- #1
karlzr
- 131
- 2
Suppose there is a real scalar field ##\phi## with some decay width ##\Gamma## to some fermion. The quantum equation of motion after one-loop correction takes the form
##\ddot{\phi}+(m^2+im\Gamma)\phi=0##
where ##m## is the renormalized mass.
The solution can be obtained as ##\phi=\phi_0 e^{imt}e^{-\Gamma t/2}##. So how do we use this complex solution? since the solution we need for application must be real. Usually we can take the real part when we have a complex solution. But In this case the real part of this solution does not solve the full quantum equation of motion due to the imaginary component.
##\ddot{\phi}+(m^2+im\Gamma)\phi=0##
where ##m## is the renormalized mass.
The solution can be obtained as ##\phi=\phi_0 e^{imt}e^{-\Gamma t/2}##. So how do we use this complex solution? since the solution we need for application must be real. Usually we can take the real part when we have a complex solution. But In this case the real part of this solution does not solve the full quantum equation of motion due to the imaginary component.