Wightman Functions in Covariant Operator Formalism of Two-Dimensional Quantum Gravity

Abstract

In the framework of the unitary, manifestly covariant zweibein operator formalism of two­ dimensional quantum gravity, presented previously, a complete set of Wightman functions is con­ structed by establishing the recurrence formulae consistent with all the two-dimensional multiple (anti)commutators. Owing to the nontrivial commutation relation between the quantum-gravity Pauli-Jordan D-function and the gravitational B·field bp , nontrivial n-point functions including bp are obtained, while the ones including only the zweibein and/or the matter fields are trivial.