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

    Symmetries in Sidney Colemans QFT script

    Hello Everybody, I am learning QFT using Sidney Colemans lecture notes (and the Peskin Schroeder book). They can be found here: http://arxiv.org/abs/1110.5013 Now, in page 40, he introduces in the paragraph Symmetries and Conservation laws some definitions which I don't quite...
  2. P

    Bogoliubov transformations in QFT

    Homework Statement I am trying to teach myself QFT and reproduce cosmological equations from papers. Given the bogoliubov transformations: i) a(conformal time η, k) = α[SUB][/k](η)a(k)+β[SUB][/k](η)b^\dagger ii) b[SUP][\dagger] = -β*[SUB][/k](η)a(k)+α*[SUB][/k](η)b^\dagger find the...
  3. N

    Is it a misprint in QFT book of Peskin?

    In QFT book of Peskin&Schroeder writing(page 252,section 7.5Renormalization of electric Charge): (e^{2}-e^{2}_{0})/e^{2}_{0}=\deltaZ_{3}\approx-2\alpha/3\pi\epsilon. Where \epsilon is 4-d(d is dim of space-time) But I think that it is misprint,because bare charge>> observed charge e,then...
  4. jfy4

    Propagator using Functional QFT

    Hi, I am trying to write down the propagator for a scalar field theory, but I want to try and get it in the functional representation. My plan is to compute the following: \langle \psi (x', t') | \psi (x,t) \rangle which gives the amplitude to go from x' to x. Now I guess I have to...
  5. L

    About propagator and poles in QFT

    Hi all, I am studying QFT using John Preskill's notes. I have a question about the propagator and poles. On page 2.91, at the bottom, he said that there is a s-channel pole, which is the pole of the exact propagator. Then he claimed that by the argument about unitarity in page 2.70, the pole...
  6. I

    Particle Annihilation in Interacting Fields: Frequency and Bound State Quanta

    I need some advice. I have read that interacting fields can lead to quanta annihilation? How often does this happen, and can bound state quanta annihilate or is it just free quanta? Thanks
  7. C

    Lagrangian vs. Hamiltonian in QFT

    I'm a little confused about why the Lagrangian is Lorentz invariant and the Hamiltonian is not. I keep reading that the Lagrangian is "obviously" Lorentz invariant because it's a scalar, but isn't the Hamiltonian a scalar also? I've been thinking this issue must be somewhat more complex...
  8. C

    Confusion from Weinberg's QFT vol1

    Hello! I came across with something that confused me while studying the book and I need some help. In section 7.3 , equation (7.3.4) should have the drivative of ε(x) in order to "vanish when ε(x) is constant" . But in the lines before this expression he says that the variation of action...
  9. O

    Looking for book on Introduction to QFT

    Hi. I'm studying (introduction to) QFT, and I'm really lost. If possible, I'd like a pointer to a good textbook on the subject. I'll give an example of my confusion with a question: I think I've understood phi(x) as a classical scalar field, what it is and how to use it in a lagngian for...
  10. A

    Deriving charge for Noether current in free complex scalar field QFT

    Homework Statement Hi I a attempting to derive the expression for the conserved Noether charge for a free complex scalar field. The question I have to complete is: " show, by using the mode expansions for the free complex scalar field, that the conserved Noether charge (corresponding to complex...
  11. haushofer

    HUP in QFT and QM:virtual particles

    Hi, I have a question about reconciling two pictures of virtual particles and the Heisenberg Uncertainty Principle (HUP). In QFT "virtual particles" show up in perturbative calculations. We try to calculate an amplitude in interacting theories, this can not be done in an exact way, so we...
  12. S

    QFT Question: What is meant by dipole form ?

    QFT Question: What is meant by "dipole form"? Hello physics people! Probably a very basic question, but here goes. I'm taking a course on QFT based on Ryder. I've heard my professor refer to propagators as having a "polar" or "dipole" form. Things like (k^2 - m^2 + ie)^(-1) For anyone who...
  13. Y

    How to interpret the field function Φ in QFT?

