I am trying to understand neutrino oscillations. The problem is I know
nothing about QFT. "Reviews" of neutrino physics usually begins with
something like "the mass term of the Lagrangian..." and then continues
with objects like (Mass_D nu_bar_R nu_bar_L + hermitian conjugate).
I do, however, know non-relativistic quantum mechanics and I have also
seen the Dirac equation, and the related gamma matrices before.
1) What is the meaning of the Lagrangian in QFT? I suppose we plug it
into the Euler-Lagrange equations? But what does it give us? Of what
object is the Lagrangian?
2) What exactly does the mass term of the Lagrangian mean?
3) What does the four-component column psi mean? Is it a solution of the
Dirac equation? Does (psi_bar gamma_mu psi) correspond to the
probability current like in the case for the Dirac equation?
4a) Is psi in the Lagrangian the wavefunction of some particle (e.g. the
tau neutrino)? Or is the wavefunction of a family of associated
particles like that of all neutrinos (tau, mu, electron)? Or is this
something we put into the Lagrangian by hand - that is do we multiply
the psi's of the mu, tau and electron neutrino in a way that is
consistent with relativity, left- and right-handedness, hermicity,
choice of whether we want our antiparticles to be equal to our
particles, etc., take various linear combinations and then see what
comes out of it after diagonalization?
4b) How exactly does one decide what kind of products occur in these
mass terms? I quoted things like relativity, antiparticle and particle
requirements, handedness, etc. but in reality I don't fully understand
how these things are exactly implemented as well. Can someone tell me
the full list of conditions one needs to consider, and how to go about
constructing a general mass term from scratch?
5) How does the mass term have anything to do with interactions? In my
case I'm guessing that the reason why these various "mass terms" are
products of psi_left and psi_right is because the weak interaction
involves (1 - gamma_5) psi?
6) As one might observe my above questions reflects my absolute
cluelessness to all these stuff. Where can I find a review where there
is some basic explanation of these issues? I need a source that
describes the relevant field theoretic concepts so that I can understand
this whole business of the Lagrangian mass term.