Cosmological constant and Euclidean space from nonperturbative quantum torsion

Abstract

Heisenberg's nonperturbative quantization technique is applied to the nonperturbative quantization of gravity. An infinite set of equations for all Green's functions is obtained. An approximation is considered where: (a) the metric remains as a classical field; (b) the affine connection can be decomposed into classical and quantum parts; (c) the classical part of the affine connection is the Christoffel symbols; (d) the quantum part is the torsion. Using a scalar and vector fields approximation it is shown that nonperturbative quantum effects give rise to a cosmological constant and an Euclidean solution.

Moduli spaces of oriented Type A manifolds of dimension at least 3

“…Although much of Riemannian geometry involves the study of the Levi-Civita connection, which is without torsion, in recent years connections which have torsion have played an important role in many developments. We refer, for example, to work on B-metrics [28,38,47,53], on almost hypercomplex geometries [46], on string theory [1,27,33,37], on spin geometries [39], on torsion-gravity [5,12,19,20,21,22,44,45,54], on contact geometries [2,28], on almost product manifolds [49], non-integrable geometries [3,9], on the non-commutative residue for manifolds with boundary [55], on Hermitian and anti-Hermitian geometry [48], CR geometry [17], hyper-Kähler with torsion supersymmetric sigma models [23,25,24,52], Einstein-Weyl gravity at the linearized level [16], Yang-Mills flow with torsion [34], ESK theories [14], double field theory [36], BRST theory [26], and the symplectic and elliptic geometries of gravity [13]. Perhaps surprisingly, even the 2-dimensional case is of interest; connections on surfaces have been used to construct new examples of pseudo-Riemannian metrics without a corresponding Riemannian counterpart [10,11,15,…”