TY - JOUR
T1 - A Clebsch portrait for Schrödinger’s theory
AU - Barbieri, Gabriele
AU - Spera, Mauro
PY - 2024
Y1 - 2024
N2 - In this note we pursue the investigation initiated in Spera M (in: Nielsen, Barbaresco, (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, Springer, Cham, 2023) by addressing geometric and topological issues concerning the zero set of the wave function, provided it is a knot in 3-space. Since, the standard Madelung velocity breaks down thereat, it is necessary to resort to the Clebsch geometry of the probability current shown in the above paper. This leads to considering several tightly interknit symplectic manifolds.
AB - In this note we pursue the investigation initiated in Spera M (in: Nielsen, Barbaresco, (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, Springer, Cham, 2023) by addressing geometric and topological issues concerning the zero set of the wave function, provided it is a knot in 3-space. Since, the standard Madelung velocity breaks down thereat, it is necessary to resort to the Clebsch geometry of the probability current shown in the above paper. This leads to considering several tightly interknit symplectic manifolds.
KW - Madelung-Schrödinger picture, moment map, vortex motion, Fubini-Study metric, Clebsch variables
KW - Madelung-Schrödinger picture, moment map, vortex motion, Fubini-Study metric, Clebsch variables
UR - http://hdl.handle.net/10807/287456
U2 - 10.1140/epjp/s13360-024-05466-8
DO - 10.1140/epjp/s13360-024-05466-8
M3 - Article
SN - 2190-5444
VL - 139
SP - 1
EP - 8
JO - THE EUROPEAN PHYSICAL JOURNAL PLUS
JF - THE EUROPEAN PHYSICAL JOURNAL PLUS
ER -