#### claymine

Summary
The result of angular frequency deduced from Eq 1.8 is quite confusing to me. Can some one walk me through it please?

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#### dRic2

Gold Member
It seems to me the author used the relation $\omega^2 = \frac k m$ for the frequency of an harmonic oscillator, where -in this case- $k = \phi_p$ and $m = \frac 1 {\rho p^2}$.

#### claymine

It seems to me the author used the relation $\omega^2 = \frac k m$ for the frequency of an harmonic oscillator, where -in this case- $k = \phi_p$ and $m = \frac 1 {\rho p^2}$.
No, I don’t think so

#### dRic2

Gold Member
Why not ? It looks like the total energy of an HO... BTW I'm sorry but that's the only thing I could think of

#### claymine

Why not ? It looks like the total energy of an HO... BTW I'm sorry but that's the only thing I could think of
cuz in his notation (eq1.8) he has rho bar he forgot the divsion symbol. this is a book called qft in stat phys by A. Abrikosov btw. previously he mentioned in low temp He4 energy is proportional to momentum

#### dRic2

Gold Member
Sorry, I'm not following. If you compare that equation with $\frac 1 2 m \dot x ^2 + \frac 1 2 k x^2$ it is straightforward to obtain $\omega ^2 = \frac k m$

#### claymine

ah you are right my apologies for being pretentious, your way is a pretty elegant solution

#### claymine

Sorry, I'm not following. If you compare that equation with $\frac 1 2 m \dot x ^2 + \frac 1 2 k x^2$ it is straightforward to obtain $\omega ^2 = \frac k m$
thank you

• dRic2