Year: 2012
Type: article
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.
Authors: Felix Finster, Andreas Grotz
Institutions: University of Regensburg, Harvard University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
Funder: Deutsche Forschungsgemeinschaft
OpenAlex ID: W2028973723