A sentence from an article:
"But the entire tenor of his book radiates a belief that adherence to the original understanding of presidential power is normatively appealing."
Would there be a difference in meaning if one substituted "the" for "a"? I don't think so; I see "a" and "the" as being interchangeable here.
However, this may not be a generally accepted or held belief, it could simply be that of the author, in which case the book would radiate "a belief [on the part of the author]........." It shows that he personally has "a belief" that .....etc etc