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. O

    QFT Commutator (momentum and Hamiltonian) Issue

    Hi, I haven't posted this in the homework section, as I don't really see it as homework as such. I'm trying to derive the Heisenberg equations of motion for the Klein Gordon field (exercise 2.2 of Mandl and Shaw). I'm trying to derive the commutator of the Hamiltonian and canonical momentum...
  2. snoopies622

    Elementary QFT question, part 2

    I'm still having trouble understanding the connection between a static electric field and harmonic oscillators. I understand that a static electric field can be expressed as a scalar (potential) field, and that through Fourier analysis this scalar field can in turn be expressed as the sum of...
  3. T

    QFT around fixed classical backgrounds

    Hi all, Does anyone know a decent set of notes/book dealing with issues re: quantum fluctuations around a (fixed) classical background? In particular say, scalar QED with a fixed background E&M field. Thanks, Dan
  4. I

    Why QFT in condensed matter physics?

    I am currently following a course of condensed matter physics and quite enjoying it. But after doig some research I found that many book deal with QFT applied to condensed matter. I wonder what all the calculus of QFT is needed to describe those phenomenas. I kinda feel that relativistic...
  5. snoopies622

    Exploring the Concept of Quantized Electromagnetic Fields in QFT"

    What does it mean for an electromagnetic field to be quantized? If I have a proton at point A, then classical physics tells me that at an electron at point B feels a constant electrical force described by Coulomb's law. If the field is quantized, does this mean that sometimes a force is felt...
  6. MathematicalPhysicist

    Did Maggiore Make an Indexing Error in QFT Textbook?

    In page 15 of the first edition of this textbook, in equations 2.6 and 2.7, he writes: (2.6)e^{i\alpha_a T^a_R} e^{i\beta_a T^a_R}=e^{i\delta_a T^a_R} where T^a_R is the generator of the group represented by R. Now in equation (2.7) he take the logarithm: (2.7) i\delta_a...
  7. P

    Has anyone have seen this QFT book?

    I got a e-book on QFT few months ago.but this one hasn't chapter 1 and title and index etc.i.e all the informations about author.but this book is really good,I want to see the full version,it's recommed to anyone who interests in QFT.It's style is a little mathematical but keep good physical...
  8. S

    How Can B Hatfield's Book Clarify QFT Through Solved Examples?

    i'm trying to learn qft. i have referred many books most of them have same pattern giving some intuitive idea followed by proof or formula derivation but i need solved examples/applications of this formulas or proofs for better understanding e.g. second quantization "momentum" and "position" are...
  9. G01

    How to Derive Specific Commutation Relations for Lorentz Generators?

    Homework Statement Derive the following commutation relations from the general commutation relation for the Lorentz generators: [J_i,J_j]=i\hbar\epsilon_{ijk}J_k [J_i,K_j]=i\hbar\epsilon_{ijk}K_k [K_i,K_j]=-i\hbar\epsilon_{ijk}J_kHomework Equations The commutator for the Lorentz...
  10. I

    In QFT how to take this derivative?

    In QFT given a Lagrangian L=\partial_a \phi^* \partial^a\phi, how do you take this derivative \frac{\partial L}{\partial_a \phi}?
  11. N

    The Meaning of Z(J) and W(J) in QFT

    I apologize for the vague title, I don't know the names for the objects I'm asking about, which also made it hard to search for more information on them. I'm reading Zee's QFT in a Nutshell and have the feeling I'm missing something. When introducing the path integral formalism, he defines a...
  12. K

    Help with Equation 9.25 in Srednicki's QFT Book?

    Can anybody help me out with equation 9.25 in Srednicki's QFT book? He says the in the eq. 9.25 an integration by parts has been carried out. I do not see how. I guess we integrate 9.9 and get then 9.25 somehow, but how? Any hints? thank you
  13. D

    Problem with source term in qft

    I have a problem understanding the effect of source terms in qft. I am interested in understanding how a static point source will interact with a massless field. Let me consider a simple example of a linear chain of masses coupled by some springs. In the continuum limit, the Lagrangian...
  14. N

    QFT Source Function: What is J Physically?

