We propose some conjectures on the generating
series of (equivariant) Euler characteristics of some vector bundles constructed from the tautological
bundles on Hilbert schemes of points on affine $k$-spaces.
We establish the surface case of these conjectures
and present some verifications of the higher dimensional cases.
We define a notion of formal quantum field theory and associate a formal quantum field theory
to K-theoretical intersection theories on Hilbert schemes of points on algebraic surfaces.
This enables us to find an effective way to compute K-theoretical intersection theories on Hilbert schemes
via a connection to Macdonald polynomials and vertex operators.