- #1
Accidently
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Sometimes we need to calculate the evolution of the scalar field [tex]\phi[/tex] with the equation of motion
[tex]\frac{\partial^2 \phi}{\partial t^2}+3H\frac{\partial \phi}{\partial t}+m_\phi^2 \phi = 0[/tex].
And we can get the field
[tex]\phi=Ae^{im_\phi t}[/tex]
where A is the amplitude of the scalar field (damped by the Hubble parameter in this case).
But when we apply the energy operator [tex]i\frac{\partial}{\partial t}[/tex] on the field, what we get is [tex]E=m_\phi[/tex]
This is incorrect. And it seems that we should include the energy/temperature of the universe somewhere, but do not know how.
[tex]\frac{\partial^2 \phi}{\partial t^2}+3H\frac{\partial \phi}{\partial t}+m_\phi^2 \phi = 0[/tex].
And we can get the field
[tex]\phi=Ae^{im_\phi t}[/tex]
where A is the amplitude of the scalar field (damped by the Hubble parameter in this case).
But when we apply the energy operator [tex]i\frac{\partial}{\partial t}[/tex] on the field, what we get is [tex]E=m_\phi[/tex]
This is incorrect. And it seems that we should include the energy/temperature of the universe somewhere, but do not know how.