Solving Gauss' Laws and Searching Dirac Observables for the Four Interactions

TL;DR

This paper reviews the progress in reducing the four fundamental interactions to Dirac's observables, focusing on classical models of particle physics and gravity with Grassmann-valued matter fields.

Contribution

It provides a comprehensive overview of classical reduction methods for all four interactions, including the standard model and tetrad gravity, with Grassmann-valued matter.

Findings

Progress in solving Gauss' laws for the four interactions.

Development of methods to identify Dirac observables in these models.

Insights into the classical structure of matter and gravity with Grassmann variables.

Abstract

A review is given of the status of the program of classical reduction to Dirac's observables of the four interactions (standard SU(3)xSU(2)xU(1) particle model and tetrad gravity) with the matter described either by Grassmann-valued fermion fields or by particles with Grassmann charges.