Recent content by Glenn Rowe

In Coleman's QFT lectures, I'm confused by equation 7.57. To give the background, Coleman is trying to calculate the scattering matrix (S matrix) for a situation in which the Hamiltonian is given by $$H=H_{0}+f\left(t,T,\Delta\right)H_{I}\left(t\right)$$ where ##H_{0}## is the free Hamiltonian...

Thanks for your help.

I guess what's confusing me is that according to the equation in Thorne & Blandford, the force is given by $$ F_{i}=T_{ij}\Sigma_{j}$$ Assuming that the stress tensor is fixed, then according to this formula, the force depends on the orientation of the surface. (Of course it also depends on...

That explains why the stress tensor is diagonal, but if the electric field exerts a pressure orthogonal to itself, there should be a force in the y and z directions, as well as the tension along the x axis, shouldn't there? In other words, is eqn 1.32 in Thorne & Blandford (above) the right way...

I'm puzzling over Exercise 1.14 in Thorne & Blandford's Modern Classical Physics. We are given that an electric field ##\boldsymbol{E}## exerts a pressure ## \epsilon_{0}\boldsymbol{E}^{2}/2## orthogonal to itself and a tension of the same magnitude along itself. (The magnetic field does the...

Of course. Stupid of me not to notice that. I guess my mind got stuck in a rut.

I guess it is the notation that misled me. They are written as the components of E and B perpendicular to the motion in the transformed frame, so it would seem that they should be parallel.

The Lorentz transformations of electric and magnetic fields (as given, for example in Wikipedia) are $$ \begin{align*} \bar{\boldsymbol{E}}_{\parallel} & =\boldsymbol{E}_{\parallel}\\ \bar{\boldsymbol{E}}_{\perp} &...

Thanks for the explanation. I'm assuming you left out a factor of ##G(t)## in the integrand of ##\tilde{G}(k_0)##?

Never mind - I figured it out and have posted my solution https://physicspages.com/pdf/Lancaster%20QFT/Lancaster%20Problems%2017.04.pdf. However, It requires using the technique developed in the previous exercise 17.3, although I have to say I'm not sure why that method works, but anyway.

I've seen a derivation similar to that somewhere else (in English as well, I think) but I don't think that's what Lancaster & Blundell have in mind, since it doesn't give the answer they ask us to prove. I have to admit I don't understand how you would introduce the harmonic oscillator into...

I'm reading through Lancaster & Blundell's Quantum Field Theory for the Gifted Amateur and have got to Chapter 17 on calculating propagataors. In their equation 17.23 they derive the expression for the free Feynman propagator for a scalar field to be...

I haven't got far enough in QFT for this to mean much to me yet, I'm afraid. Lahiri's book does mention the Ward-Takahashi identity, but not for another 3 chapters beyond where I am now, and I haven't come across N-point functions either. I'm not sure what you mean by the 'polarization matrix'...

I think my main problem is that I don't know where to start to solve the problem of deriving the differential cross-section using equation (2) above rather than equation (3). In their problem statement, Lahiri & Pal say that we're not allowed to use the condition which they derive from gauge...

I'm working through Lahiri & Pal's book A First Book of Quantum Field Theory, Second Edition and I'm stuck on their explanation of the polarization vector in quantum electrodynamics in Chapters 8 and 9. In section 8.8, they derive a formula for the sum over the transverse polarization modes of...