On the Dirac's Indefinite Metric Space

An Indefinite Kähler Metric on the Space of Oriented Lines

The total space of the tangent bundle of a Kähler manifold admits a canonical Kähler structure. Parallel translation identifies the space T of oriented affine lines in R with the tangent bundle of S. Thus, the round metric on S induces a Kähler structure on T which turns out to have a metric of neutral signature. It is shown that the isometry group of this metric is isomorphic to the isometry g...

The Clifford-Klein Space Forms of Indefinite Metric

Indefinite Almost Paracontact Metric Manifolds

In this paper we introduce the concept of (ε)-almost paracontact manifolds, and in particular, of (ε)-para Sasakian manifolds. Several examples are presented. Some typical identities for curvature tensor and Ricci tensor of (ε)-para Sasakian manifolds are obtained. We prove that if a semi-Riemannian manifold is one of flat, proper recurrent or proper Ricci-recurrent, then it can not admit an (ε...

An Indefinite Metric Model for Interacting Quantum Fields on Globally Hyperbolic Space-Times

We consider a relativistic ansatz for the vacuum expectation values (VEVs) of a quantum field on a globally hyperbolic space-time which is motivated by certain Euclidean field theories. The Yang-Feldman asymptotic condition w.r.t. an “in”-field in a quasi-free representation of the canonic commutation relations (CCR) leads to a solution of this ansatz for the VEVs. A GNS-like construction on a ...

ADMITTING CENTER MAPS ON MULTIPLICATIVE METRIC SPACE

‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎s...