Derivation of Field Equations from the Principle of the Fermionic Projector

TL;DR

This paper introduces a principle for formulating physical equations in discrete space-time using the fermionic projector, deriving classical field equations from a discrete framework that aligns with Lorentzian geometry.

Contribution

It proposes the principle of the fermionic projector as a new foundational approach to derive classical field equations from discrete space-time.

Findings

Discrete space-time can be connected to Lorentzian manifolds.

Classical field equations emerge as a limit of the discrete framework.

The principle unifies several fundamental physical principles.

Abstract

With the concept of "discrete space-time" the space-time continuum is resolved into discrete points at the scale of the Planck length. We postulate with the "principle of the fermionic projector" that physical equations must be formulated intrinsically in discrete space-time with the projector on fermionic states. This principle combines the Pauli principle, a local gauge principle and the principle of relativity, but does not include a locality or causality principle. It is shown that a well-established limit yields the structure of a Lorentzian manifold. The equations of discrete space-time reduce to classical field equations. This preliminary text is intended as introduction. Detailed calculations can be obtained from the author on request.