FY3403/FY8913 Particle Physics 2025
Breaking news
Detailed solution to exam 2012 problem 2 that was covered in today's question hour: available here.
A question was posed today regarding why the mass term in the Proca Lagrangian has the opposite sign of the mass term in both the K-G and Dirac Lagrangian. The answer (which is technical and unfortunately not intuitively easily understood) is that the mass term must have this sign in order for the corresponding proca Hamiltonian (which can be constructed from the Lagrangian density) to have only positive energy eigenvalues and be bounded from below. A small consolation is that although the mass term in the Proca Lagrangian is +m^2 A_mu A^mu, three of the components of the A-field have the same sign of as the K-G and Dirac equation since A_mu A^mu = A_0 A^0 - A_i A^i.
Regarding the first part of the question 1e in the exam of 2012, here is an example of answer which would have given full score. In the experiment, Lee and Yang prepared radioactive atoms in such a way that the spins of these atoms pointed in the same direction. This was done by applying a strong magnetic field causing the atom spins to align in the same direction. The electrons emitted from these radioactive atoms in the form of \beta-decay were then measured: specifically, the direction along which the electrons were emitted was observed. Lee and Yang observed that electrons preferentially were emitted in a certain direction relative the atom spin. In the parity-reversed version of the experiment, spin would remain invariant but the emitted direction of the electron would change. Since this process was not observed to take place, the conclusion was that parity must be broken.
