A Variational Principle in Discrete Space-Time - Existence of Minimizers

TL;DR

This paper introduces a variational principle for projectors in indefinite inner product spaces and proves the existence of minimizers in different scenarios, advancing the mathematical understanding of discrete space-time models.

Contribution

It formulates a new variational principle in discrete space-time and establishes the existence of minimizers, which was previously unproven in this context.

Findings

Existence of minimizers proved in various cases

Formulation of a variational principle for projectors

Advances mathematical understanding of discrete space-time

Abstract

We formulate a variational principle for a collection of projectors in an indefinite inner product space. The existence of minimizers is proved in various situations.