    I just picked up a book on QFT and have already found myself stuck on something that appears to be quite elementary. When disturbing the field, the potential gets an added term with a source function J, J(x, t) \phi(x). I'm not quite getting what J physically represents. It 'describes how...
  15. P

    Which QFT book is better? Peskin & Shroder or Weinberg?

    The title is my question. What are the relative merits of the two books? I've only read part of Peskin & Schroder, and one of my complaints is that the book doesn't cover canonical quantization of QED which I need for my course. I don't know much about Weinberg's book, but it seems to be have...
  16. P

    QFT Counter Terms example calculation?

    I'm reading a QFT text right now and to fully understand the physical perturbation theory method I would like anyone to suggest a refrence or supply an example of a calculation using the physical perturbation theory: As an example to start a discussion consider. L = \frac{1}{2}((\partial...
  17. D

    N-point Green's function in QFT

    Hello! Something about N-point Green's function in QFT really troubles me... In the path-integral formalism,why will we introduce the N-point Green's function? I mean is it enough because we have calculated the 2-point green's function. And in the canonical formalism, it seems we can finish...
  18. P

    Definition of Thermal State of Scalar Field in QFT

    What is the definition of thermal state of scalar field in QFT. Is it possible to express the condition in algebraic way (without referring to palticluar choice of representation).
  19. W

    QFT Video Lectures with David Tong

    Here are some cool video lectures on introductory QFT: QFT Video Lectures
  20. D

    Problems on quantum field operators in QFT

    Hello! I met some annoying problems on quantum field operators in QFT.They are as follows: (1)The quantum field operator( scalar field operator, for example),is often noted as φ（r,t). Can it be interpreted as like this: φ（r,t) is the coordinate represetation of a...
  21. P

    QFT - interaction between field

    Let's assume that we have two fields which doesn't interact at the beginning. But after some time this fields start to weakly interact. Interaction lasts only finite period of time. The density of lagrangian is: L = \partial_{\mu} \psi \partial^{\mu} \psi + m^2 \psi^2 + \partial_{\mu} \phi...
  22. S

    Zee QFT In a Nutshell Propagator Question

    I've started working through Zee's book and have got to question I.3.2 - calculation of D(x) in 1+1 dimensions for t=0. The expression to evaluate becomes (omitting constant multipliers for simplicity) \int^{\infty}_{-\infty} dk \frac{e^{ikx}}{\sqrt{k^2+m^2}} This is singular at k=+im...
  23. S

    Peskin's Introduction to QFT 3.82 - What Has He Done?

    peskin`s introduction to QFT [3.82],do not know what he had done to the underline
  24. V

    QFT question - anti-commutator

    For this question, note that curly brackets {..} is an anti-commutator eg. {AB} = AB+BA where A and B are matrices. Also note that I4 is the identity 4x4 matrix. I would like to understand why { γµ,{γργσ} } = 2 { γµ, I4 }\eta^{\rho \sigma} I understand that { γµ,{γργσ} } = 2{ γµ,\eta^{\rho...
  25. N

    QFT textbook where Schwinger effect is described

    Could you pls advise me QFT textbooks where the Schwinger effect is described... Thanks a lot
  26. B

    Understanding Peskin's QFT: Deriving Equations (2.35) and (2.54)

    Homework Statement Hi, I have two stupid questions about Peskin's QFT book. (1) P23, How to derive from (2.35) to (2.36) (2) P30, How to derive (2.54) Homework Equations (1) (2) The Attempt at a Solution (1) If I consider the dual-space vector, \langle \mathbf{q} | = \sqrt{2...
  27. A

    What Are the States in Quantum Field Theory?

