Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories

Elaborating on our previous presentation, where the term dipolar quantization was introduced, we argue here that adopting L-0 - (L-1 + L-1)/2 L-0 - (L-1 + L-1)/2 as the Hamiltonian instead of L-0 + 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.