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A puzzle of two scalar dynamics 
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#1
Sep811, 12:30 AM

P: 37

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


#2
Sep811, 01:00 AM

Sci Advisor
PF Gold
P: 9,360

You are confusing scalar quantities with vector quantities.



#3
Sep911, 04:19 AM

Sci Advisor
P: 4,782




#4
Sep1411, 08:51 AM

P: 37

A puzzle of two scalar dynamics



#5
Sep1411, 08:59 AM

P: 37




#6
Sep1411, 10:12 AM

Sci Advisor
P: 4,782

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 [itex]\lambda^2 = m_1^2 + m_2^2[/itex], 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 fullyspecified by the behavior of one of the particles. If you try to get larger offdiagonal terms, the mixing matrix ceases to make any sort of physical sense. 


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