Field Theories on the Poincaré Disk

Abstract

The massive scalar field theory and the chiral Schwinger model are quantized on a Poincaré disk of radius $\rho$. The amplitudes are derived in terms of hypergeometric functions. The behavior at long distances and near the boundary of some of the relevant correlation functions is studied. The exact computation of the chiral determinant appearing in the Schwinger model is obtained exploiting perturbation theory. This calculation poses interesting mathematical problems, as the Poincaré disk is a noncompact manifold with a metric tensor which diverges approaching the boundary. The results presented in this paper are very useful in view of possible extensions to general Riemann surfaces. Moreover, they could also shed some light in the quantization of field theories on manifolds with constant curvature scalars in higher dimensions.

22 pages, Plain TeX+harvmac

References in corpus (2)

• The generalized chiral Schwinger model on the two-sphere
• On the Schwinger Model on Riemann Surfaces

Cited by in corpus (2)

• de Sitter at all loops: the story of the Schwinger model
• Topologically Nontrivial Sectors of the Maxwell Field Theory on Algebraic Curves