Recent content by Xezlec

I was afraid of that.

I wasn't sure whether to post this in here or in computer programming, since it touches on both. I have a personal project that is based on a 2-dimensional finite-element fluid simulation (which already works just fine) but needs to be able to simulate an elastic membrane stretched across a...

OK, I think I figured it out: since \Lambda is arbitrary, we ought to be able to choose a \Lambda that makes the boundary term go away, and the Lagrangian should be invariant. When we do that, we find that charge must be conserved. I guess I was thinking of the idea as being that gauge...

Whoops! Duh. Thanks. Not sure how I confused myself on that. Now I can rephrase my problem in terms of post #7 on that other thread: I now fully agree that if we restrict \Lambda to be constant on \partial D_1 and \partial D_2, everything works out properly. But why should that restriction...

Maybe I'm just missing something really obvious, but I can't seem to follow that discussion. Specifically, I don't understand the first equality in post #1, nor what \Lambda represents. This seems to be a different presentation of gauge symmetry than the one in my book. The book I'm reading...

Sorry, can you elaborate any? What part was unclear? Do you understand the derivation that I'm referring to? I can paste the book's exact wording if that would help. I'm just trying to understand why the boundary terms can be neglected.

Hello. I'm trying to wrap my head around how Lagrangians work in classical field theory. I have a book that is talking about the gauge invariance of the Lagrangian: \mathscr{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-J^\mu A_\mu. It shows that we can replace A^\mu with A^\mu+\partial^\mu\chi for...

Thanks. It's clearly been too long since I've done anything with covariant and contravariant vectors. I need to go back and refresh before jumping back into this stuff.

So I have this book that considers the problem of a flexible vibrating string, taking \phi(x,t) as the string's displacement from equilibrium. It then writes a Lagrangian density in terms of this \phi, takes \delta \mathcal{S} = 0, and eventually concludes that \frac{\partial}{\partial...

Thanks! I also finally found this magical page on Wikipedia which clarified some of the terminology that was confusing me. Now I see that a Fock state is not just any element of Fock space, but rather, only a state that is "on an axis", so to speak, while the majority of Fock space consists...

So you're saying we define the term "Fock space" to refer not to the space of all states that can be reached through some combination of creation operators on \mid 0\rangle, but to the space spanned by the axes made up of multiples of those states? In that case it's the terminology on Wikipedia...

Hello and sorry for the following dumb question. I was reading about quantum field theory out of general curiosity about the subject and I was confused by the way it seems like the web pages I've read imply that the operators we define in QFT (say, the annihilation operator, or the...

OK, I may have tracked down part of what's confusing me now. I've always been told that if two operators don't commute then they can't have a common eigenstate, but looky here. If A = \begin{bmatrix}-1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \end{bmatrix} and B = \begin{bmatrix}0 & 1 & 0 \\1 & 0 &...

Wow. I had forgotten those didn't commute. Now I'm really confused. Back to the drawing board. Thanks!

Hello, I'm looking at the Dirac Equation, in the form given on Wikipedia, and (foolishly) trying to understand it. \left( c \boldsymbol{\alpha}\cdot \mathbf{\hat{p}}+\beta mc^2 \right ) \psi = i\hbar\frac{\partial \psi}{\partial t}\,\! So I picture a wavefunction in an eigenstate of the...