Algebraic quantum theory

TL;DR

This paper proposes an algebraic space-time framework for elementary particles aiming to unify quantum field theory and general relativity through the Langlands program, involving algebraic groups and representations.

Contribution

It introduces an algebraic space-time structure for particles within the Langlands program, connecting quantum theory with advanced algebraic concepts.

Findings

Development of an algebraic space-time model for particles

Introduction of algebraic quanta, strings, and fields

Potential unification of quantum field theory and general relativity

Abstract

The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global program based on the infinite dimensional representations of algebraic groups over adele rings. In this context, algebraic quanta, strings and fields of particles are introduced.