Qft Definition and 980 Threads

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. G

    QFT: Does Dirac Equation Reduce to Pauli's?

    Hello: In quantum field theory, there is the Klein-Gordon Equation that describes particles with Spin 0, this equation reduces to the SchÖdinger equation when the non relativistic limit is taken, Does the Dirac equation that describes particles with spin ½, reduce to Pauli's...
  2. R

    Quantum Chromodynamics for QFT Students

    What is a good introductory book on Quantum Chromodynamics that assumes QFT as a prerequisite?
  3. H

    Should QFT Be Taught from First Principles Like Weinberg?

    Looking at most textbooks, I found Weinberg's Quantum Theory of Fields to be by far the most superior and I think that's how QFT should be taught as well. I also think the way Weinberg presenting the subject from first principle is the way to make progress in research in fields such as...
  4. MTd2

    Can Quantum Field Theory Be Applied in Loll's Fractal Universe?

    Let me be more rephrase what I wrote, to not sound rediculous as usualy I am. Loll's universe seems to mimick some futures of our universe, but I just can't see anywhere how a QFT can be defined over that space. To begin with, the space we observe in this universe is not a single one, but an...
  5. D

    Is there a description of collapse in QFT ?

    In QM we have the postulate of measure giving rise to the notion of wave function collapse throught measurement. Is there an analog description of collapse in QFT (even an effective one) ? And what is then collapsing ? The field ? What would that mean ? I'm interested for references on the...
  6. P

    What is the Correct Form of the Free Propagator in QFT?

    Homework Statement from Zee QFT in a nutshell the free propagator between two "sources" on the field is given by D(x_\mu) = -i \int \frac{d^3k}{(2\pi)^3 2 \omega_k}[e^{-i(\omega_kt-k\bullet x)} \Theta(x_0) + e^{i(\omega_k t-k\bullet x)} \Theta(-x_0) for a space like separation ( x_0 = 0 )...
  7. L

    QFT and local gauge invariance

    Why is local gauge invariance needed in qft? I read that is allows interactions whereas global gauge invariance does not but was given no reason.
  8. P

    How Is the Equation of Motion Derived from the Classical String Model?

    Homework Statement I'm starting QFT and many books I've started to read start with the introduction of a field in a classical string model with a Lagrange equation L(q,\dot{q}) = \sum[\frac{m}{2}\dot{q}_{j}^{2}-\frac{k}{2}(q_{j}-q_{j+1})^{2}] the equation of motion becomes m...
  9. U

    QFT: Find Poincare Group Generators in QFT

    Hi I need to find the generators of the Poincare group in the representation of a clasical scalar field. Every textbook I found let them as P and M. But any buk does not what are they. I'm wondering if anybody help me to find this Uda
  10. I

    What are some common questions about Peskin's QFT book?

    Dear all, While I was reading chap2 of Peskin, I got some questions. (1) The vanishment of the commutator of fields [\phi(x),\phi(y)]=0 means that the measurements at x and y do not interfere at all. Is this a postulate? Is this the so-called micro-causality? (2) How Peskin deform the...
  11. L

    Abstract Schrödinger's equation in QFT

    Hi folks! A QFT question: you start from the lagrangian, compute the hamiltonian via Legendre transform and promote the the fields to operators with canonical equal-time commutation relations. Now you can compute the relation [H,F(x)]=-\mathrm{i}\partial_0 F(x) \ , where H is the hamiltonian...
  12. maverick_starstrider

    QFT and Electrons: Is Instantaneous Orbital Change Possible?

    My mathematical knowledge of QFT is nonexistant (I'm only just starting grad school) so I was wondering if anyone could clear up a questions I have: 1) Can the time it takes for an electron (which has just absorbed a photon of the correct frequency) to move to a higher orbital be said to be...
  13. T

    How Do I Work Out the Anti-Commutation Relations in QFT? (Srednicki)

    I have been working through Srednicki this summer to teach myself qft, and all too often I've gotten stuck on a small point and ended up spending a great deal of time clearing it up by myself. While this is probably an important part of the learning process, I am progressing a bit too slowly, so...
  14. I

    Coleman's QFT lectures on video

    Coleman's QFT lectures on video! Everybody check out John Baez TWF 264 where he reports Coleman legendary QFT lecture notes are now online!
  15. J

    Which books are recommended for mastering QED calculations in QFT?

