Problem 1 - 12:26

Edit: I kept saying "the field configuration that minimizes the action" throughout the discussion (e.g. around 37:42), but this is actually a bit misleading! Although there may only be one configuration that minimizes the action (e.g. we saw for T>T_c that psi_0 = 0); there can also be many configurations that minimize the action (e.g. we saw for T<T_c there are infinitely many constant solutions all related by a constant phase shift). Anyway, I really should have been saying "a field configuration that minimizes the action".

Edit: at 46:36, I forgot to add a star to the complex conjugate of the field!

- I meant to write:  psi^* -> exp( - i theta ) psi^*