The Eisenhart Lift for Field Theories

Understand

We present the Eisenhart-lift formalism in which the dynamics of a system that evolves under the influence of a conservative force is equivalent to that of a free system embedded in a curved manifold with one additional generalised coordinate.

• As an illustrative example in Classical Mechanics, we apply this formalism to simple harmonic motion.
• We extend the Eisenhart lift to homogeneous field theories by adding one new field.
• Unlike an auxiliary field, this field is fully dynamical and is therefore termed fictitious.