I am reading the 7th chapter of Di Francesco's CFT book. It builds, for example in section 7.3, a null state |x> which is orthogonal to the whole Verma Module. The author asserts that the field x representing the state has the property that any correlation function containing the field x vanishes, which the author does not provide the reader with a justification.
Now I am confused by the assertion. Why is the assertion true? Can anyone give me an explanation? Thanks.