    Hello, this is quite a basic question I know, but something I'm not sure I've fully got my head around. In classical particle mechanics the dynamical variable is the position vector x, and in classical field theory the dynamical variable becomes the field \phi(x) , with x being relagated to...
  28. P

    Defining Spin in QFT in Curved Spacetime

    How one can define a spin in Qunatum Filed Theory in curved spacetime. If the space is flat it's invarainat under Poincare group - so in particular it's invariant under SO(3). Spin operators are simply generators of SO(3). If the space isn't flat we cannot define spin in this way. I know that...
  29. P

    Solve Bound State Problems in QFT | Identify Space of States

    How does one solve bound state problems in QFT(like an electron positron atom)? How does one identify the space of states. The Fock space seems to lose it definition when a bound state problem is discussed. There is also no meaning to wave functions or potentials that are used in standard...
  30. N

    What Are Divergent Green's Functions in This Context?

    Homework Statement I am being asked to consider a Dirac spinor with two complex components and the following Lagrangian: L = L_{Dirac}-\stackrel{g}{4}{(\psi\bar{\psi})^{2}} I am asked to derive the Feynman rules for this theory which I can do using the standard methods. However, I am...
  31. D

    Magnitude of the scattering ampliudes in QFT

    I have yet another question... I was always thinking that the scattering amplitudes one computes in QFT are complex numbers of modulus between 0 and 1. And I was thinking that because it is supposed to be related to the probability of some transition between states happening. And then I tried...
  32. S

    Beta function in Euclidean and Minkowskian QFT

    Hi! I have a question regarding the renormalization group Beta function, i.e., \beta = \mu \frac{dg_R}{d \mu} where g_R is the renormalized coupling constant and \mu the renormalization scale. My question in a nutshell: are the Beta functions calculated for QFT and, respectively...
  33. L

    Srednicki QFT chapter 8 question

    Hi, In chapter 8 Srednicki employs the 1-i \epsilon trick. He multiplies the Hamiltonian desity, H=\frac{1}{2} \Pi^2+\frac{1}{2}(\nabla\phi)^2+\frac{1}{2}m^2\phi^2 by this 1-i \epsilon , and says it's equivalent to if we replaced m^2 with m^2-i \epsilon . I can't see how this is...
  34. F

    QFT: calculating decay rates from invariant matrix element M

    Hi! I am currently taking a first course in QFT with Peskin & Schroeder's book. I've got stuck with the equation that relates the differential decay rate of a particle A at rest into a set of final particles with the invariant matrix element M of the process. M can be found from the Feynman...
  35. M

    QFT general properties operators

    Hi all, I have quite basic questions about the general properties of operators in quantum field theory. When quantizing the free scalar field, for instance, you promote the classical fields to operators and impose suitable commutation relations (canonical quantization). In momentum space the...
  36. MathematicalPhysicist

    What are the Mathematical Prerequisites for QFT?

    Can someone please inform me what are the formal mathematical tools used in QFT? I plan to learn the maths beforehand or in parallel with QFT in the summer, and I don't like how physicists treat maths so that's it.
  37. P

    Solving QFT Problem: Deriving <k'|(\partial_\mu \phi^\dag)\phi|k>

    Somehow I have problems with figuring out the following problem: I know that the scalar field is obeying the follwoing equations: <0|\phi(x)|k> = e^{ikx} <0|\phi(x)^\dag|k> = 0 <k'|\phi(x)^\dag|0> = e^{-ik'x} <k'|\phi(x)|0> = 0 And I was told that I can deduce the following result from the...
  38. K

    Stuck on Problem 6.2 in Peskin's QFT Book?