    Hi, I have a question that how to interpret the field function Φ in Quantum Field Theory. As I can see, it is an operator through second quantization and the co-ordinate representation no long exist after second quantization. So we cannot regard it as wave function any more. Could...
  14. Alesak

    Preparing for QFT: Best Way to Approach Non-Physics Student's Thesis

    Hi guys, I need to get into QFT because of my thesis, yet I study nothing near physics so I need your guidance how to best proceed. I've got two questions, any answers appreciated: 1) how much QM should I learn? In my book (zettili) I'm in chapter about harmonic oscillator and the rest of...
  15. A

    QFT Lagrangian Problem: Find Free Particle Action Hermitian Way

    Hello, I've started a course on QFT and I'm having some troubles trying to find the solution of this exercise: Write the action of a non-relativistic spineless free particle in a manifestly hermitian way The problem should be simple but I'm a bit lost in the hermitian way part... What does it...
  16. S

    QFT Index Question Homework: Solving Euler-Lagrange Equations w/ F_{mu,nu}

    Homework Statement I'm learning QFT and trying to do a basic problem finding the equations of motion from the Euler-Lagrange equation given a lagrangian. The lagrangian is in terms of: F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu} so then my issue comes in with this part of the...
  17. Q

    How to understand the standard momentum introduced in Weinberg's QFT

    How to understand the "standard" momentum introduced in Weinberg's QFT I'm reading Weinberg's QFT Volume I. In page 63, you can find a formula (2.5.3) which states that the new state vector obtained by a Lorentz transformation is a linear combination of a whole bunch of other vectors...
  18. C

    How can one obtain conserved charges from a symmetry transformation in QFT?

    Homework Statement From the Lagrangian density L = \frac{1}2 \partial_\mu \phi_a \partial^\mu \phi_a - \frac{1}2 \phi_a \phi_a, where a = 1,2,3 and the transformation \phi_a \to \phi _a + \theta \epsilon_{abc} n_b \phi_c show that one gets the conserved charges Q_a = \int d^3x...
  19. C

    QFT - rewriting a conserved quantity

    Hey! I'm trying to learn QFT now and I'm currently reading David Tong's online lectures; http://www.damtp.cam.ac.uk/user/tong/qft/one.pdf. At page 17 finds the conserved current j^\mu = - \omega^\rho_{\ \nu} T^{\mu}_{\ \rho} x^\nu where i have understood T to be the energy momentum tensor...
  20. C

    Understanding the Composition Rule and Transformation Law in Weinberg's QFT

    Hello, a confusion has arose during my so far study of the above book. According to the composition rule (2.3.11) it should be: U\left( \Lambda ,a \right)=U\left( \mathbf{1},a \right)U\left( \Lambda \right) and according to transformation law (2.5.3) and the eigenvalue equation which follows...
  21. A

    QFT: Solving the integral for the Wightman function in Minkowski spacetime.

    Homework Statement How does one actually solve the integral for the Wightman function for a massless quantum scalar field in 4D Minkowski spacetime? That is, what is the integration technique to go from: \langle \hat{\phi}(x) \hat{\phi}(y) \rangle = \int_c d^4k \, \frac{1}{(2 \pi...
  22. C

    Which mathematical subjects must I learn to understand basic QFT?

    So I did QFT at university and didn't feel that I really understood what was being done. We just did some calculations, heuristic guesswork and dwelled on phenomenology. I want to do it the way I personally understand things best: by learning the mathematics in detail, almost at the level of a...
  23. F

    Studying Topological QFT: A Guide

    Hello, Can anyone tell me how to go about studying Topological QFT. I am fine with QFT, Fibre bundles and currently doing Cohomology from Nakahara. Should i directly start with Witten's paper or are there any more elementary review papers? Thanks.
  24. S

    Prerequisites for learning QFT

    I have already done quantum mechanics (and general relativity if it is relevant) and have all the associated math prerequisites but not much more than that. Is there anything I should add before attempting QFT and what text would be best for these? In addition, what text would you recommend for...
  25. I

