In the Peskin&Schröder's QFT book there's an exercise that's about a pair of scalar fields, ##\phi_1## and ##\phi_2##, having the field equations(adsbygoogle = window.adsbygoogle || []).push({});

##\left(\partial^{\mu}\partial_{\mu}+m^2 \right)\phi_1 = 0##

##\left(\partial^{\mu}\partial_{\mu}+m^2 \right)\phi_2 = 0##

where the mass parameter is the same for both fields. Now I can make a "rotation",

##\phi_{1}^{'} = \cos \alpha \phi_1 - \sin \alpha \phi_2##

##\phi_{2}^{'} = \cos \alpha \phi_2 + \sin \alpha \phi_1##

which mixes the two fields. The generator of this rotation apparently has properties of angular momentum, but has nothing to do with spacetime. The symmetry can also remain if a four-point interaction is added in the form of terms proportional to ##(\phi_1)^4##, ##(\phi_2)^4## and ##\phi_1^2 \phi_2^2## in the Lagrangian density.

From other sources I got the impression that this has something to do with the Higgs mechanism... How does this extend to more than 2 scalar fields, and can a pair of vector, tensor or spinor fields have a similar property? If the fields have almost the same mass, is there some useful way to treat the mass difference as some kind of a perturbation?

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

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

# A Scalar Fields with the Same Mass

Tags:

Have something to add?

Draft saved
Draft deleted

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