    Homework Statement In fact this is not homework, I'm self-studying QFT by reading Peskin's book, and I'm stuck with Problem 6.2.Homework Equations In part (e), I cannot get the factor (1+(1-x)2)/x in the cross section.The Attempt at a Solution Maybe I'd already been wrong in earlier parts, the...
  39. W

    Confusing integral in Zee's QFT

    This is probably really simple. In chapter I.4 the jump from (4) -> (5) is sort of eluding W(J) = - \iint dx^0 dy^0 \int \frac{dk^0}{2\pi} e^{i k^0(x - y)^0} \int \frac{d^3k}{(2 \pi)^3} \frac{e^{i \vec{k}(\vec{x_1} - \vec{x_2})}} {k^2 - m^2 + i\epsilon} and \omega^2 = \vec{k}^2 +...
  40. O

    Is this a mistake in Steven Weiberg's QFT II textbook?

    I guess it should be my mistake somewhere. o:) https://www.amazon.com/dp/0521670543/?tag=pfamazon01-20 On Page 30, for the derivation of EQ. (15.7.19), the nilpotency of BRST operator on the ghost for gauge transformation, \delta _{\theta}s\omega_\alpha &=& -...
  41. H

    Maxwell propagator in Kaku's QFT book

    In Michio Kaku's QFT book, p. 106, he writes: [To illustrate problems with direct quantization due to gauge invariance] let us write down the action [of the Maxwell theory] in the following form: \mathcal L=\frac12 A^\mu P_{\mu\nu}\partial^2A^\nu where...
  42. R

    Feynman Looking for A Particle Version of QFT

    Feynman Looking for A "Particle Version" of QFT Hey, I think I read somewhere (though can't find it now) that Feynman was looking for a 'particle' version of quantum field theory which he didn't find but this instead led to the path integral approach of quantum mechanics. Can anyone shed any...
  43. P

    Peskin & Schroeder QFT 5.6 Need help

    Hey! I need some help for problem 5.6 (b) in Peskin + Schroeder QFT. I can't get rid of the term including three gamma matrices in my amplitude. I get two terms of the form: \frac{-\gamma^{\nu}*\slash{k_2}*\gamma^{\mu} + 2\gamma^{\nu}p_1^{\mu}}{-2*p_1*k_2} and the same with k_1 <->...
  44. F

    Exploring Bound State Calculations in Quantum Field Theory

    Can anybody recommend a good review article (or a book) for bound state calculations in QFT? I have never seen anything along these lines, other than brief sections or paragraphs in various textbooks about the connection to the Schrodinger equation in the non-relativistic limit for two particle...
  45. T

    Incertitude relations from QFT

    Hello, There are no incertitude relations in QFT. On the other hand, these incertainty relations do exist in non-relativistic QM. How can we reconcile these two facts ? Is it possible to "derive" uncertainty relations from QFT by "taking the non-relativistic limit" ? Thanks !
  46. P

    Why no EOM in QFT with higher than second order derivatives in time and space?

    When we write down a Lagragian for a quantum field theory, it is said that it should not depend on the second and higher order time and space derivatives of \phi, because we want the equation of motion(EOM) to be at most second order. Why is it so important. What trouble will a higher order EOM...
  47. J

    Mathematical Requirments for QFT

    Can anybody give or link me to a relatively complete list of mathematical requirements for being able to fully grasp Quantum Field Theory at an advanced level? This may be a lot to ask but I've learned quantum mechanics (mainly from the Cohen-Tennoudji text) and whenever I've tried to access...
  48. J

    Basic question on QFT and the standard model

    The standard model comprises a particle model of reality, implying that every observable is either a particle of matter or a force carrying particle. QFT seems to imply that particles are merely manifestations of underlying fields - ie, particles are "ripples" in the field. if QFT is the...
  49. G

    What is the QFT picture of forces?

    According to QFT, how do two masses attract? Is the action instantaneous? How is momentum/energy conserved? Is the action non-local?
  50. P

    QFT: Checking Causality w/ Commutators: Examples & Criteria

    The Feynman propagator in QFT is not zero for space-like separation, but we say this does not mean that causality is violated, we should check the commutator of field operators instead, and the commutators vanish for space-like separation. My question is: why do we use commutators to check...
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