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## Main Question or Discussion Point

Hi,

If I have a Lagrangian that looks like [tex] L=-\frac{1}{2} \partial^a{\phi}\partial_a{\phi}-\frac{1}{2} \mu \phi^2 -\frac{1}{24}\lambda \phi^4 [/tex].

Where [tex]\lambda>0 [/tex]

Then how do I figure out the mass for small fluctuations about [tex] \phi=0 [/tex] ?

I don't think I really understand what it means for some parameter to represent the mass. I mean without the phi^4 term, it would just lead to KG equation and obviously there [tex] \mu [/tex] represents the mass when you find the dispersion relation.

Should I just therefore find the equations of motion, then plug in some superposition type solution to find out the dispersion relation, and thus find a term that I would normally call the mass in a relation of the form [tex] E^2=P^2+m^2 [/tex]? or is there something else to this?

I'm not really sure how to incorporate the phi=0 expansion into this, I was originally thinking just Taylor expand but then I would have expanded about [tex] \phi(0,\vec(0)) [/tex], as oppose to the trivial [tex] \phi=0 [/tex] solution.

Thanks for any help

If I have a Lagrangian that looks like [tex] L=-\frac{1}{2} \partial^a{\phi}\partial_a{\phi}-\frac{1}{2} \mu \phi^2 -\frac{1}{24}\lambda \phi^4 [/tex].

Where [tex]\lambda>0 [/tex]

Then how do I figure out the mass for small fluctuations about [tex] \phi=0 [/tex] ?

I don't think I really understand what it means for some parameter to represent the mass. I mean without the phi^4 term, it would just lead to KG equation and obviously there [tex] \mu [/tex] represents the mass when you find the dispersion relation.

Should I just therefore find the equations of motion, then plug in some superposition type solution to find out the dispersion relation, and thus find a term that I would normally call the mass in a relation of the form [tex] E^2=P^2+m^2 [/tex]? or is there something else to this?

I'm not really sure how to incorporate the phi=0 expansion into this, I was originally thinking just Taylor expand but then I would have expanded about [tex] \phi(0,\vec(0)) [/tex], as oppose to the trivial [tex] \phi=0 [/tex] solution.

Thanks for any help