    Hi all, I'm currently learning QFT out of Mandl and Shaw supplemented by Peskin and Schroeder. What are the best books for getting experience with QED calculations? Problems with worked solutions would be ideal.
  16. V

    What are the Best Books for Learning Elementary Quantum Field Theory and Particle Physics?

    Could someone suggest a good book for elementary QFT and particle physics?(I don't know which to read first). I have very little idea about QFT. Could someone also tell me what maths knowledge is required?
  17. pellman

    Calculate something with QFT - I dare you

    Sort of kidding with the title here. But seriously I am having trouble making progress in my study of QFT because I can't see where it is going. Please give me an example of something to calculate with QFT that corresponds to a measurable quantity, hopefully something which cannot be...
  18. pellman

    Experimental verification of QFT?

    What are the important experimental verifications of QFT that someone studying QFT should be familiar with? The wikipedia QED article mentions the anomalous magnetic moment of the electron and the Lamb shift. The Higgs Mechanism article states "Although the evidence for the Higgs mechanism...
  19. W

    QFT: Computing S-Operator to 1st Order in Coupling Constant lambda

    Homework Statement Compute the S-operator to first order in the coupling constant lambda. Homework Equations The given Lagrangian density is L = : \frac{1}{2} (\partial_{\mu} \phi)^2 - \frac{1}{2}m^2\phi^2 + \frac{1}{2}\frac{\lambda}{4!}\phi^4 : where phi is a scalar field. The...
  20. K

    Exercises and problems on QED and QFT ?

    I'm trying to study QFT using P&S book. Now I'm on the chapter 13 but I feel that I'm rather bad at solving practical problems on QFT and QED. Could anyone suggest a good source of problems (preferably with solutions) on QFT and QED (near the level of P&S ch. 1-13) to practise ? Thanks in advance !
  21. R

    Help with page 73 of Weinbergs QFT, vol.1

    In equation (2.5.47), I am getting U(R(\hat p) = e^{+i \phi J_3} e^{+i \theta J_2} Instead of the "-" signs in the exponential. This makes a phase difference under parity and time reversal of a massless particle. Is this one of the active rotation vs. passive rotation problem? If so...
  22. K

    Summary of the key formula of QFT

    When I learned QFT in school, I got lost among all the steps involved. There were the Feynman rules, wick's theorem, the interaction picture, the LSZ reduction formula, the S matrix, the T matrix, the transition amplitude matrix, and on and I lost track of the big picture pretty quickly. Later I...
  23. L

    When Is a Quantum Field Theory Exactly Solved?

    A question I would like to get an answer is when is a QFT exactly solved? E.g. if I know the solution of the equation for the two-point function I have got all about the theory? This equation is classical in nature being the two-point function defined in the sense of distributions. I have read...
  24. B

    Understanding Zee's QFT: Simplified Gauge Derivative Calculation on Page 236

    In Zee's QFT in a nutshell on page 236 between equations (1) and (2), the authors goes to polar coordinates and gets a new gauge derivative.Sure it 's simple, but I can't see how he gets it. thanks for any help
  25. L

    Preparing for a QFT Course with One Semester of Quantum

    Is one semester of quantum sufficient preparation for a QFT course?
  26. H

    Microcausality in algebraic QFT

    The condition of microcausality (commuting fields for spatially separated points) can be shown to hold in the Fock representation in quantum field theory (see e.g. Peskin & Schroeder section 2.4). However, in algebraic quantum field theory the condition of microcausality is postulated as an...
  27. D

    QFT Course: Electric & Magnetic Fields, but No Fields for Electrons?

    I'm studying a QFT course, and we've been asked to consider why classical physicists found it useful to introduce electric and magnetic fields, but not fields for electrons or other particles. I'm completely stumped, and would appreciate any hints. thanks
  28. J

    How can we reconcile Zee's claims about QFT integration on page 26?

