LOG#069. CP(n), spheres, 1836.

Data:         where we take the radius of the sphere equal to 1 without loss of generality. Thus, is 6!=720 times the volume of the complex projective space . I have not found any other (simpler) way … Continue reading

LOG#067. SM(IX): Summary.

What is the SM? What it does?What is not the SM? What it does not? 1) A local relativistic quantum field theory describing matter-energy and the electroweak and strong interactions up to a distance . It is a “correct”, “effective” … Continue reading

LOG#066. SM(VIII): tests.

The weak scale and the weak angle The Fermi constant is defined through a beautiful and simple mathematical formula:     This formula for the Fermi constant was very important in the long path towards the EW unification since knowing … Continue reading

LOG#065. SM(VII): phenomenology.

The above picture is a cool mind map by the cosmologist and particle physicist Sean Carroll. It summaries somehow the phenomenological charges of the Standard Model plus the gravitational sector we do not know at quantum level. Physical Higgs sector … Continue reading

LOG#064. SM(VI): total lagrangian.

The total SM lagrangian can be written now, with some subtle notational changes, from the previous posts. It is really a monster “thing”: From what you have learned in previous log-entries, can you identify the meaning of every lagrangian piece … Continue reading

LOG#063. SM(V): Gauge fixing.

Gauge theories require that we select “a gauge” in order to calculate physical observables. That is, you have to fix the gauge to eliminate field configurations that are physically equivalent ( they can not be distintinguished, as field configurations). The … Continue reading

LOG#062. SM(IV): SSBEW&Higgs.

We have seen that the SM, under general considerations such as gauge invariance and renormalizability, does NOT initially allow EXPLICIT mass terms in the lagrangian framework for the gauge bosons AND/OR the chiral fermions. Note that every SM fermions is … Continue reading

LOG#061. SM (III): EW sector.

The above picture is the EW lagrangian! Is it simple? Is it beautiful? It depends on your taste! It is called the GSW (Glashow-Salam-Weinberg) lagrangian. The electroweak (EW) part/theory is based on the gauge symmetry group. Before spontaneous symmetry breaking, … Continue reading

LOG#060. SM (II): The QCD sector.

QCD or Quantum ChromoDynamics acts on quarks and hadrons (both baryons and mesons, “colored” particles). There are lots of baryons and mesons, and I have listed some of them in the two tables above as “an apetizer”. Please, remeber that … Continue reading