In this Letter a first-order Lagrangian for the Schr¨odinger–Newton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D 56(8) (1997) 4844–4877]. Then Noether’s theorem is applied to the Lie point symmetries determined by Robertshaw and Tod [Lie point symmetries and an approximate solution for the Schr¨odinger–Newton equations, Nonlinearity 19(7) (2006) 1507–1514] in order to find conservation laws of the Schr¨odinger–Newton equations.
Conservation laws for the Schrödinger-Newton equations
NUCCI, Maria Clara
2012
Abstract
In this Letter a first-order Lagrangian for the Schr¨odinger–Newton equations is derived by modifying a second-order Lagrangian proposed by Christian [Exactly soluble sector of quantum gravity, Phys. Rev. D 56(8) (1997) 4844–4877]. Then Noether’s theorem is applied to the Lie point symmetries determined by Robertshaw and Tod [Lie point symmetries and an approximate solution for the Schr¨odinger–Newton equations, Nonlinearity 19(7) (2006) 1507–1514] in order to find conservation laws of the Schr¨odinger–Newton equations.File in questo prodotto:
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