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Homework Statement
I'm working with a complex scalar field with the lagrange density [tex] L= \partial_{\mu} \phi^{\ast} \partial^{\mu} \phi - m^2 \phi^{\ast} \phi [/tex] And I've shown that's its hamilton density [tex] H= \int d^3 x ( \pi^{\ast} \pi + \nabla \phi^{\ast} \cdot \nabla \phi + m^2 \phi^{\ast} \phi ) [/tex]
Now the annihilation and creation operateurs are introduced. And I have to show that hamilton density H is diagonalizable by writing
[tex] \phi(x) = d^3 p \left( \frac{1}{(2 \pi)^3} \frac{1}{\sqrt{2E_p}} (a_{\vec{p}} e ^{-i p \cdot x} + b_{\vec{p}}^{\dagger} e^{ip \cdot x}) \right) [/tex]
I also have to show that the theory contains two particles with mass m. How do I do this? I don't really know how to get started? Neither with how to show it is diagonalizable or how to find the masses:(