A formulação de Eisenhart para teorias de campos escalares

Abstract

In the present work, we discuss the Eisenhart lift, introduced by L. P. Eisenhart in 1928, when dealing with analytical mechanics. The core idea behind the lift is to look at a lagrangian mechanical or field system that is initially a “minimally-coupled” system with a corresponding interaction term, and look for equivalent expressions of it, in which the new fields are all “free”.

We make an exposition of the works by Eisenhart, K. Finn, S. Karamitsos e A. Plaftsis on the subject, and we also introduce a new viewpoint on the mathematical structure of said lifts, allowing for more fexibile choices of the new field spaces. We also obtain a general differential equation for the problem, which we hope to yield proper harmonic solutions for fields, as they weren’t possible in the previous approaches.