What is the intuitive reasoning for requiring that a Lagrangian describing a free-field contains terms that are at most quadratic in the field?(adsbygoogle = window.adsbygoogle || []).push({});

Is it simply because this ensures that the EOM for the field arelinearand hence the solutions satisfy the superposition principle implying (at least in the classical) sense, that wavepackets do not interfere with one another as they propagate past one another, i.e. they are free-fields?!

Furthermore, what is the motivation for including the term ##\frac{1}{2}m^{2}\phi^{2}## in the free-field case? I get that the parameter ##m## is attributed to the mass of the field a posteriori, but is the reason for the inclusion of such a term in the first place? Is it simply because a priori there is no reason not to - one should include all possible terms up to quadratic order?! Or is there also some physical motivation as well, in that from quantum mechanics, the wave function of a relativistic particle (of mass ##m##) should satisfy the Klein-Gordon equation?!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Why are free-field Lagrangians quadratic in fields?

Tags:

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**