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

IR HANDLE

Search this article

Abstract

Elaborating on our previous presentation, where the term dipolar quantization was introduced, we argue here that adopting L0−(L1+L−1)/2+L̄0−(L̄1+L̄−1)/2 as the Hamiltonian instead of L0+L̄0 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.

Journal

Details 詳細情報について

Report a problem

Back to top