Recent content by jameson2

Homework Statement Given the Lagrangian density L(\phi^{\mu})=-\frac{1}{2}(\partial_{\mu}\phi^{\nu})(\partial^{\mu}\phi_{\nu}) + \frac{1}{2}(\partial_{\mu}\phi^{\mu})^2+\frac{m^2}{2}(\phi^{\mu}\phi_{\mu}) and gauge transformation \phi^{\mu}\rightarrow \phi^{\mu} + \partial^{\mu}\alpha...

I'm having a bit of trouble working through the induction proof they give in the book. The step I don't understand is: (page 90 in the book, halfway down) N(\phi_2...\phi_m)\phi_1^+ + [\phi_1^+,N(\phi_2...\phi_m)] = N(\phi_1^+\phi_2...\phi_m) + N([\phi_1^+,\phi_2^-]\phi_3...\phi_m +...

I'm working through the start of the Quantum Field Theory book by Peskin and Schroeder. The first section deals with an electron and positron colliding to give a positive and negative muon traveling along a line at an angle theta to the line of the e,p collision.(This is using center of mass...

Ah, that makes sense. The last thing I need is converting seconds to units of magnetic field. My best guess so far is, say I have 1 second (hypothetically), then frequency is 1, and then I just multiply this by h, divide by g and the Bohr magneton, and say it's that many teslas? Seems to just...

For the B/I ratio, 0.00427 is the experimental value compared to 0.0048 from the theory. My thinking was basically like this: The original deriviation for a current carrying loop assumes an infinitely thin loop. But in a Helmholtz coil (320 turns in my case), it definitely has a spatial extent...

Yes, that is my experiment. I didn't want to put in a huge amount of detail in case it put people off reading my questions... So the DC field is large and the AC just moves it up and down past resonance, so I can see the power absorption on the oscilloscope? You can see by the amount of...

I've a few questions about an EPR experiment I did recently. It involved setting up a Helmholtz pair, placing a sample in a uniform field inside the pair, and observing results on an oscilloscope. You can calculate the field at the centre of a Helmholtz pair using the formula for one...

So just get \theta^{10} + 5\theta^8\frac{1}{\gamma^2} on the bottom line? Is this what it means by only keep the leading power of gamma? I'm still not sure how to go about integrating this though.

Homework Statement Given the formula for power radiated into a solid angle, evaluate the total power radiated to all angles by an ultra relativistic particle, keeping the leading power of \gamma only. Homework Equations The power formula: \frac{dP'}{d\Omega}=\frac{q^2 \alpha^2}{\pi^2...

Homework Statement Given the Lagrangian density: L= -\frac{1}{2} \partial_{\mu}A_\nu \partial^{\mu}A^\nu -\frac{1}{c}J_\mu A^\mu (a) find the Euler Lagrange equations of motion. Under what assumptions are they the Maxwell equations of electrodynamics? (b) Show that this Lagrangian...

Homework Statement Given the Lagrangian density: L= -\frac{1}{2} \partial_{\mu}A_\nu \partial^{\mu}A^\nu -\frac{1}{c}J_\mu A^\mu (a) find the Euler Lagrange equations of motion. Under what assumptions are they the Maxwell equations of electrodynamics? (b) Show that this Lagrangian...

Homework Statement I have to evaluate P(t)=|<+,n|\exp{\frac{-iHt}{\hbar}}|+,n>|^2 where H=\hbar \omega_0 S_z + \hbar \omega a^+a+\hbar \lambda(a^+S_-+aS_+) and |+,n>=\left( \begin{array}{c} 1\\0 \end{array} \right) Homework Equations Eigenvalues of H are E_\pm =\hbar \omega (n...

Homework Statement Given the Hamiltonian for the harmonic oscillator H=\frac{p^2}{2m}+\frac{1}{2}m\omega^2 x^2 , and [x,p]=i\hbar . Define the operators a=\frac{ip+m\omega x}{\sqrt{2m\hbar \omega}} and a^+=\frac{-ip+m\omega x}{\sqrt{2m\hbar \omega}} (1) show that [a,a^+]=1 and that...

Got it, thank you very much for your help.

I was thinking that since \phi is a scalar field, the derivative is just zero. I guess that's wrong then.