Qft Definition and 956 Threads

I would like to ask if anyone can give me a hand with the understanding of the counterterms. I am reading by myself Chapter 10 of Peskin & Shroeder and got stuck in the middle of their example of how to renormalize \phi^{4} theory. What is puzzling me is how to obtain from the new Lagrangian...

Is there a (theoretical) partial or total inconsistency in QFT's postulate/premise/description of elementary particles as dimensionless, point-like objects with respect to the wave-particle duality nature of QM? This is in the sense that such description is *only* particle-like. Clearly, even...

The footnote at &7.6 page 329 writes: '' Recall that by canonical transformation, we mean a transformation from a set of phase space coordinates \Psi^{a},\Pi_{a} to some other phase space \tilde{\Psi}^{a},\tilde{\Pi}_{a} such that [\tilde{\Psi}^{a},\tilde{\Pi}_{b}]_{P}=\delta^{a}_{b} and...

Homework Statement I'm working with the Yukawa theory, where the interaction term in the Lagrangian density is g\varphi\overline{\psi}\psi. As an exercise for getting used to using the Feynman rules for the theory, I'm asked to show explicitly (i.e. I'm not allowed to invoke charge...

Hi, I would like to ask whether if a course in Quantum Field Theory (in particle physics context) would be of any use to future condensed matter physicist. Is it beneficial to be exposed to things like Canonical Quantization, Interacting Fields, Dirac Equation, Quantizing Dirac field and QED? I...

In pages 41-42 of these notes: http://www.damtp.cam.ac.uk/user/tong/qft/two.pdf , it is said that |\vec{p}|\ll m implies |\ddot{\tilde{\phi}}|\ll m|\dot{\tilde{\phi}}| Why is this so?

What background one needs to have to study QFT? I have a good background in calculus, linear algebra, PDEs, and quantum mechanics (at Shankar's level). Are these enough?

Homework Statement Prove that \gamma^{a}\gamma^{b}\gamma^{c}\gamma^{d}\gamma^{e}\gamma_{a} = 2\left(\gamma^{e}\gamma^{b}\gamma^{c}\gamma^{d}+\gamma^{d}\gamma^{c} \gamma^{b}\gamma^{e}\right) Each of the \gamma^{i}s are as used in the Dirac equation. Homework Equations...

Hello everyone ! First of all, Quantum Field Theory is not my field of research. However, I have to investigate on some problems in QFT and I'm trying to get familiar with it again. I'm basically working with scalar fields and I encounter some problems in dealing with renormalization...

I'm reading a paper by Art Hobson called "There are no particles, there are only fields" and had a question about something in there. (http://arxiv.org/abs/1204.4616) (Page 20-21) He basically says that since the vacuum in QFT has energy and non-vanishing expectation values, it is ultimately...

Hello! I'm finally starting to get a grip around quantum field theory. The last hang up is the following: I've been told that since we are quantizing a field, the field strength is the observable. Now analogous to QM we then define a field of hermitian operators, ##\phi(x)##, which give a...

In &5.6 writes: "An (A,A) field (A is spin) contains terms with only integer spins 2A,2A-1,...,0, and corresponds to a traceless symmetric tensor of rank 2A.(Note that the number of independent components of a symmetric tensor of rank 2A in four(space-time) dimensions is...

This seems to be the most interesting development in QG currently. I want to know what you think might present serious obstacles to completing the program. Where could it go wrong? The idea is that QFT and quantum statistical mechanics (QSM) need to be given a general covariant formulation...

The problem is on pages 323 and 324 of the second edition. Homework Statement Given the lagrangian \mathcal{L} = -\frac{1}{4}F_{\mu\nu}(x)F^{\mu\nu}(x) - \frac{1}{2\alpha}(\partial_{\mu}A^{\mu})^2 show that the momentum space photon propoagator is given by D_F^{\mu\nu}(k) =...

I'm seeing lots of underlying connections between the canonical formulism of QFT and QM. But I'm getting a bit confused by their differences. I'll just write down my thought process: QM is a one parameter system (t) in a space with three quantized operators (x,y,z) QFT is a four parameter...

I'm looking for a good online introductory course in QFT for physiscists (i.e. at university level, for someone who already has the basics of CM, QM and relativity, but for one reason or another worked in completely different fields). I see there are several courses online, but it is not so easy...

This is discussed in Weinberg's Quantum Theory of Fields, in the chapter on Relativistic Quantum Mechanics. The point I am somewhat confused about occurs on page 63 - 64, if you have the book. He operates on a single particle state with the unitary homogeneous lorentz transformation...

Hello! Im currently reading Ryder's QFT book and am confused with the variation of a scalarfield. He writes that the variation can be done in two ways, \phi(x) \rightarrow \phi'(x) = \phi(x) + \delta \phi(x) and x^\mu \rightarrow x'^\mu = x^\mu + \delta x^\mu. This seems...

Hi, I read the following in an online source: In relativistic settings, momentum and energy are equal so the uncertainty principle, for a particle of mass m which is trapped in a box of size L, becomes delta E>= \hbarc/L. If uncertainty exceeds delta E=2mc^2, we get pairs of particles and...

