Timeline for Non-relativistic limit of complex scalar field Lagrangian

8 events

when toggle format	what		by	license	comment
Apr 13, 2017 at 12:39	history	edited	CommunityBot		replaced http://physics.stackexchange.com/ with https://physics.stackexchange.com/
Jul 1, 2015 at 5:07	vote	accept	Physics_Plasma
Jun 27, 2015 at 19:05	history	edited	Qmechanic♦	CC BY-SA 3.0	Added explanation
Jun 27, 2015 at 18:45	comment	added	Physics_Plasma		Oh, I might see it now. If the energy E that is remaining is not including the rest energy, then $E = \frac{p^2}{2m}$. Since we are investigating the case where $E\ll m$, then given E is just kinetic energy, then we get $E \ll \frac{p^2}{2E}$, or $E \ll p$.
Jun 27, 2015 at 18:10	comment	added	Qmechanic♦		Only indirectly.
Jun 27, 2015 at 17:48	comment	added	Physics_Plasma		Ok, so if I plug the plane wave expansion into the Lagrangian and keep the terms in the same order as they are in my second equation from the bottom, then I get $\mathcal{L} = E\Psi^{\dagger}\Psi + \frac{E^2}{2m}\Psi^{\dagger}\Psi - \frac{p^2}{2m}\Psi^{\dagger}\Psi -\frac{\lambda}{4m^2}(\Psi^{\dagger}\Psi)^2. $ I can clearly see how the second term is negligible compared to the first. Is there a reason why the second term is negligible compared to the third term, with the square of the momentum?
Jun 27, 2015 at 9:02	history	edited	Qmechanic♦	CC BY-SA 3.0	added 19 characters in body
Jun 27, 2015 at 8:49	history	answered	Qmechanic♦	CC BY-SA 3.0