  The explicit computation of higher-point conformal blocks in any dimension is
usually a challenging task. For two-dimensional conformal field theories in
Euclidean signature, the oscillator formalism proves to be very efficient. We
demonstrate this by reproducing the general n-point global conformal block in
the comb channel in an elegant and direct manner. Exploiting similarities to
the representation theory of two-dimensional CFTs, we extend the oscillator
formalism for the computation of higher-point conformal blocks in four
Euclidean dimensions. As a proof of concept, we explicitly compute the scalar
four-point block with scalar exchange within this framework.