I'm looking for a book on QFT that is both introductory and somewhat rigorous. I have Zee's book but for me it is kind of hard to follow. I would prefer something that is more like a textbook introduction to the subject - not necessarily covering the whole subject but logically rigorous for...

The vacuum-vacuum expectation value in the absence of a source is in general not equal to 1, but exp[-iEt], where E is the energy of the vacuum. For some reason in QFT, we say E=0 (i.e., we normalize Z[0]=1, the generating functional), but we don't need to do this and one can in fact calculate E...

Infinities in QFT come from high momenta. I sometimes hear that is equivalent to coming from short distances, but I'm not sure I see the connection. The free propagator G(x-y) which I think goes like 1/|x-y|^2 is singular for short distances (when x=y). In momentum space G(x)= ∫d^4k exp[ikx]...

I'm trying to fit together my understanding of quantum mechanics, quantum field theory, given my lacking maths education. In quantum mechanics we have a time displacement operator and a space displacement operator, which are respectively: \hat{T}(t) = e^{-i\hat{H}t} \hat{D}(\underline{x}) =...

Hi everybody, I thought I'd give this a shot and see if anyone would like to be a sort of "mentor" for me this summer? I have not taken Quantum mechanics and I am actually working on a QFT-esque REU project for the next 8 weeks (!). Anyone interested in maybe answering (I will definitely...

Hi, I'm an undergrad that has not taken quantum mechanics... What exactly is the distinction between quantum mechanics and quantum field theory? Does quantum mechanics describe the interactions of particles? Are Feynman diagrams used in quantum mechanics? I have been doing some...

I know in ordinary QM, the spectrum of the Hamiltonian \{ E_{n}\} gives you just about everything you need for the system in question (roughly speaking). So what happens to this spectrum in QFT where |\psi\rangle is now a multiparticle wavefunction in some Fock space? I've been trying to...

Hello. I'd like to know of good suggestions of books on QFT. I have a somewhat firm grasp on non-relativistic Quantum Mechanics, and already know of some good books about it, so I'd like to understand some Quantum Field Theory if at all possible. Thank you in advance for your suggestions :)

In ordinary QFT, everything is formulated in terms of a Fock basis so when we write |\psi\rangle we mean that this is a product of single particle states covering every momentum mode. This leads to a Hamiltonian that's typically of the form \hat H=\int \frac{d^{3}k}{(2\pi)^{3}} [\omega_{k}(\hat...

Has anyone ever heard of treating a particle and antiparticle as identical based on the formalism of quantum field theory? The argument given is that the creation operator for a particle is the annihilation operator for its antiparticle, but I can't find this idea of treating them as identical...

Fourier Transform on the "connected part" of QFT transition prob. Homework Statement Calculate ⟨0|T[ϕ(x₁)ϕ(x₂)ϕ(x₃)ϕ(x₄)]|0⟩ up to order λ from the generating functional Z[J] of λϕ⁴-theory. Using the connected part, derive the T-matrixelement for the reaction a(p₁) + a(p₂) → a(p₃) +...

Explain "crossing" without invoking QFT? Hi there For someone learning particle physics for the first time (Griffiths' intro book, no knowledge of QFT yet): Why can you "cross" a reaction? Is there an intuitive answer or does one truly need understanding of scattering amplitudes, quantum...

I have the following process: two ingoing particles, a photon hitting a nucleus, and two outgoing particles, the nucleus and a pion. I have computed |M|2 and the differential cross section in the center of mass frame dσ/dΩCM; I now have to go into the lab frame, where the nucleus is initially at...

Hi there Iive been reading the intro chapter to Peskin and Schroder's 'An intro to QFT' I have a question regarding the conservation of angular momentum during particle collisions/scatterings As an example they talk about e+ e- --> μ+ μ- The take the Centre of Mass (CM) frame...

State space of QFT,CCR and quantization,spectrum of a field operator? In the canonical quantization of fields, CCR is postulated as (for scalar boson field ): [ϕ(x),π(y)]=iδ(x−y) ------ (1) in analogy with the ordinary QM commutation relation...

We know that a free scalar field on a diff-invariant 1+1 dimensional background (i.e. bosonic string theory on the worldsheet) contributes to the central charge of the Virasoro algebra with a constant term. Is there any examples of a 1+1d QFT that has instead a central charge contribution...

Hello Everybody, In page 86, in Peskin & Schroeders Introduction to QFT, the following expression is introduced to analyze \left | \Omega \right >; the ground state of the interacting theory: e^{-iHT} \left | 0 \right >. Where |0> is the ground state of the free theory and H is the...

In Weinberg's textbook on QFT(google book preview), he discussed the phase acquired after interchanging particle labels in the last paragraph of page 171 and the footnote of page 172. It seems he's suggesting interchanging particles of same species but different spin states will only bring a...

I'm currently teaching myself some QFT trough Peskin and Schroeders Introduction to QFT and I've noticed that in several arguments they rely on appealing to the Born approximation of non-relativistic QM scattering theory. For example on page 121 equation (4.125) they appeal to the scattering...

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...

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...

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...

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...

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

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...

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...

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...

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...

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...

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...

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...