## A puzzle of two scalar dynamics

I have a puzzle when I study the hybrid inflation model.

Suppose we have two scalar fields, $\phi_1 and \phi_2$
first, lets consider the situation where they are in their independent potentials
$V(\phi_i)=m_i^2\phi_i^2, i = 1,2$
with initial value
$\phi_i^{ini}$
We can solve the scalar dynamic equations for them. And they are both in harmonic oscillation. This is Okay.

But when a 'mixing term' $\lambda^2 \phi_1\phi_2$ is introduced, $\phi_1$ and $\phi_2$ get infinite values, if \lambda is large. This can be showed numerically. What I thought is the large mixing term would lead to $\phi_1 = \phi_2$. So why it goes to infinite?

And we can rotate $\phi_1$ and $\phi_2$ to a basis where there is no mixing term. In this basis, we would not get infinite values for $\phi_1$ or $\phi_2$. So it seems I get a different result working in different basis. What is the problem
 PhysOrg.com science news on PhysOrg.com >> Galaxies fed by funnels of fuel>> The better to see you with: Scientists build record-setting metamaterial flat lens>> Google eyes emerging markets networks
 Recognitions: Gold Member Science Advisor You are confusing scalar quantities with vector quantities.

Recognitions:
 Quote by Accidently I have a puzzle when I study the hybrid inflation model. Suppose we have two scalar fields, $\phi_1 and \phi_2$ first, lets consider the situation where they are in their independent potentials $V(\phi_i)=m_i^2\phi_i^2, i = 1,2$ with initial value $\phi_i^{ini}$ We can solve the scalar dynamic equations for them. And they are both in harmonic oscillation. This is Okay. But when a 'mixing term' $\lambda^2 \phi_1\phi_2$ is introduced, $\phi_1$ and $\phi_2$ get infinite values, if \lambda is large. This can be showed numerically. What I thought is the large mixing term would lead to $\phi_1 = \phi_2$. So why it goes to infinite? And we can rotate $\phi_1$ and $\phi_2$ to a basis where there is no mixing term. In this basis, we would not get infinite values for $\phi_1$ or $\phi_2$. So it seems I get a different result working in different basis. What is the problem
How large are we talking? I don't think you can go above $\lambda^2 = m_1^2 + m_2^2$ and have sensible results.

## A puzzle of two scalar dynamics

 Quote by Chronos You are confusing scalar quantities with vector quantities.
do you mean scalars can not mix? I thought about that. But my understanding is two fields can mix if they have exactly the same quantum number.

 Quote by Chalnoth How large are we talking? I don't think you can go above $\lambda^2 = m_1^2 + m_2^2$ and have sensible results.
The limit sounds reasonable. But why do we have this limit? Unfortunately, I am consider some process which can go beyond this limit (for example, a fast scattering between the two scalars, bringing the two fields to equilibrium.)

Recognitions:
If your cross term is zero, then the mixing matrix is diagonal, and the particles we observe are the fundamental particles. If, however, the mixing term is at the limit $\lambda^2 = m_1^2 + m_2^2$, then the mixing matrix is saying that there are is in actuality only one fundamental particle that is mixed into these two, and the behavior of the system is fully-specified by the behavior of one of the particles. If you try to get larger off-diagonal terms, the mixing matrix ceases to make any sort of physical sense.