Advances in Theoretical and Mathematical Physics

A Lorentzian quantum geometry

Felix Finster and Andreas Grotz

Full-text: Open access

Abstract

We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce precisely to the common objects of Lorentzian spin geometry, up to higher-order curvature corrections.

Article information

Source
Adv. Theor. Math. Phys., Volume 16, Number 4 (2012), 1197-1290.

Dates
First available in Project Euclid: 20 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1408559163

Mathematical Reviews number (MathSciNet)
MR3053970

Zentralblatt MATH identifier
1346.82002

Citation

Finster, Felix; Grotz, Andreas. A Lorentzian quantum geometry. Adv. Theor. Math. Phys. 16 (2012), no. 4, 1197--1290. https://projecteuclid.org/euclid.atmp/1408559163


Export citation