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| Original language | English |
|---|---|
| Publication status | E-pub ahead of print - 7 Feb 2024 |
Abstract
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2024.
Research output: Working paper/Preprint › Preprint
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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 -