On the Schrödinger-Newton equation and its symmetries: a geometric view

Christian Duval (1, 2) , Serge Lazzarini (2, 1)

1 CPT - E2 Géométrie, Physique et Symétries
2 CPT - Centre de Physique Théorique - UMR 7332

The \SN (SN) equation is recast on purely geometrical grounds, namely in terms of Bargmann structures over $(\d+1)$-dimensional Newton-Cartan (NC) spacetimes. Its maximal group of invariance, which we call the SN group, is determined as the group of conformal Bargmann automorphisms that preserve the coupled Schr\"odinger and NC gravitational field equations. Canonical unitary representations of the SN group are worked out, helping us recover, in particular, a very specific occurrence of dilations with dynamical exponent $z=(\d+2)/3$.

Mots clés: Bargmann structures; Schr\"odinger-Newton equation; Symmetry groups

Domaines: Physique mathématique [math-ph]; Relativité Générale et Cosmologie Quantique [gr-qc]; Physique des Hautes Energies - Théorie [hep-th]

Christian Duval, Serge Lazzarini. On the Schrödinger-Newton equation and its symmetries: a geometric view. Classical and Quantum Gravity, 2015, 32, pp.175006. ⟨hal-01143011v3⟩