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

Christian Duval (1) , Serge Lazzarini (1)

1 CPT - Centre de Physique Théorique - UMR 7332

The Schrödinger-Newton (SN) equation is recast on purely geometrical grounds, namely in terms of Bargmann structures over (n + 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 Schrödinger 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 = (n + 2)/3.

Mots clés: Schr\"odinger-Newton equation; Bargmann structures; 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. 2015. ⟨hal-01143011v1⟩