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...
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...
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...
Recently I saw a talk stating that the hadron resonance gas model, which is basically all the known hadrons put together as ideal gases, describes lattice QCD "data" really well.
Like in this paper:
http://arxiv.org/abs/hep-ph/0303108
In this paper Fig. 1 is what I am looking at.
I tried that...
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...