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Let's say we have a complex scalar field [itex]\varphi[/itex] and we separate it into the real and the imaginary parts:

[itex]\varphi[/itex] = ([itex]\varphi1[/itex] + i[itex]\varphi2[/itex])

It's Lagrangian density L is given by:

L = L([itex]\varphi1[/itex]) + L([itex]\varphi1[/itex])

Can you tell the argument behind the idea that in summing the densities of cpts. we treat the imaginary part on equal basis with the real.

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# Lagrangian density for a complex scalar field (classical)

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