Nonlinear Gauge Transformations and Exact Solutions of the Doebner-Goldin Equation

The Lorentz covariance of a non-linear, time-dependent relativistic wave equation is demonstrated; the equation has recently been shown to have highly interesting and significant empirical consequences. It is established here that an operator already exists which ensures the relativistic properties of the equation. Furthermore, we show that the time-dependent equation is gauge invariant. The equation however, breaks Poincare symmetry via time translation in a way consistent w...

In this paper we study a general nonlinear Schr\"odinger equation with a time dependent harmonic potential. Despite the lack of traslational invariance we find a symmetry trasformation which, up from any solution, produces infinitely many others which are centered on classical trajectories. The results presented here imply that, not only the center of mass of the wave-packet satisfies the Ehrenfest theorem and is decoupled from the dynamics of the wave-packet, but also the sh...

In their reply arXiv:1408.2230, the authors corrected some inappropriate sentences and clarified misleading descriptions in their original manuscript arXiv:1407.5194v1.

In this second part, we establish the existence of special solutions of the nonlinear Schr\"odinger system studied in the first part when the diamagnetic field is nul. We also prove some symmetry properties of these ground states solutions.

We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed, in particular, the motion in the constant magnetic field is studied in detail.

We present the results of a study of the gauge dependence of spacetime perturbations. In particular, we consider gauge invariance in general, we give a generating formula for gauge transformations to an arbitrary order n, and explicit transformation rules at second order.

The action principle is frequently used to derive the classical equations of motion. The action may also be used to associate group elements with curves in the space-time manifold, similar to the gauge transformations. The action principle is shown here to be an equivalence relation between the infinitesimal elements so defined for a collection of closed curves and the identity element. The action principle is then extended by requiring the equivalence of global elements with...

Gauge theories have been a cornerstone of the description of the world at the level of the fundamental particles. The Lagrangian or the action describing the corresponding interactions is invariant under certain gauge transformations. This symmetry is reflected in terms of the Ward-Green-Takahashi (or the Slavnov-Taylor) identities which relate various Green functions among each other, and the Landau-Khalatnikov-Fradkin transformations which relate a Green function in a parti...

The aim of this paper is to introduce and analyze a new gauge symmetry that appears in complex holomorphic systems. This symmetry allow us to project the system, using different gauge conditions, to several real systems which are connect by gauge transformations in the complex space. We prove that the space of solutions of one system is related to the other by the gauge transformation. The gauge transformations are in some cases canonical transformations. However, in other ca...

We investigate certain invariance properties of quantum fluids subject to a nonlinear gauge potential. In particular, we derive the covariant transformation laws for the nonlinear potentials under a space-time Galilean boost and consider U(1) gauge transformations. We find that the hydrodynamic canonical field equations are form-invariant in the case of external gauge functions, but not for nonlinear gauge functionals. Hence, nonlinear gauge potentials are non-trivial potenti...