Peskin Definition and 115 Threads

Hi everyone! I'm going through Peskin & Schroeder's Chapter 19 (Perturbation Theory Anomalies) and it seems to be that equation 19.74 in page 666 has a minus sign missing on the RHS. Namely, I think the correct equation should read \begin{align} (i\not\!\! D)^2 = -D^2 -...

In Peskin P85: It says the Time-ordered exponential is just a notation，in my understanding, it means $$\begin{aligned} &T\left\{ \exp \left[ -i\int_{t_0}^t{d}t^{\prime}H_I\left( t^{\prime} \right) \right] \right\}\\ &\ne T\left\{ 1+(-i)\int_{t_0}^t{d}t_1H_I\left( t_1 \right)...

Hey all, I am currently having trouble understanding equation (12.52) in Peskin's QFT book. Specifically the term for external leg corrections, in which they tack on an additional prefactor of ##(-ig)##. Normally with external leg prefactors, we don't see the coupling constant multiplied onto...

Hi all, I am currently reading through Peskin's QFT book and have a question regarding an equation that seems very simple in nature: On page 121, below equation (4.121), there is an equation ##(p'-p)^2 = -|\textbf{p}'-\textbf{p}|^2 + \mathcal{O}(\textbf{p}^4)## I was just wondering where exactly...

I'm using a Peskin & Schroeder's copy that looks like it has all typos corrected and I wonder if the following is an undetected typo: On pp. 103 and on the RHS of the bra expression just after (4.68), shouldn't the ##\phi_f({\mathbf p}_f)## be complex conjugated?

In chapter 20 of Peskin&Schroeder about spontaneous symmetry breaking, he considers and example on page 696 of spontaneous symmetry breaking of SU(3) gauge group with generators taken in adjoint representation. Covariant derivative is defined with: $$D_\mu\phi_a = \partial\phi_a +...

\begin{align} \psi_L \rightarrow (1-i \vec{\theta} . \frac{{\vec\sigma}}{2} - \vec\beta . \frac{\vec\sigma}{2}) \psi_L \\ \psi_R \rightarrow (1-i \vec{\theta} . \frac{{\vec\sigma}}{2} + \vec\beta . \frac{\vec\sigma}{2}) \psi_R \end{align} I really cannot evaluate these from boost and rotation...

In P&S, it is shown that $$e^{-iHT}\ket{0}=e^{-iH_{0}T}\ket{\Omega}\bra{\Omega}\ket{0}+\sum_{n\neq 0}e^{-iE_nT}\ket{n}\bra{n}\ket{0}$$. It is then claimed that by letting $$T\to (\infty(1-i\epsilon)) $$ that the other terms die off much quicker than $$e^{-iE_0T}$$, but my question is why is this...

On p. 246 in the Peskin QFT textbook, below is stated where Z3 is defined as the residue of the q2 = 0 pole, explicitly as $$Z_3=\frac{1}{1-\Pi(0)}$$ and e is the bare charge. In advance, the exact photon two point function is calculated as $$\frac{-ig_{\mu\nu}}{q^2(1-\Pi(q^2))}$$ Though...

My attempt at solution is in the HW template, though this is not an HW question.

I'm reading peskin QFT textbook. In page 196 eq. (6.58) it says $$F_2(q^2=0)=\frac{\alpha}{2\pi}\int ^1_0 dx dy dz \delta (x+y+z-1) \frac{2m^2z(1-z)}{m^2(1-z)^2}\\=\frac{\alpha}{\pi}\int ^1_0 dz\int ^{1-z}_0 dy \frac{z}{1-z}=\frac{\alpha}{2\pi}$$ I confirmed the conversion from the first line...

They write the following on page 646: Now, equation (17.17) reads: ##\alpha_s(Q) = \frac{2\pi}{b_0 \log(Q/\Lambda)}##, so if I plug ##\alpha_s(Q^2) = \frac{2\pi}{b_0 \log(Q^2/\Lambda)}## into Eq. (18.204) I get: ##\frac{a^f_n}{4b_0}\frac{1}{\log(Q^2/\Lambda)}M^-_{fn}##. Perhaps the...

They write on page 618: where for those who don't have the book at hand, I'll write the related equations: $$(18.94) \ \ \ \sigma(e^+ e^- \to \text{hadrons})=\frac{4\pi \alpha^2}{s} [ I am c^1(q^2)+Im c^{\bar{q}q}(q^2) \langle 0| m\bar{q}q|0\rangle+ $$ $$+Im c^{F^2}(q^2)\langle 0 |...

On page 105 of Peskin and Schroeder's book it says that the integral over ##d^2b## in the expression: $$d\sigma = \left(\Pi_f \frac{d^3 p_f}{(2\pi)^3}\frac{1}{2E_f}\right) \int d^2b\left(\Pi_{i=A,B} \int \frac{d^3 k_i}{(2\pi)^3}\frac{\phi_i(k_i)}{\sqrt{2E_i}} \int \frac{d^3...

