# What is Peskin: Definition and 115 Discussions

Aaron Dan Peskin (born June 17, 1964) is an American elected official in San Francisco, California. He serves as a member of the San Francisco Board of Supervisors representing Supervisorial District 3, and is currently Dean of the Board. He was elected in 2015, having previously served two terms in 2001–2009.District 3 includes the neighborhoods of North Beach, Chinatown, Telegraph Hill, North Waterfront, Financial District, Nob Hill, Union Square, Maiden Lane, Polk Gulch and part of Russian Hill.

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1. ### High Energy Possible typo in Peskin & Schroeder's QFT Textbook (p. 666)?

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 -...

7. ### Weyl Spinors Transformation, QFT1, Peskin, Chapter 3

\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...
8. ### I Ground State in Peskin and Schroeder

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...
9. ### The meaning of the "physical" electron charge in Peskin (Chap 7)

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...
10. ### A mathematical derivation in Peskin and Schroeder on page 722.

My attempt at solution is in the HW template, though this is not an HW question.
11. ### Calculation of g-factor correction in Peskin p. 196

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...
12. ### A A possible mistake in Equations (18.204)-(18.205) in Peskin & Schroeder

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...

15. G

### A Fermion mass terms in Peskin and Schroeder's book

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...
16. ### A Smart Algebra of Exp. on Pg 191 of Peskin & Schroeder

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...
17. ### ##CP^N## model in Peskin & Schroeder problem 13.3

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?

21. ### A Yang-Mills 3 boson Lagrangian term in Peskin and Schroeder

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...
22. ### The superficial degree of divergence in Peskin and Schroeder

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...
23. ### I How to Calculate Page 14 of Peskin Schroeder without Getting Stuck?

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...
24. ### Trouble with Peskin QFT textbook

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...
25. ### Peskin complex scalar field current

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...

30. ### Peskin and Schroeder eq. 18.84

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...
31. ### A Peskin Shroeder quantum field 7.31 pag 221

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!
32. ### Peskin shroeder quantum field 7.31 pag 221

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!
33. ### Peskin & Schroeder - page 5 - Computation of ##\mathcal{M}##

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...
34. ### Peskin and Schroeder - page 4 - spin and cross section

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...
35. ### Peskin and Schroeder - page 4 - choice of notation

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...
36. ### Peskin and Schroeder page 38

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...
37. ### Peskin and Schroeder - Derivation of equation (2.45)

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) -...
38. ### S matrix Unitarity Proof, pg 298 Peskin Schroeder

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...
39. ### Contour Integral from Peskin & Schroeder Intro to QFT

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...
40. ### Solving Peskin Equation 12.66 Problem

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...
41. ### Cross Section Calc. in Peskin QFT - How to Deal with g^μν.g_μν?

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...
42. ### Questions from Peskin and Schroeder

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...
43. ### Dimensional Regularization in Peskin

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...
44. ### Momentum states normalization

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}}...
45. ### Symmetry in Integrals: Peskin's Equation 6.43 & 6.44

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...
46. ### Verifying Ward Identity: Need Help With Algebra?

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.
47. ### Have you conquered Peskin's computation challenges?

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.
48. ### Question on peskin and schroeder

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...
49. ### Understanding Peskin Eq 3.50-3.53 and Dirac Spinor

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) -...
50. ### Peskin QFT - Noether's theorem

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...