A slow one

Hi there.

This week even is was exciting, was very slow.

In the particle course we introduce the quarks in stage...more or less trivial after spendt couples of weeks on the lepton sector, the only non-trivial issue is to assure the no Flavour-Changing--Neutral-Currents or (FCNC).

But, What does FCNF means?

From the GWS (Glashow-Weinberg-Salam) model the exchange of a neutral boson (as the Z), cannot changing the flavour of the quarks (nor leptons). So, that's it, a neutral current (particle) couldn't change the flavour -----> no FCNC.

Thus, the flavour changing must be carried just by the charged bosons (W).

The answer to this problem began with Cabbibo, who suggested that d and s quarks were mixed. Later, Glashow-Illiopoulos-Maiani suggested the existence of another quarks rather like the u, it was called charm or c. Still a mixing between d and s should be there. Finally, the inclusion of the 3rd generation of quarks (b and t), enhanced the mixing of the ``down"-like ones by a 3x3 matrix, known as the Cabbibo-Kobayashi-Maskawa matrix.

Moreover, the inclusion of this matrix overpass the expectancy, 'cause additional to the quark mixing it contains a physical phase, which implies the CP violation.
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On the other hand, the Renormalization Group is turning interesting.

I'm reviewing the Wilson's approach to the RG. This a nice subject. Despite my taste, a good book to introduce the subject is ``An introduction to Quantum Field Theory'' by Peskin and Schoeder.

In the very introduction to the subject the authors link the RG to the construction of effective theories, giving you a procedure to eliminate the irrelevant terms.
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Changing theme. I'm trying to understand a paper of the RG flow in gravity theories. Happens that one of the professors, whose research goes in that direction, was in the Villa de Leyva School 2007... which I should reject on behalf of my qualifying examination. Jesus...!!!

Ok, That's it for the week. C U.

After a long time

Hello! What a long time...!!!

Well, but finally I'm back. This week was very interesting. Finally I did my first electroweak calculations.


So, the low energy scattering of leptons is a studied stuff... As well a the high energy behavior of the electron-positron annihilation.

Also, the renormalization group seems to be a not so difficult subject. Of course I reviewed a lot of renormalization and dimensional regularization in order to finally get the ideas of RG. And easy picture of the renormalization group is just the pass through different scales for describing the same set up, my favorite example is that one can get the thermodynamics from statistical mechanics. Other example is the spin chain, you can describe it spin by spin or macroscopically by taking block of spin and average over the block. Important: One can go from the micro to the macro, but not the other way around... this is because when you average lose information about the individual spins or micro-states.

Ok... it was just a bit of the week. I'll write more next week, 'cause I'm tired today. Cya.

Week 1

Here I am again...

In this blog I pretend to write the thing learned through the week and comment different stuff related with physics as well as mathematics.

Particle Physics.

After half an afternoon, I finally got the whole set of vertices of the electroweak theory... It makes me feel such more sure about Yang-Mills theories.

In the last two weeks I have learnt a lot about Yang-Mills, spontaneous symmetry breaking and resonances. A nice reference to review is the book by Chris Quigg, GAUGE THEORIES OF THE STRONG, WEAK AND ELECTROMAGNETIC INTERACTIONS. Despite the step by step procedure is not in the book, it is a quick guide of the subject.

At the SPIRES page, there is a section of videos, in there you can also find a set of lectures on the subject, as well as in the CERN page.

Quantum Mechanics.

At the beginning of the semester my professor said it'd be interested to understand the shape of the line spectrum. As you figure... I ask myself, Why is that important?, Well, as usual he was right.

Fermi's golden rule include a delta distribution of the energy, that means that if the initial and final energies are not exactly the same the transition does not take place. Nonetheless, uncertainty implies there is a gap of energy in which the transitions indeed happens.

One can calculate the width of the shapes, and at the end of the day it is related with the decay width of the transition. (Amazing!)

That's not all... the same procedure can be used to correct the amplitudes of certain process, and the imaginary part is that gives the resonances. So, I learnt a lo about particle physics just by studying quantum mechanics.

For the future.

Now, I'm reviewing some stuff on supersymmetry and renormalization group. If things go well, the final task is to know some about the new methods of renormalization of gravity. Also, a small ``project" on particles is to do the theoretical analysis of electron-positron annihilation at high energies, in order to see the Higgs (if possible).

Oscar.