I'm currently looking at how fermion masses are produced via the Higgs mechanism in "An Introduction to Quantum Field Theory" by Peskin and Schroeder. It all makes a lot of sense and I've been fine with it so far, but I ended up getting stuck on something that's driving me nuts. I feel silly...

Hi all, I have a problem working out the algebra of the following expression in Peskin & Schroeder in a smart way to give the result. It is on page 191, regarding the numerator of the vertex correction function. We want to get from the LHS to the RHS of the following expression...

My naive attempt to expand the log was##log(k2+A2−λ)=log[(k2−λ)(1+A2(k2−λ))]=log(k2−λ)+log(1+A2(k2−λ))≈log(k2−λ)+A2(k2−λ)##but it did not help me so far since the second term vanishes. Can someone point me to the right direction?

P&S had calculated this expression almost explicitly, except that I didn't find a way to exchange the $$\nu \lambda$$ indices, but I'm sure the below identity is used, $$ \begin{aligned}\left(\overline{u}_{1 L} \overline{\sigma}^{\mu} \sigma^{\nu} \overline{\sigma}^{\lambda} u_{2...

I am trying to verify 2.50 on pg 27 of peskin but did it in my own way, I am sure i made some mistakes here but i was able to get the right answer. Can someone highlight why some of these steps are invalid and explain how peskin git from 2.50 to the first step used in the text for 2.51. And yes...

Hi! Just a couple questions on the Compton scattering calculation in P&S. I feel like I'm missing something very simple here but can't quite figure out what it is. On page 166, the amplitude to be evaluated is $$ i\mathcal M = -ie^2 \epsilon_\mu(k)\epsilon^*_\nu(k^\prime) u_R^\dagger(p^\prime)...

Hi all, I'm not certain if this is the correct section of the forum for this thread but I'm trying to understand ghosts and BRST symmetry and my starting point is chapter 16 of Peskin and Schroeder where I've found a nagging issue. My issue is regarding the derivation of equation (16.6) on...

Homework Statement I have in the picture attached a screenshot from Peskin's textbook. I don't understand how did they get that for the two last diagrams that ##D=-2##. The question is from pages 316-317 of Peskin's textbook. Homework Equations $$D=4-N_{\gamma}-3/2N_e$$ where ##N_e##=number of...

Hi Everybody, I am trying to do the calculation of Peskin Schroeder page 14, namely the first block of equations. The author moves from: U(t) = \frac{1}{2 \pi^3} \int d^3p e^{-i(p^2/2m)t} e^{ip \cdot (x-x_0)}. to U(t) = (\frac{m}{2 \pi i t})^{3/2} e^{im(x-x_0)^2/2t}. I guess the way to go...

I'm trying to work through a scattering calculation in the Peskin QFT textbook in chapter 5, specifically getting equation 5.10. They take two bracketed terms 4[p'^{\mu}p^{\nu}+p'^{\nu}p^{\mu}-g^{\mu\nu}(p \cdot p'+m_e^2)] and 4[k_{\mu}k'_{\nu}+k_{\nu}k'_{\mu}-g_{\mu\nu}(k \cdot...

Homework Statement i'm trying to calculate the charge operator for a complex scalar field. I've got the overal problem right but I'm confused about this: On page 18 of Peskin, it is written that the conserved current of a complex scalar field, associated with the transformation ##\phi...

Hey there I'm trying to reconstruct the entire table of all Dirac bilinears under C, P, T and CPT transformations of page 71 and hit a wall on charge conjugation. It's a computational problem, really. Here's a specific problem: Equation 3.145 we have $$-i\gamma ^2 \left( \psi ^{\dagger...

Hello! I am reading Peskin's book on QFT and I reached a part (in chapter 4) where he is analyzing the two-point correlation function for ##\phi^4## theory. At a point he wants to find the evolution in time of ##\phi##, under this Hamiltonian (which is basically the Klein-Gordon - ##H_0## - one...

Hello! Those who used Peskin's book on qft, in chapter 2, Causality (2.4) there are 2 integrals for ##D(x-y)##. Can someone explain to me how does he solve them, as I tried for a bit and didn't manage to do them (actually to get the behavior as ##t \to \infty##). Thank you!

How the authors came to the conclusion (eq. 4.25) that $$ U(t,t')=e^{iH_0(t-t_0)} e^{-iH(t-t')} e^{-iH_0(t'-t_0)} $$

Homework Statement So I am self-studying the book of Peskin&Schroeder, and there is something I don't understand on page 616. In eq. 18.80, there is a numerical factor of ½ and going from e2 to α will introduce a factor 4π when proceeding to eq. 18.84. But then there should be a numerical...

I can't do the derivative 7.31 at page 221. I try to do the derivative dΣ/dpslash, but my result is different from 7.31 Someone can help me writhing the right derivative? Thank you in advance!

I can't do the derivative 7.31 at page 221. I try to do the derivative of Σ in dp slash, but my result is different from 7.31 Someone can help me writhing the right derivative? Thank you in advance!

The following is taken from page 5 of Peskin and Schroeder. It talks about the computation of ##\mathcal{M}## for the annihilation reaction ##e^{+}e^{-}\rightarrow \mu^{+}\mu^{-}##. Even for this simplest of QED processes, the exact expression for ##\mathcal{M}## is not known. Actually this...

