Modified Measures as an Effective Theory for Causal Fermion Systems

TL;DR

The paper investigates how modified measure theories (MMT) and causal fermion systems (CFS) relate as frameworks for gravity and quantum fields, arguing that classical spacetimes can emerge as a continuum limit of CFS and that certain MMTs may serve as effective descriptions of CFS modifications. It analyzes foundational differences (classical manifolds with independent measures in MMT vs. operator manifolds with a fundamental measure in CFS), the distribution of metric tasks, and how field equations arise in each approach, emphasizing the role of regularization length $\varepsilon$ and the need for modified measures in curved spacetimes. A key focus is on identifying which MMTs can be consistent with the causal action principle of CFS, with baryogenesis providing an explicit example where modified measures are essential. The work sets the stage for cross-approach phenomenology, outlining how constraints derived from CFS could inform viable MMT models and pave the way for cosmological and astrophysical predictions.

Abstract

We compare the structures of the theory of causal fermion systems (CFS), an approach to unify quantum theory with general relativity (GR), with those of modified measure theories (MMT), which are a set of modified gravity theories. Classical spacetimes with MMT can be obtained as the continuum limit of a CFS. This suggests that MMT could serve as effective descriptions of modifications to GR implied by CFS. The goal is to lay the foundation for future research on exploring which MMTs are consistent with the causal action principle of CFS.

Figures (3)

• Figure 1: Causal propagation of a wave function.
• Figure 2: Probing with many wave functions.
• Figure 3: Probing an electromagnetic field.

Theorems & Definitions (3)

• Definition 2.1
• Definition 2.2
• Definition 2.3