7th
Nobel Prize in Physics 2008-Want To Understand What It’s About?
Congratulations to Yoichiro Nambu (1/2 prize) , Makoto Kobayashi , and Toshihide Maskawa. Of course Nambu wins the prize due to his work on spontaneous symmetry breaking done back in 1960. It’s a beautiful piece of work which has permeated many fields of physics from the Standard Model to condensed matter systems (think of ferromagnets above/below Curie temperature). An illustrative idea of spontaneous symmetry breaking is the pencil on its tip. When it’s balanced on its tip it is in a symmetrical configuration-but is highly unstable. A small perturbation will cause it to pick out a random direction on the table. It’s of particular significance at the moment with the hope we’ll be seeing our friend the Higgs at the LHC by the spring time. The idea goes like this:
Consider a new complex scalar field. Add a kinetic term and a potential term of a general renormalizable form. This scalar field picks up a non-zero vacuum expectation value (what does that mean? Ask me later). This, like giving the pencil a nudge, will break the symmetry of the Lagrangian and the field will then pick out a random direction in what’s called weak isospin-hypercharge space. Our SU(2) x U(1) has been broken. Now according to Goldstone’s theorem you’ll get 3 NAMBU-Goldstone bosons due to broken symmetry. But since we’re talking about gauge theories, specifically SU(2) in this situation, you can gauge these away to reappear as longitudinal modes of the Ws and Z. This procedure of having the gauge degrees of freedom ‘eating’ the massless goldstone modes allows the Ws and Z to acquire the required degrees of freedom but also a mass. This in essence is the Higgs Mechanism.
Why is it important? Well, without a Higgs field in the electro-weak Lagrangian, the gauge fields have no mass which is certainly a problem. But through this procedure of spontaneous symmetry breaking, first investigated by Nambu, the Higgs mechanism allows one to generate mass for the gauge degrees of freedom. This can be extended to leptons/fermions etc…
Perhaps tomorrow I’ll talk about why Kobayashi and Maskawa won. It goes to the idea of symmetry breaking and why there are 3 generations of quarks (also CP symmetry violations which is another story)…
PS-This was probably a little technical. It serves as a means to make sure I remember how these things work, however…so sorry about that.
