Qft Definition and 956 Threads

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...

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...

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

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...

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

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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 +...

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...

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...

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 <->...

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...

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 !

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...

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...

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...

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

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...

Im still in 2year college, and studyin QM alone, would like to know a good book for QFT that I can understand. I have some questions that seems can only be answered with QFT, right now, I am half way through the Griffith's QM book..! thx a lot guys..!

I understand that the formal structure of QFT has resisted axiomatization (so far) and that what formal structure presently exists is really a set of recipes. Can somebody outline the recipe please.

Hi In Halzen's "Quarks & Leptons" all discussed particle interactions conserve particle number in some sense (Actually particle number is not conserved but if you count the particles minus the antiparticles before the reaction you get the same "particles minus the antiparticles" number after...

Question concerns the existence of the interaction in boost operator in the instant form of relativistic dynamics. (referring to "Relativistic quantum dynamics" after E.V.Stefanovich, http://arxiv.org/abs/physics/0504062) From the existence of interactions in boosts (e.g., in instant form...

Hello, I plan on continuing to study physics, mathematics and Earth science. (independently) What are the mathematical pre-requisites for learning relativistic quantum field theory as smoothly as possible. On MIT's opencourseware, it indicates that a class on advanced ODEs is enough, but we...

Hi, I was going through section 9.2 of Peskin and Schroeder, and came across equation 9.16 which reads \int\mathcal{D}\phi(x) = \int \mathcal{D}\phi_{1}({{\bf{x}}}) = \int \mathcal{D}\phi_{2}({{\bf{x}}}\)int_{\phi(x_{1}^{0},{\bf{x}})\\\phi(x_{1}^{0},{\bf{x}})}\mathcal{D}\phi(x) What does the...

Can anybody recommend a good introduction to QFT book? I'm looking for something that just barely classifies as a textbook, with lots of tutorial verbiage between the equations. Thanks in advance.

I have a question in Srednicki's book regarding path integrals, but first I'll set it up so that no familiarity of the book is required to answer the question. The vacuum to vacuum transition amplitude for the photon field in the presence of a source is given by: <0|0>_J=\int \mathcal D A...

********************** Hi, I did some searching and found quite some questions about the Srednicki book on QFT, so apparently there are more people working with it. I thought maybe it would be a nice idea to have some sort of "questions about QFT encountered while reading Srednicki's...

Hi, Is it meaningful to inquire about the classical limit of a quantum field theory? Specifically, is it possible to formally recover NRQM and RQM from quantum field theory? I am told this is a wrong/ill-posed question, so I wanted to get a clearer idea about it...after all, in a QM course...

According to Steven Weinberg ('The quantum theory of fields', vol.1), the principle of gauge invariance stems from the fact, that one cannot build the 4-vector field from the creation/annihilation operators of massless bosons with spin >= 1. This '4-vector field' ('vector potential'), if we...

What preliminary knowledge of QM should I know before learning QFT, or should I learn QFT in parallel with me learning QM?

Hi, In Lewis Ryder's QFT book on page 160, the propagator for the case when the Lagrangian can be written as L = \frac{p^2}{2m} + V(q) is given as \langle q_f t_f|q_i t_i \rangle = \lim_{n\rightarrow\infty}\left(\frac{m}{i\hbar\tau}\right)^{(n+1)/2}\int...

Has anyone read the book (at least the first volume) by Eberhard Zeidler called "Quantum Field Theory: A Bridge Between Mathematicians and Physicists"? I started reading it last year and thought it was amazing. It's so ambitiously comprehensive! But no-one ever mentions it, and it's not in...

Are there any attempts to synthesize between these two theories? I mean are there methods from QFT being used in QC and vice versa? I asked one professor from my univ if I were to research under his belt in QC, would I need some QFT knowledge and he said not. So I wonder are they really...

What is the general rule behind why for any given lagrangian (QED/QCD show this) that any vectors or tensors contract indices? I know it must be something simple, but I just can't think of it offhand. QED : F_{\mu\nu}F^{\mu\nu} Proca (massive vector): A_\mu A^\mu QCD : G^{\alpha}_{\mu\nu}...

hi all, i have a question regarding page 81 in Srednicki's QFT book. He states there that the sum over all connected diagrams with a single source is zero. Then he says that if you replace this single source by an arbitrary subdiagram the sum will still be zero. Can somebody explain why this...

The historic roots of string theory are in an explanation of the strong force. Nowadays QCD is the accepted theory of strong force. But having heard several lectures on the large N limit (SU(N)) of gauge theories it seems these theories start to looklike string theories in this limit. I believe...

Hello all Since there seems that quite many here have followed Professor Srednickis QFT book, I want to ask a couple of question I have from his chapter on Supersymmetry. i) on page 617 he defines the kinetic term of the Chiral Superfields as: L_{\text{kin}} = \Phi^{\dagger} \exp(-2gV)...

Hi all, I'm trying to teach myself the basics of QFT. I'm using Peskin and Schroeder, and having a few difficulties reproducing a couple of the calculations. I don't think I've made careless algebraic slips, so before I show my working explicitly and beg for proof-reading I'd like to ask a...

Does anyone have any ideas? Marcus, do you have?

Does fact that QFT in imaginary time is equivalent to QSP represents the proof that many-particle quantum physics is equivalent to quantum theory of fields? To elaborate a little, I had some discussion with some engineers, and when I was explaining them Standard Model I had to invoke concepts...

Consider the SUSY charge Q= \int d^3y~ \sigma^\mu \chi~ ~\partial_\mu \phi^\dagger~ The SUSY transformation of fields, let's say of the scalar field, can be found using the commutator i [ \epsilon \cdot Q, \phi(x)] = \delta \phi(x) using the equal time commutator...