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1) Is the ground state of the field, one of the eigenstates of ## \hat \varphi(\vec x) ##, i.e. is ## \hat \varphi(\vec x)|0\rangle=0 ## correct?( At the bottom of page 224 of his book "A modern introduction to quantum field theory", Maggiore calls ## \phi(\vec x)=0 ## the vacuum. It seems to me its related to my question. Is he correct or just being sloppy? )

2) What is the relationship between the Fock states that are created by ## \hat a_k ## and ## \hat a_k^\dagger ## and their superpositions that are created by ## \hat \varphi(\vec x) ## and ## \hat \varphi^\dagger(\vec x) ## and the eigenstates of ## \hat \varphi(\vec x) ##? Can we say that the eigenstates of ## \hat \varphi(\vec x) ## are some kind of a coherent state because ## \hat \varphi(\vec x) ## is an anihilation operator for Fock states?

Thanks