    Polarization vector in Peskin & Schroeder QFT

    Hi all, A friend and I are working through Peskin and Schroeder, and we're both stumped with only the fourth equation! The interaction in question is e^+ + e^- \to \mu^+ + \mu^- with a virtual photon as the inner branch. P&S state that \mathcal{M}\propto \langle \mu^+\mu^- | H_I | \gamma...
  26. Y

    Math for Quantum Field Theory (QFT)

    Hello, I am trying to find out (searching did not return anything useful) what kind of mathematical background one needs to understand QFT comfortably (if such state can ever be attained :D). By comfortably I mean being able to concentrate almost entirely on the physics part rather than pick up...
  27. K

    Which QFT Book Should I Choose for a Deep Theoretical Understanding?

    Hello! I´m currenly considering buying a complete QFT book, I have done some classical field theory and glossed around in Zee's nutshell book. I also have knowledge from advanced QM up to Klein Gordon eqn and 2nd quantization. My question is now which one you think will fit me the best, my...
  28. S

    Is the delta in the commutation relations of QFT a dirac delta or a kronecker?

    If it's a dirac delta doesn't it mean it's infinite when x=y? Or is it a sort of kronecker where it's equal to one but the indices x and y are continuous? I'm confused.
  29. P

    Srednicki QFT chapter 67, LSZ formula

    Homework Statement I would like to know how to get from eq. (67.3) to (67.4) in Srednicki's book on QFT. The problem is the following: Given the LSZ formula for scalar fields \langle f|i \rangle = i \int d^{4}x_1e^{ik_1x_1}(\partial^{2}+m^{2})\ldots \langle 0|T\phi(x_1)\ldots|0\rangle This...
  30. K

    Useage of the term field in QFT

    useage of the term "field" in QFT Wikipedia defines a field as "a physical quantity associated with each point of spacetime". So contrary to a particle, where physical quantities are associated with properties like position or momentum, the field itself is a physical quantity. (This definition...
  31. LarryS

    Entanglement in QFT: Free Particle Decay

    All definitions of entanglement, that I have encountered, were expressed in the language of non-relativistic QM. Suppose a free, massive particle decays into 2 other massive particles. The 2 new particles would be entangled in linear momentum. Can QFT define that type of entanglement? Any...
  32. N

    QFT w/ Negative Mass: Spin 0 vs Spin 1/2

    In the Klein-Gordon equation (spin 0), the mass dependence is (only) through m^2, whereas in the Dirac equation (spin 1/2) it's through m. Does this mean that for spin 0 particles, we can just as well describe them as having negative mass without changing any of the physics (whereas for the...
  33. R

    What's the difference between QFT and Atomic physics

    For physics between QM and String Theory I've heard a lot of different names. Quantum Electrodynamics seems to be the physics of the electron and the photon. Quantum Chromodynamics seems to be the physics of quarks. But High Energy/Nuclear/Particle Physics, Atomic physics, QFT, I don't...
  34. N

    How can we consider static electromagnetic field in QFT point of view?

    Hi everybody! Please explain to me how can we consider static electromagnetic field in point of view of Quantum Field Theory.Because varying electromagnetic field can quantize to photons,so we can consider varying electromagnetic field like a ''set'' of photons. Thanks very much in advance.
  35. S

    When is operator phi(x) an observable in QFT?

    In QFT of a real Klein-Gordon-Field, the field operator \phi(x) is an observable. Mathematically, this is the case because it is a sum (over all k) of a and a^\dagger and this yields a Hermitian operator. Physically, I can understand this because this equation would describe, for example, a...
  36. L

    Vacuum in qft, what are we refering to?

