Schroeder Definition and 68 Threads

G'day from Australia! I loved physics and maths in high school and I have been trying to teach myself some physics on the side whilst doing another course at university. So far, I have read and done problems from "Introduction to Thermal Physics (Schroeder)" [I got up to around 7.4] and...

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 +...

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...

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

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...

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...

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)...

Hey guys, so I am reading this book and on pages 89-90, the author says: "Increasing temperature correspond to a decreasing slope on Entropy vs Energy graph", then a sample graph is provided, and both in that graph and in the numerical analysis given in page 87 the slope is observed to be an...

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...

Hello all. I am studying Thermal Physics from Schroeder's book. I really like this book, but the number of worked examples and solved problems is minimum. Could you please suggest me a complemetary book with worked examples and problems? The ideal book should be similar to Schroeder's, with the...

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...

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...

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...

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) -...

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...

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...

Hi, I'm facing a slight problem with getting a good version of the Schroeder: Introduction to thermal physics. According to my lecturer the newest 2013 international edition by Pearson (ISBN: 9781292026213) is not recommended, as it lacks some aspects. And anyway the course is built around the...

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...

I am having some problems in evaluating the current problem's question (b)... I have reached the point (writing only the term which I have problem with): A_{3}= - \frac{1}{2} \int_{t_{0}}^{t} dt' dt'' \int d^{3}x \int d^{3}y j(x,t') j(y,t'') D_{F}(x-y) So for some unknown reasons, I cannot...

In page 30 of book "An introduction to quantum field theory" by Peskin and Schroeder in the derivation of Klein-Gordon propagator, why p^0=-E_p in the second step in equation (2.54). and why change "ip(x-y)" to "-ip(x-y)"? I thought a lot time, but get no idea. Thank you for your giving me an...

**Please can an administrator move this to the "Maths and Physics Learning Materials" section- I can't post there for some reason. Thank you!** Hello, I am interested in learning some more technical Quantum Mechanics, and was wondering how accessible the Peskin and Schroeder textbook is as...

Hi I am studying qft with worldwidely used text, written by Peskin and Schroeder, An introduction to qft. I have trouble with the calculation of thr numerator on pp. 192. I got additional term ## 2m(z-xy)(mγ^μ - p^μ) ## between spinors, which seems not vanishing. Is there any idea to treat this...

Hello Everybody, I am trying to get the second line of 2.54 from the last line; I want to get: \int \frac{d^3p}{{2 \pi}^3} \{ \frac{1}{2 E_\vec{p}} e^{-ip \cdot (x-y) }|_{p^0 = E_\vec{p}} + \frac{1}{-2 E_\vec{p}} e^{-ip \cdot (x-y) }|_{p^0 = -E_\vec{p}} \}, from \int...

Hi, I am currently studying quantum field theory with worldwidely used text written by Peskin and Schroeder. On page 165 of that text it says, " the amplitude vanishes unless the final photon is right-handed." But I cannot figure out how it works. With ε = (0,1,i,0), I get same expression...

In Peskin and Schroeder at page 323 second paragraph the author state 'To obtain finite results for an amplitude involving divergent diagrams, we have so far used the following procedure: Compute the diagrams using a regulator to obtain an expression that depends on the bare mass (m0), the...

At page 285 in Peskin and Schroeder's Introduction to quantum field theory the author defines the integration measure D\phi = \Pi_i d\phi(x_i) where space-time is being discretised into a square lattice of volume L^4. He proceeds by Fourier-transforming \phi(k_n) = \frac{1}{V} \sum_n e^{-i...

I'm reading about path integrals in Peskin and Schroeder's Introduction to Quantum field theory and there is a few things in the text which I find puzzling. At page 283 in the section about correlation functions we are considering the object (equation 9.15) \int D\phi(x) \phi(x_1) \phi(x_2)...

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...

I'm a bit confused by something Peskin & Schroeder say about differential cross sections. In my printing, this is on page 101 in the paragraph preceding the one that contains eq. 4.62: "In the simplest case, where there are only two final-state particles, this leaves only two unconstrained...

I had a question about about the integration measure for the path integral after a unitary change of variables. First they consider a 4D spacetime lattice with volume L^4. The measure is \mathcal{D}\phi = \prod_i d\phi(x_i) They expand the field variables in a Fourier series...

Hi all, I'm stuck with proving the last step of (2.51) in Peskin and Schroeder: $$\begin{align} D(x-y) &= \frac{1}{4\pi^2}\int^\infty_m dE \sqrt{E^2 - m^2}e^{-iEt}\\ & \approx_{t \to \infty}\ \ e^{-imt}\end{align}$$ I've read on another post that the solution is to use the method of...

Hi all, A friend and I are working through Peskin and Schroeder, and we're both stumped with only the fourth equation! The interaction in question is e^+ + e^- \to \mu^+ + \mu^- with a virtual photon as the inner branch. P&S state that \mathcal{M}\propto \langle \mu^+\mu^- | H_I | \gamma...

My question concerns the 1/2 factor in the exponential of Eq. (3.49) of Peskin and Schroeder. This equation concerns the Lorentz boost transformation of a spinor along the z-axis (or 3-direction). According to Eq. (3.26): S^{03} = -\frac{i}{2}\begin{bmatrix}\sigma^3 & 0 \\0 &...

This isn't a HW problem - I am just having a hard time following one of his examples. On page 47 near Eq. 1.71 he says "As a quick example, consider a drop of food coloring added to a glass of water. Imagine that the dye has already spread uniformly through half of the glass. How long would...

I am trying to show that (for 4x4 matrices) the representation given by equation 3.18 (Peskin and Schroeder, page 39): (J^{\mu\nu})_{\alpha\beta} =i(\delta^{\mu}_{\alpha}\delta^{\nu}_{\beta}-\delta^{\mu}_{\beta}\delta^{\nu}_{\alpha}) implies the commutation relations in 3.17...

This doubt is about a text in Peskin Schroeder Pg 86. I reproduce it here. -------------------------------- U(t,t') satisfies the same differential equation (4.18), i \frac{\partial}{\partial t} U(t,t') = H_I(t) U(t,t') but now with the initial condition U=1 for t=t'. From this...

Hi, I am learning QFT in the Peskin/Schroeder book and I found 4.56 on page 98 really weird, it is: \rho_{vaccum\: energy\: density} = \frac{i\sum_{all\: disconnected\: diagramms}amplitude}{(2\pi)^4\delta^{(4)}(0)} The authors do not comment really this result, but could someone tell me at...

Homework Statement Problem 3.4e of Peskin & Schroeder Introduction to Quantum Field Theory. Quantize the spinor theory of item (a) of this exercise, where the spinor \chi is the first two components of the Dirac spinor (\psi_L). Find a Hermitean Hamiltonian and the correct...

Hi I am struggling to justify D(x-y) \approx e^{-i m t} as t \rightarrow \infty from \int dE \sqrt{E^2-m^2} e^{-i E t} . I thought I might get some insight from discretizing, as e^{-i m t} \sum_{n=0}^{\infty} \epsilon \sqrt{ n \epsilon ( 2 m + n \epsilon ) } e^{-i...

Here is a list of questions that have been posted in the past concerning Peskin & Schroeder, An Introduction to Quantum Field Theory. If you have a question about the book, you can look here first to see if it has already been answered. One caveat, sometimes the page numbering that I used can be...