Principal Symbol of Euler-Lagrange Operators

TL;DR

This paper introduces the principal symbol for Euler-Lagrange operators, characterizes well-posed initial value problems, clarifies constraint origins in covariant theories, and sketches a quantization approach inspired by Loop Quantum Gravity.

Contribution

It extends the concept of principal symbols to Euler-Lagrange operators and applies this to analyze well-posedness and constraints in covariant theories, proposing a quantization method.

Findings

Principal symbol for Euler-Lagrange operators introduced.

Characterization of well-posed initial value problems achieved.

Sketch of a quantization procedure based on Loop Quantum Gravity.

Abstract

We shall introduce the principal symbol for Euler-Lagrange operators and use them to charac- terise well-posed initial value problems. We shall clarify how constraints can arise in Lagrangian covariant theories by extending the standard treatment in GR. Finally, we sketch a quantization procedure based on what done in LQG.