Peskin schroeder Definition and 23 Threads

I've managed to account for all the terms except for two, which seem to have a minus sign I cannot get rid of. When expanding the variation, one of them comes from the ##\phi## variation: $$-i \partial^\mu \phi \epsilon^\dagger \sigma^2 \partial_\mu \chi^* =-i \partial^\mu \phi \partial_\mu...

In Peskin and Schroeder's QFT book, while deriving the cross section formula for particles ##A## and ##B##, a Dirac delta appears in Eq 4.77: \begin{align} \nonumber \int d\bar{k}^z_A \, \left. \delta ( F ( \bar{k}^z_A ) ) \right\vert_{\bar{k}^\perp_A = k^\perp_A, \, \bar{k}^\perp_B = k^\perp_B}...

I am reading Peskin-Schroeder's QFT text, and there on pg. 98 Equation (4.56) they derive the expression for the vacuum energy density (relative to the zero of energy set by ##H_0|0\rangle = 0##): $$ \frac{E_0}{\rm{Volume}} = \frac{i\,\sum\text{(all disconnected pieces)}}{(2\pi)^4\,\delta^4(0)}\...

I am stuck at the final part where one is supposed to show that the derivative of the second term of the action gives the mass term in the Majorana equation. For $$\chi^T\sigma^2\chi = -(\chi^\dagger\sigma^2\chi^*)^*$$ we get $$\frac{\delta}{\delta\chi^\dagger}(\chi^\dagger\sigma^2\chi^*)^*$$...

\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...

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...

I don't understand a step in the derivation of the propagator of a scalar field as presented in page 291 of Peskin and Schroeder. How do we go from: $$-\frac{\delta}{\delta J(x_1)} \frac{\delta}{\delta J(x_2)} \text{exp}[-\frac{1}{2} \int d^4 x \; d^4 y \; J(x) D_F (x-y) J(y)]|_{J=0}$$ To...

$$<p_1 p_2|p_A p_B> = \sqrt{2E_1 2E_2 2E_A 2E_B}<0|a_1 a_2 a_{A}^{\dagger} a_{B}^{\dagger} |0>$$ $$=2E_A2E_B(2\pi)^6(\delta^{(3)}(p_A-p_1)\delta{(3)}(p_B-p_2) + \delta^{(3)}(p_A-p_2)\delta^{(3)}(p_B-p_1))$$ The identity above seemed easy, until I tried to prove it. I figured I could work this...

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! 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)...

In Peskin's textbook section 7.3 The Optical Theorem for Feynman Diagrams(Page233), he said it is easy to check that the corresponding t- and u-channel diagrams have no branch cut singularities for s above threshold. But I can't figure out how to prove it. Can angone help me? Thanks!

I'm self-studying QFT and attempting exercise 2.2 on Peskin & Schroeder. First off, I'm a bit confused on the logic the authors use in the quantization process. They first expand the fields in terms of these ##a_{\vec{p}},a_{\vec{p}}^\dagger## operators which, if I understand correctly, is...

In Peskin's textbook chapter 7 Radiative Corrections: Some formal developments (page 229), he said the Z factors are irrelevant for calculations at the leading order of perturbation theory, but are important in the calculation or higher-order corrections. My question is how can the Z factor be...

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...

In the Peskin&Schröder's QFT book there's an exercise that's about a pair of scalar fields, ##\phi_1## and ##\phi_2##, having the field equations ##\left(\partial^{\mu}\partial_{\mu}+m^2 \right)\phi_1 = 0## ##\left(\partial^{\mu}\partial_{\mu}+m^2 \right)\phi_2 = 0## where the mass parameter...

I've discovered a potential treasure horde tucked away in the deep dark folds of the world wide web. A 1625 page mammoth on all aspects of quantum field theory by Prof. Hagen Kleinert. There's a draft ed. for free available here -...

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...

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...

Hi, May you please asdvise me where in Peskin Schroeder it is described how to derive 1/r potential for electrodynamics... (I mean from quantum field point of view) Thanks

Dear PF, I have one question form Peskin Schroeder...could you pls help me It is very simple question... Since I don't know how to write formulas here I put my question in attachment. Thank you very much.

Sorry for bothering... How does righthand side of formula 5.94 is derived from its left handside after some approximation? Probably it is very simple question but I could't get that expression:confused: Thank u very much

Gentlemen, Could you help me please, I am sure it is not even worthy of your attention, but anyway... In Peskin, Schroeder - from expresion <0|\phi(x)\phi(y)|0> survives <0|a_p a_q^\dag|0> so it creates one-particle state |q> at position y and another one-particle state | p> at postion...