    When we talk about the vacuum in qft, what are we referring to? The lowest state vector of the Fock space or the lowest energy field configuration that minimize the Lagrangian? Also related, when we sandwich the free field between two vacuum states, we get zero plus quantum fluctuations. But...
  37. S

    What is the interpretation of the vacuum correlation function in QFT

    I'm currently trying to make some intuitive sense out of Quantum field theory, but I'm not really understanding the vacuum. Consider a real (or complex, with + in the right places) scalar particle (a Klein-Gordon field). Now consider the propagator (or correlation function) G(x-y)=...
  38. snoopies622

    Looking for a Dirac book on qft

    I just happily bought a used copy of Dirac's Lectures on Quantum Mechanics from Amazon.com. I also want his Lectures on Quantum Field Theory but they don't carry it. Anyone know where I can find a copy?
  39. G

    Question about this interaction in QFT

    Question about this "interaction" in QFT Hi, I started two months ago my course in QFT, and since I heard about the fact that the bare mass appearing in the Lagrangian of a theory isn't the physical mass of a particle (due to self interaction, I guess), I tried to find an example explicitly...
  40. L

    Weinberg QFT - Inner product relations, Standard momentum, Invariant integrals

    Weinberg in his 1st book on QFT writes in the paragraph containing 2.5.12 that we may choose the states with standard momentum to be orthonormal. Isn't that just true because the states with any momentum are chosen to be orthonormal by the usual orthonormalization process of quantum mechanics...
  41. E

    Time in QFT and in special relativity

    Special relativity gives that time for a (traveler on) photon do not run. It also gives that every moving elementary particle rest in some inertial system, but photon does not rest in any inertial system. But how this can be visible in Quantum field theory or in QED? An electron and a photon...
  42. maverick280857

    Topology of Aharonov Bohm Effect - Lewis Ryder's QFT book.

    Hi, I am reading through Section 3.4 of Lewis Ryder's QFT book, where he makes the statement, This makes some sense intuitively, but can someone please explain this direct product equivalence to me as I do not have a firm background in topology (unfortunately, I need some of it for a...
  43. C

    Bound state transitions in QFT

    In non-relativistic QM, we spend a lot of time examining bound states--energy levels, spatial distributions, and all that. We can determine that an electron put into a Coulomb potential will have certain Hamiltonian eigenstates, which correspond to the orbitals of a hydrogen atom. However, in...
  44. A

    Best book for learning QFT and the SM?

    I have the basics of CM, relativity and non relativistic QM but never went much beyond KG and the Dirac equation. So I need a good intro to QFT, particle physics and the SM. Ideally with an emphasis more on the theoretical side than only experimental. I had a good feeling with "An...
  45. G

    Do we really need a cutoff in QFT

    Does the cutoff really have to go to infinity in QFT? It seems that once we replace bare parameters by experimental (i.e. physical) parameters, the cutoff vanishes from the expressions for physical quantities, so it didn't matter what the value of the cutoff was, whether it's 0, 10000000000, or...
  46. MathematicalPhysicist

    Ax 4 in page 19 of Ticciati's QFT textbook.

    The axiom says: "The interaction between two observations is constrained by causality |x-y|^2 <0 \Rightarrow [\phi(x),\phi(y)]=0 " But |x-y|^2<0 is always false that means the if the condition applies then by simple logic the consequnet of the condition can occur or not occur, I don't...
  47. M

    How to normalize wave functions in QFT? such as \lambda \phi 4 theory?

    In quantum mechanics, most wave functions are normalized with \int |\phi|^2 dx^3 =1. But I did not see any field in the quantum field theory is normalized. I understand they maybe just plain waves and does not need to be normalized. But in some cases, if we do not expand the field as plain wave...
  48. snoopies622

    What are the postulates of QFT?

    I like the way quantum mechanics can be expressed as a set of five or six axioms, like in Daniel T. Gillespie's A Quantum Mechanics Primer or David McMahon's Quantum Mechanics Demystified. Is there a similar set of axioms for quantum field theory?
  49. A

    Exploring the Hilbert Space of QFT

    Hi everyone. Many texts when describing QFT start immediately discussing about free field theories, Fock spaces etc.. I want to understand general properties of the Hilbert space, and how to find a basis of it, and how to find a particle interpretation. I know there are very mathematical...
  50. W

    Time as Parameter in QM vs Coordinate in QFT

    According to Peterdonis in an old thread According to Matterwave in https://www.physicsforums.com/showthread.php?t=573589 msg #11: Peterdonis said Time is a parameter in non-relativistic QM while as a coordinate in relativistic QM/QFT. But Matterwave said parameter and coordinate has...
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