In chapter 1 of Peskin and Schroeder, the reaction ##e^{+}e^{-}\rightarrow \mu^{+}\mu^{-}## is studied in detail. The related following paragraph is taken from page 4 of Peskin and Schroeder: Both the electron and the muon have spin ##1/2##, so their spin orientations must be specified. It is...

In page 4, Peskin and Schroeder has the following diagram: The diagram shows the collision of an electron beam and a positron beam to produce a ##\mu^{+}## beam a ##\mu^{-}## beam. My question is this: The electron and positron beams are shown to have momenta ##\textbf{p}## and...

In page 39, Peskin and Schroeder write that (3.15) ##{\bf{J}}={\bf{x}} \times{\bf{p}}= {\bf{x}}\times(-i \nabla) ## can be used to derive the Lorentz algebra (3.12) for the rotation group: ##[J^{i},J^{j}] = i \epsilon^{ijk}J^{k}##. I am trying to prove it. Here's my attempt. Can you please...

I'm having trouble deriving equation (2.45) on page 25. In particular, in the derivation of ##i\frac{\partial}{\partial t}\pi({\bf{x}},t) = -i(-\nabla^{2}+m^{2}) \phi({\bf{x}},t)##, I need to show that ##\frac{1}{2}\pi({\bf{x}},t) \phi({\bf{x'}},t)(-\nabla^{2}+m^{2}) \phi({\bf{x'}},t) -...

I have a question regarding a derivation in Peskin and Schroeder's QFT book. On page 298, he is discussing a method for defining a gauge invariant S matrix. He does this by defining projection operators ##P_0## that project general particle states into gauge invariant states, and then defining...

1. I'm having some trouble with some of the contour integrals covered in Chapter 2 of Peskin & Schroeder's Intro to QTF. I'm not so much as looking for answers to the integral (in fact, the answers are given in the textbook), but I was hoping someone could point me to some resources to use to...

I have a problem with that equation. I understand (dont know if I'm right) that ##p = - M##. But than, isn't ##g\left( { - {{{p^2}} \over {{M^2}}}} \right)## just equal ##g\left( { - 1} \right)##? And my bigest problem: in 12.66 ##\left[ {p{\partial \over {\partial p}} - \beta \left( \lambda...

Hello, I'm doing the calculation of the unpolarized cross section in peskin QFT and i am facing a little obstacle, after the calculation of two traces i get terms containing ##g^{\mu \nu}.g_{\mu \nu}## and my question is how to deal with them? does this product equal to a numerical value...

On page 42 of Peskin, at the bottom they say that the next transformation should follow: ##[i\gamma^\mu\partial_\mu - m ]\psi (x) \rightarrow [i\gamma^\mu(\Lambda^{-1})^\nu_\mu \partial_\nu - m ] \Lambda_{1/2} \psi (\Lambda^{-1}x)## But why does the factor ##\Lambda_{1/2}## appear there...

Homework Statement I'm trying to understand dimensional regularization with Peskin. There is a transitions that is not clear. Homework Equations On page 250, the general expression for the d-dimensional integral is given: ##\int \frac{d^d...

What is the value of ##\left\langle {{\bf{p}}|{\bf{p}}} \right\rangle ## when ##a_{\bf{k}}^ + k\left| 0 \right\rangle = \sqrt {2{E_{\bf{p}}}} \left| 0 \right\rangle ##? (like in Peskin) I suppose that ##\left\langle {\bf{k}} \right|{a_{\bf{k}}}{\bf{P}}a_{\bf{k}}^ + \left| {\bf{k}}...

In peskin p. 192, they says that the denominator (that is equation 6.43) is symmetric under x<--> y. Thay all so say that you can see it in equation 6.44. But one of the terms in the denominetor is y*q which dose not have that symmetry! Looking at (6.43) and removing the summetric parts leave...

In peskin p. 160 forth paragraph they say to verefy Ward identity in equation 5.74. I don't succeed, they say some algebra is needed. I conjecture that this some algebra is what i miss. Any help will be appreciated - thanks a lot.

Hello everyone,Has anybody already did the computations to reach equations 10.41, 10.44 and 10.45 in Peskin's book? It would be very much appreciated and useful.

If you go to page 20 and 21 where the Fourier expansion of the klein-gordon field operator is derived, you'll see equation (2.27). Now there are some small details of this whole calculation that I'm confused about. I followed all the way through to (2.25), but here I feel a bit weird. Isn't he...

Hi, all I'm reading peskin by myself. I can't understand from eq(3.50) to eq(3.53). i) What should I interpret \sqrt{p\cdot\sigma}? I guess below, but I can't understand \sqrt{\;\;} of matrices. \begin{eqnarray} p\cdot\sigma=E \left(\begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array}\right) -...

Hi all Maybe you could help me understanding this bit from the beginning of the book (peskin - intro to QFT). Homework Statement In section 2.2, subsection "Noether's theorem" he first wants to show that continuous transformations on the fields that leave the equations of motion...