Constructing differential operators in discrete spacetimes emerging from Causal Sets

• Grant number: 25/12786-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2025
• End date: September 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Gustavo Pazzini de Brito
• Grantee: Mateus Moreira Diniz
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

This project investigates the construction of differential operators in discrete spacetimes described by the Causal Set approach, a promising theory for quantum gravity. The main objective is to develop new operators capable of extracting geometric information in the continuum limit, contributing to the understanding of the quantum dynamics of spacetime. The methodology combines differential geometry and statistics. The project aims to establish a starting point for defining extensions of the Benincasa-Dowker action, which may play an important role in describing the dynamics of Causal Sets with a well-defined continuum limit. (AU)