Ok... To be honest, that is a bit of a red flag! QFT is a tricky subject in its own right, but it relies heavily on classical mechanics. So you may want to pick up a good book and learn Lagrangians, variational calculus and Noether's theorem properly as soon as possible. Otherwise I think you...
As Peskin and Schroeder present it, the calculus is essentially that of partial derivatives while treating \phi and \partial_\mu \phi as independent variables. For a given Lagrangian density \mathcal{L}, he defines the current in eq. (2.12). However, the current depends on the symmetry at hand...
What is going on is essentially this: Suppose you are integrating a constant (equal to unity for convenience) from x=1 to x=0 along the x axis. Would you say that because we are moving in a negative direction, dl=-dx, and thus
\int_1^0 dl = -\int_1^0 dx = 1
or would you just say that the...
At some level, what matters is what we can measure. In this case it is the force (basically energy difference), \mathbf{F}=-\nabla U. On integration, we are free to add any integration constant to U. So what matters is the functional form of U(r), not its value. If you study more classical...
This paper was published in PRL last year. And given the ongoing research on dynamical and non-linear systems it's obviously not impossible to find something new in classical mechanics worthy of publication, but whether you can do it depends on whether you can find an interesting new result or...
This is nothing mysterious, it is just that z=0 for the equations in \hat{x} and \hat{y}, so that equation works for all three cases. If that doesn't make sense, do the three integrals and compare the results.
As atyy pointed out, {σ} means that, for each spin in the <i,j> sum, you sum over all possible spin states for both the i and j spins. And the <i,j> symbol denotes that you sum over i and j, but only include nearest neighbors.
Does the sum make sense to you in the simplest case, i.e. 1D?
I guess you don't know much statistical physics? Because most of your questions are answered and best described in that language. You might want to look at some textbook in that field, specifically to look up partition functions and "thermal averages".
The point is exactly that we do not know...
Thanks to both of you for your replies. This punchline
is particularly illuminating, and makes a lot of sense. It pays to think of the physical motion (on the configuration manifold) and the Lagrangians (as defined on the tangent bundle) separately then, something I might have neglected at...
Hi,
I'm trying to clear up a confusing point in the book by José and Saletan, concerning equivalent Lagrangians (in the sense that they give you the same dynamics). It is clear that if
L_1 - L_2 = \frac{d\phi ( q,t )}{dt},
then L_1 and L_2 will have the same equations of motion. However...
The general idea is to take the first (n-th) derivative of the free energy and to see that it is discontinuous. The van der Waals transition is a bit complicated given its coexistence region though. I'm sure the proof is available in some lecture notes online or you can find the details in some...