TY - UNPB

T1 - On gauge transformations in twistless torsional Newton–Cartan geometry

AU - von Blanckenburg, Arian L.

AU - Schwartz, Philip K.

PY - 2024/2/7

Y1 - 2024/2/7

N2 - We observe that in type I twistless torsional Newton–Cartan (TTNC) geometry, one can always find (at least locally) a gauge transformation that transforms a specific locally Galilei-invariant function—that we dub the ‘locally Galilei-invariant potential’—to zero, due to the corresponding equation for the gauge parameter taking the form of a Hamilton–Jacobi equation. In the case of type II TTNC geometry, the same gauge fixing may locally be performed by subleading spatial diffeomorphisms. We show (a) how this generalises a classical result in standard Newton–Cartan geometry, and (b) how it allows to parametrise the metric structure of a Galilei manifold as well as the gauge equivalence class of the Bargmann form of TTNC geometry in terms of just the space metric and a unit timelike vector field.

AB - We observe that in type I twistless torsional Newton–Cartan (TTNC) geometry, one can always find (at least locally) a gauge transformation that transforms a specific locally Galilei-invariant function—that we dub the ‘locally Galilei-invariant potential’—to zero, due to the corresponding equation for the gauge parameter taking the form of a Hamilton–Jacobi equation. In the case of type II TTNC geometry, the same gauge fixing may locally be performed by subleading spatial diffeomorphisms. We show (a) how this generalises a classical result in standard Newton–Cartan geometry, and (b) how it allows to parametrise the metric structure of a Galilei manifold as well as the gauge equivalence class of the Bargmann form of TTNC geometry in terms of just the space metric and a unit timelike vector field.

M3 - Preprint

BT - On gauge transformations in twistless torsional Newton–Cartan geometry

ER -