y) is birth of particle at position y. So if I consider both expressions...
  48. E

    QFT Lorentz transformation question

    Hi, Today in QFT class, we examined an infinitesimal Lorentz transformation. From this we showed that a LT is represented by an anti-symmetric matrix. But this means that the diagonal elements should all be zeros. My question is how this reduces to the standard LT with gamma, gamma...
  49. R

    QFT Normal Ordering: Exploring Its Benefits & Limitations

    Hi, I have a question regarding normal ordering in QFT. I know that it moves dagger operators to the right and that it gets rid of infinite constants turning up and that 'with observables defined in normal products their vacuum expectations vanish.' (Mandl and Shaw) I have a couple...
  50. S

    Extended Bodies in QFT: String Theory & Phenomenology

    Is string theory the (more-or-less) only way of dealing with 'extended bodies' in a theory like QFT? Or does it only deal with very specific actions, or ones representing 'particles' with special dimensionalities (e.g 1+1 only)? If it is general, is all the commonly-stated phenomenology (11...
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