Gauge transformations for a family of nonlinear schrödinger equations

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Abstract

An enlarged gauge group acts nonlinearly on the class of nonlinear Schrödinger equations introduced by the author in joint work with Doebner. Here the equations and the group action are displayed in the presence of an external electromagnetic field. All the gauge-invariants are listed for the coupled nonlinear “Schrödinger-Maxwell” theory. Time-dependent gauge parameters result in additional terms of the type introduced by Kostin and Bialynicki-Birula and Mycielski, but Maxwell’s equations for the (non-quantized) gauge-invariant electric and magnetic fields remain linear.

Original languageEnglish (US)
Pages (from-to)6-11
Number of pages6
JournalJournal of Nonlinear Mathematical Physics
Volume4
Issue number1-2
DOIs
StatePublished - 1997

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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