Recent content by evilcman

All meromorphic functions can be written as the ratio of two holomorphic functions, that is true. The second statement is not true. In general a holomorphic function can't be written as a product of monomials. You will in general also have an exponential in it. And the exponential in it can...

Is this statement true: "If two meromorphic functions have the same poles(all simple) and the same zeros(all simple), than they are proportional."? If it is true, than why? Thanks for the help...

I have a scalar function f dependent on a few variables $x_i$, and I would like to change variables, so that y_i = \sum_j {M_{ij} x_j}, where M is an invertible matrix independent of the x_i-s, and compute: \frac{\partial f}{\partial x_i} = \frac{\partial f}{\partial \left( \sum_j...

You are right. My bad.

In calculations of weak interaction processes in the Fermi-theory, there are some amplitudes of the form: \bar{a}(\gamma_{\alpha} + \lambda \gamma_{\alpha}\gamma_{5}) b \bar{c}(\gamma^{\alpha} + \gamma^{\alpha}\gamma_5)d where a,b,c,d are Dirac-spinors. Now, if this is a Lorentz-scalar. In that...

There are similarities, and there are nuclei produced in heavy ion collisions from the recombination of nucleons, but the processes are still quite different. I think one way to look at this is to think about interaction rates (number of interactions per second per particle) compared to the...

What about above the W threshold?

Well I am sure that would be the case if the weak interactions was a pure SU(2) gauge theory, but the full SM is more complicated, and I am not sure this still applies.

If one wants, to calculate the self energy correction to the electron propagator(using the approach where one introduces a photon mass \mu to deal with IR divergences), one gets after some work an integral like this (this is from the Itzykson Zuber book equ. 7-34): \int_ 0 ^ 1 d\beta \beta...

Simple regularization doesn't help either, if we sum up to state N only, then we get: -<E> = \frac{\sum E_0 exp(-\beta E_0 / n^2 )}{\sum n^2 exp(-\beta E_0 / n^2 )} < \frac{N E_0 exp(-\beta E_0)}{N^3} \to 0 which would mean that at ANY temperature, all hydrogen atoms are at a highly excited...

Calculating energies with respect to the ground state just means adding E_0 to all energies, that is multiplying the partition function with exp(\beta E_0) and the sum will still diverge.

Is there some kind of resolution to the Hydrogen atom problem in statistical physics, that is the fact that canonical partition function diverges for E_n = - E_0/n^2 with degeneracy n^2 since Z = \sum n^2 exp(-\beta E_0/n^2) > \sum n^2 exp(-\beta E_0) , which makes the H atom problem seem...

A way to start can be the book Gauge Theory of Elementary Particle Physics by Cheng and Li. It has a nice chapter about Chiral Symmetry which introduces the linear Sigma model, than there is a supplementary book to it (Problems and Solutions) which has a few things about both the linear and...

Does anyone recognize this expression for the pressure: p(T,\mu) = T s^*(T,\mu) where s^* is the extreme right singularity in the Laplace transform of the grand canonical partion function. If someone knows this, I am curious in the derivation, and in what cases it is applicable. (In the...

a) The partial wave analysis expansion is one of the commonly used orthogonal expansions in physics. This means that any function can be decomposed into infinity partial waves. If a fit includes 42 partial waves that means they truncated the expansion at 42 terms, which will supposedly give a...