62 citations · 152 across the 17 of their papers we have counts for
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A Universal Kinematical Group for Quantum Mechanics
Gerald A. Goldin, David H. Sharp
In 1968, Dashen and Sharp obtained a certain singular Lie algebra of local densities and currents from canonical commutation relations in nonrelativistic quantum field theory. The…
On gauge transformations of Bäcklund type and higher order nonlinear Schrödinger equations
Gerald A. Goldin, Vladimir M. Shtelen
We introduce a new, more general type of nonlinear gauge transformation in nonrelativistic quantum mechanics that involves derivatives of the wave function and belongs to the class…
On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics
Gerald A. Goldin, Vladimir Shtelen
Recent experimental results on slow light heighten interest in nonlinear Maxwell theories. We obtain Galilei covariant equations for electromagnetism by allowing special nonlineari…
Perspectives on Nonlinearity in Quantum Theory
Gerald A. Goldin
An enlarged group G of nonlinear transformations, modeled on the general linear group GL(2,R), leads to a beautiful, apparently unremarked symmetry between the wave function's phas…
Gauge Transformations in Quantum Mechanics and the Unification of Nonlinear Schrödinger Equations
H. -D. Doebner, G. A. Goldin, P. Nattermann
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different ti…
A FAMILY OF NONLINEAR SCHRÖDINGER EQUATIONS: LINEARIZING TRANSFORMATIONS AND RESULTING STRUCTURE
H. -D. Doebner, G. A. Goldin, P. Nattermann
We examine a recently-proposed family of nonlinear Schrödinger equations [J. Phys. A: Math. Gen. 27:1771(1994)] with respect to a group of transformations that linearize a subfamil…