  Elaborating on our previous presentation, where the term {\it dipolar
quantization} was introduced, we argue here that adopting
$L_0-(L_1+L_{-1})/2+{\bar L}_0-({\bar L}_1+{\bar L}_{-1})/2$ as the Hamiltonian
instead of $L_0+{\bar L}_0$ yields an infinite circumference limit in
two-dimensional conformal field theory. The new Hamiltonian leads to dipolar
quantization instead of radial quantization. As a result, the new theory
exhibits a continuous and strongly degenerated spectrum in addition to the
Virasoro algebra with a continuous index. Its Hilbert space exhibits a
different inner product than that obtained in the original theory. The
idiosyncrasy of this particular Hamiltonian is its relation to the so-called
sine-square deformation, which is found in the study of a certain class of
quantum statistical systems. The appearance of the infinite circumference
explains why the vacuum states of sine-square deformed systems are coincident
with those of the respective closed-boundary systems.