    Homework Statement In Zee's book on QFT, I'm confused on page 26 by how we gets from Eq (4) W(J) = - \int\int dx^0 dy^0 \int \frac{dk^0}{2\pi}e^{ik^0(x-y)^0}\int \frac{d^3k}{(2\pi)^3}\frac{e^{i\vec{k} \cdot(\vec{x}_1 - \vec{x}_2)}}{k^2 - m^2 + i\varepsilon} to Eq (5). W(J) = \left(...
  29. J

    Why Do Mass Terms Not Cancel in N+pi to N+pi Scattering in QFT?

    [SOLVED] N+pi->N+pi exercise in QFT The due date of this exercise was several weeks ago, but I'm still struggling with this. Since some of the QFT exercises are kind of exercises, that are probably the same all over the world, I assumed there could be a non-zero probability that somebody...
  30. C

    Choosing a QFT Book: Easy to Understand & Good Exercises

    i am having a big issue in deciding whether to read zee's qft in a nutshell book. peskin and schroeder's intro to qft, or ryder's qft book. I have heard the first chapter of zee's qft book is great but the other chapters get progressively worse because they are a general outline of the...
  31. J

    QFT in a nutshell: From field to particle

    Homework Statement I don't understand how Zee gets Eq. (2) on p. 24: W(J) = - \frac{1}{2}\int \frac{d^4k}{(2\pi)^4} J(k)^\ast\frac{1}{k^2-m^2+i\varepsilon}J(k) Homework Equations W(J) := - \frac{1}{2}\int d^4x\int d^4y J(x)D(x-y)J(y) The Attempt at a Solution I don't see where the d^4k...
  32. P

    Discover the Basics of QFT & GR: A Comprehensive Guide for Beginners

    I'm looking for absolute basic but respectable introductions to QFT and GR. Any choices? What level of QM is recquired to learn QFT?
  33. N

    Is There a Sign Issue in Propagator Integration for QFT?

    Homework Statement I'm trying to show that the general form of the propagator is D(x) = - \int \frac{d^3k}{(2\pi)^32\omega_k}[e^{-i(\omega_k t - \vec{k}\cdot\vec{x})}\theta(x^0) + e^{i(\omega_k - \vec{k}\cdot\vec{x})}\theta(-x^0)] but my answers always seem to differ by a sign. Homework...
  34. N

    Integration by Parts in Zee's QFT: Understanding Eq. (14) to Eq. (15)

    Homework Statement I'm studying from Zee's QFT in a nutshell. On page 21, I don't understand how he uses integration by parts to get from Eq (14) to Eq (15), ie from Z = \int D \varphi e^{i \int d^4 x \{ \frac{1}{2}[(\partial \varphi)^2 - m^2 \varphi^2] + J\varphi \}} to Z = \int D \varphi...
  35. S

    Looking for solutions to Srednicki's QFT book?

    Hi! Does anybody of you own the solutions of Mark Srednicki's Quantum Field Theory book? I work on my on this book. Thus it would be very helpful to have the solutions! Stilo
  36. O

    Euclidean QFT and thermodynamic analogy

    I have been wondering now for quite some time about the meaning of Euclidean Quantum Field Theory. The Wick rotation t\to it allows us to transform a QFT in Minkowski space to a QFT in Euclidean space (positive definite metric). After that the expectation values of observables can be...
  37. S

    How can one ensure Lorentz invariance when using an external field in QFT?

    Some friend asked me the following question: For a real scalar field \phi, assume that H = H_free - \int d^3 x\ J \phi. J(x, t) is just some real number, source, or background field, without second quantization. Now, what is the amplitude \psi(x, t) for finding a particle at time t(before...
  38. V

    How are the positions of particles described in QFT?

    If I understand correctly positions of particles cannot have exact values in QFT, there are no eigenvectors of position (right?). But the positions of particles must correspond approximately to some state in QFT because position is meaningful in QM and classical physics, and QFT is supposed to...
  39. N

    Very basic questions about QFT

    A few months ago I started a thread asking some basic questions about QFT and it led to a large number of posts that were extremely interesting and that I am still going through. But the thread started to go in several directions (all very interesting!) away from my initial basic questions...
  40. Z

    What Is the Best Order to Study Group Theory, Tensor Analysis, and QFT?

