Recent content by Theage

Thank you! I was just getting lost in the indices, but now I understand.

On page 51 Peskin and Schroeder are beginning to derive basic Fierz interchange relations using two-component right-handed spinors. They start by stating the trivial (but tedious) Pauli sigma identity...

Homework Statement [/B] Sakurai problem 1.20: find the linear combination of spin-up and spin-down S_z eigenkets that maximizes the uncertainty product \langle(\Delta S_x)^2\rangle\langle(\Delta S_y)^2\rangle. Homework Equations [/B] In general, we can write a normalized spin-space ket as...

Homework Statement I am currently working on a seemingly straightforward eigenvalue problem appearing as problem 1.8 in Sakurai's Modern QM. He asks us to find an eigenket \vert\vec S\cdot\hat n;+\rangle with \vec S\cdot\hat n\vert\vec S\cdot\hat n;+\rangle = \frac\hbar 2\vert\vec S\cdot\hat...

This is one of the key "weirdnesses" of quantum mechanics. When we build a Hamiltonian to specify a system, we take a classical standpoint - the formula E=\frac{p^2}{2m} is inherently classical since p=mv\implies\frac{p^2}{2m}=\frac{m^2v^2}{2m} = \frac{1}{2}mv^2 = E_{free}. Indeed, for a free...

Thanks! Amazingly the 2\pi's work out using Gaussian integral methods.

This type of integration is a special case of something that occurs over and over in QM and QFT (it's everywhere in Peskin and Schroeder), but I am having a bit of trouble working out the details. Set \hbar=1 and consider the propagation amplitude for a free, nonrelativistic particle to move...

Homework Statement I'm reading Peskin and Schroeder to the best of my ability. Other than a few integration tricks that escaped me I made it through chapter 2 with no trouble, but the beginning of chapter three, "Lorentz Invariance in Wave Equations", has me stumped. They are going through a...

Note: I'm posting this in the Quantum Physics forum since it doesn't really apply to HEP or particle physics (just scalar QFT). Hopefully this is the right forum. In Peskin and Schroeder, one reaches the following equation for the spacetime Klein-Gordon field: $$\phi(x,t)=\int...

The most obvious way to explain these approximations is truncating the Taylor series about zero. If you haven't seen these, they're basically infinite series for the trig functions. In the case of sine and cosine, they are $$\sin\theta = \sum_{n=0}^\infty \frac{(-1)^n...

In Srednicki's text on quantum field theory, he has a chapter on quantum Lorentz invariance. He presents the commutation relations between the generators of the Lorentz group (equation 2.16) as follows: $$[M^{\mu\nu},M^{\rho\sigma}] =...

Greetings, I've been addicted to mathematics and physics for about a year now. I discovered calculus through MIT OCW and took their 18.01 and 18.02 courses online, and from that point onward I've been hooked on learning. I'm currently self-studying quantum field theory from Srednicki's great...