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I would be glad if some one can clarify, all the books talk about boundary conditions which are finite at spatial infinity and give the general solution for canonical quantization of scalar field,

1) how can we apply any particular boundary condition ?

2) when we write [tex]\phi(x)[/tex] in terms of creation and annihilation operator what do we mean by [tex]\phi(x)|0\rangle[/tex], I mean what do we get ? [tex]\phi(x)[/tex] which is lorentz invariant scalar field and not an operator field, but then how can we get a scalar field by creating and Annihilation particles.

3) what is the value for [tex]x|0\rangle[/tex], we can do that for quantum harmonic oscillator can we do it similarly for scalar field ?

Please help me clarify these doubts