Five Lectures on the Jet Methods in Field Theory

TL;DR

This paper introduces jet manifold methods in field theory, explaining their mathematical foundations and applications to gauge theories, aiming to bridge the gap between differential geometry and physics.

Contribution

It provides an accessible introduction to jet manifolds and their use in Lagrangian and Hamiltonian formalisms for fundamental field models.

Findings

Jet manifolds offer a comprehensive framework for field dynamics.

Application to gauge theories enhances understanding of field models.

Bridges the gap between differential geometry and theoretical physics.

Abstract

The fibre bundle formulation of gauge theory is generally accepted. The jet manifold machinery completes this formulation and provides the adequate mathematical description of dynamics of fields represented by sections of fibre bundles. Theory of differential operators, Lagrangian and Hamiltonian formalisms on bundles have utilized widely the language of jet manifolds. Moreover, when not restricted to principal connections, differential geometry also is phrased in jet terms. However, this powerful tool remains almost unknown to physicists. These Lectures give introduction to jet manifolds, Lagrangian and Hamiltonian formalisms in jet manifolds and their application to a number of fundamental field models.