    I want to study 3 subjects on my own,the subjects are Group Theory, tensor analysis, and QFT. I know this might be a silly question, but regardless of what textbook material i have or how much I know, what is the best order to study these 3 subjects ? I feel I should leave QFT to the last...
  41. P

    How do we obtain the Lagrangian of the EM field in Ryder QFT, 2nd Edition?

    We have the Lagrangian of EM field: L=-\frac{1}{4}F_{\mu\nu}F^{\mu\nu} Variation of Lagrangian give Maxwell's equations: \partial_{\mu} F^{\mu\nu}=0. or (g_{\mu\nu}\partial_{\mu}\partial^{\mu}-\partial_{\mu}\partial_{\nu})A^{\mu}=0. (equation 7.3, p.241) Ryder, then, claims that...
  42. C

    Understanding Light Propagation for Quantum Field Theory

    do you need to know about the propagation of light to understand quantum field theory? note: when i speak of propagation of light i am only talking about these topics only: geometrical optics, intensity, the angular eikonal, narro bundles of rays, image formation with broad bundles of rays...
  43. J

    How to understand equation 6.51 in Ryder QFT 2nd ed. Page 192?

    [SOLVED] Ryder QFT 2nd ed. Page 192 Homework Statement equation 6.51. This equation is actually 2 equations separated by a comma. I don't understand either one and would appreciate any help to get me started. For the time being, I would like to concentrate on the first one...
  44. J

    How Does Ryder's QFT Text Handle Complex Gaussian Integrals on Page 168?

    Homework Statement I have edited Ryder's text to emphasize the issue I am having. The actual text is approx. 40% down from the top of the page. (\frac{2\alpha}{i})^{3/2}\int exp(\frac{i}{2\hbar}\mathbf{P\cdot x} + i\alpha \mathbf{x}^2)d\mathbf{x} The integral may be evaluated by appealing to...
  45. J

    Why Does Ryder Use a 2π Factor in Equation 4.4 of QFT?

    Homework Statement The first expression in equation (4.4) is: \frac{d^4k}{(2\pi)^4}2\pi\delta(k^2 - m^2)\theta(k_0) Homework Equations Ryder is most ungenerous on this page. Some concepts, important to understanding the entire chapter are left unexplained. For instance, the reasoning...
  46. mjsd

    QFT Cutting Rules: Improved Versions & Worked Examples

    I am wondering whether someone can suggest a good ref or two (preferrably with worked example) on how to use Cutkosky (or whatever it is called) cutting rules in QFT to help pick out the absorptive/Imaginary part of a 1- or 2-loops diagrams. I have already tried Peskin and Schroeder, which is...
  47. J

    Ryder, QFT 2nd Ed. Page 47, eqn (1.122)

    Homework Statement (1 - \frac{i}{2}\mathbf{\sigma\cdot\theta})\mathbf{\sigma}(1 + \frac{i}{2}\mathbf{\sigma\cdot\theta}) = \mathbf{\sigma - \theta\times\sigma} Homework Equations The Attempt at a Solution At one point in this, I temporarily ignore the y and z components. I hope the notation is...
  48. C

    Why is the Fourier Transform in QFT Divided by (2pi)?

    is Fourier analysis in qft just used for going from a position wavefunction to a wavefunction described by the wave vector (k)? also why is the integral divided by [2(pi)]^n where n is the number of dimensions and how do you know when to divide the integral by the 2(pi) factor or not?
  49. J

    Ryder QFT Page 57 Homework: Solving Equation

    Homework Statement There is an unnumbered equation in the top half of the page: (1 - i\mathbf{K\cdot\phi})(1 - iP\cdot a)(1 + i\mathbf{K\cdot\phi})(1 + iP\cdot a) = 1 + [P_{\mu},P_{\nu}]a^{\mu}a^{\nu} + 2[P_{\mu}, K_i]a^{\mu}\phi_i + [K_i,K_j]\phi_i\phi_j Homework Equations The...
  50. J

    Verifying $\gamma = \frac{E}{m}$ in QFT

    Homework Statement On page 41 of Ryder's QFT, just below eqn (2.84), it says: \gamma = E/m I was unable to verify this, unless it is meant to be true only for small speeds. Homework Equations E = \pm(m^2c^4 + p^2c^2)^{1/2} (2.24) page 29, but as suggested n the book, we let c = 1, so E =...
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