# On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics

@article{Goldin2001OnGI, title={On Galilean invariance and nonlinearity in electrodynamics and quantum mechanics}, author={G. Goldin and Vladimir M. Shtelen}, journal={Physics Letters A}, year={2001}, volume={279}, pages={321-326} }

## 22 Citations

Generalizations of nonlinear and supersymmetric classical electrodynamics

- Physics, Mathematics
- 2008

We first write down a very general description of nonlinear classical electrodynamics, making use of generalized constitutive equations and constitutive tensors. Our approach includes non-Lagrangian…

Galilean and U(1)-gauge symmetry of the Schrödinger field

- Physics
- 2008

Abstract This paper undertakes a study of the nature of the force associated with the local U ( 1 ) -gauge symmetry of a non-relativistic quantum particle. To ensure invariance under local U ( 1 )…

Generalizations of Yang–Mills theory with nonlinear constitutive equations

- Mathematics, Physics
- 2004

We generalize classical Yang–Mills theory by extending nonlinear constitutive equations for Maxwell fields to non-Abelian gauge groups. Such theories may or may not be Lagrangian. We obtain…

Square-integrable solutions to a family of nonlinear schrödinger equations from nonlinear quantum theory

- Mathematics
- 2005

The Pauli–Lubański vector, complex electrodynamics, and photon helicity

- Physics
- 2015

We critically analyze the concept of photon helicity and its connection with the Pauli?Luba?ski vector from the viewpoint of the complex electromagnetic field, sometimes attributed to Riemann but…

Symmetries and couplings of non-relativistic electrodynamics

- Physics
- 2016

A bstractWe examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell’s equations and Galilean electrodynamics (GED) which is the…

On Lagrangian and non-Lagrangian conformal-invariant nonlinear electrodynamics

- Physics, Mathematics
- 2019

A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of…

The Pauli-Lubanski Vector in a Group-Theoretical Approach to Relativistic Wave Equations

- Physics
- 2016

Chapter 1 introduces some key elements of important topics such as; quantum mechanics, representation theory of the Lorentz and Poincaré groups, and a review of some basic relativistic wave equations…

Some Variations on Maxwell’s Equations

- Physics
- 2007

Maxwell’s equations are among the most beautiful in physics, unifying the forces of electricity and magnetism in a classical field theory that explains electromagnetic waves [1]. Some well-known,…

Carroll versus Newton and Galilei: two dual non-Einsteinian concepts of time

- Physics, Mathematics
- 2014

The Carroll group was originally introduced by Levy-Leblond (1965 Ann. Inst. Henri Poincare 3 1) by considering the contraction of the Poincare group as c → 0. In this paper an alternative…

## References

SHOWING 1-10 OF 39 REFERENCES

Gauge transformations in quantum mechanics and the unification of nonlinear Schrödinger equations

- Physics
- 1999

Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we…

Gauge Transformations for a Family of Nonlinear Schrödinger Equations

- Mathematics
- 1997

Abstract An enlarged gauge group acts nonlinearly on the class of nonlinear Schrodinger equations introduced by the author in joint work with Doebner. Here the equations and the group action are…

Introducing nonlinear gauge transformations in a family of nonlinear Schrödinger equations.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1996

The group of nonlinear gauge transformations necessary to interpret the nonlinear time-evolution equations for quantum mechanics are introduced and justified physically, and the parameters that are actually gauge invariant and describe some of their properties are determined.

The Galilean covariance of quantum mechanics in the case of external fields

- Physics
- 1999

Textbook treatments of the Galilean covariance of the time-dependent Schrodinger equation for a spinless particle seem invariably to cover the case of a free particle or one in the presence of a…

On Feynman’s proof of the Maxwell equations

- Physics
- 1992

Feynman’s proof, as recounted by F. J. Dyson [Am. J. Phys. 58, 209–211 (1990)], that the Lorentz force law and two of Maxwell’s equations can apparently be deduced from minimal assumptions about the…

Nonlinear Schrodinger dynamics of matrix D-branes

- Physics
- 2001

We formulate an effective Schrodinger wave equation describing the quantum dynamics of a system of D0-branes by applying the Wilson renormalization group equation to the world sheet partition…

Galilean electromagnetism

- Physics
- 1973

SummaryConsistent nonrelativistic electromagnetic theories are investigated by stressing the requirements of Galilean relativity. It is shown that Maxwell’s equations admit two possible…

Classical Electrodynamics

- Nature
- 1969

Electrodynamics of Particles and PlasmasBy P. C. Clemmow and J. P. Dougherty. (Addison-Wesley Series in Advanced Physics.) Pp. ix + 457. (Addison-Wesley London, September 1969.) 163s.

Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics

- Mathematics
- 1993

Preface. Preface to the English Edition. Introduction. 1. Poincare Invariant Nonlinear Scalar Equations. 2. Poincare-Invariant Systems of Nonlinear PDEs. 3. Euclid and Galilei Groups and Nonlinear…

Slow light in cool atoms

- PhysicsNature
- 1999

An experiment with atoms at nanokelvin temperatures has produced the remarkable observation of light pulses travelling at velocities of only 17 m s−1. The large optical nonlinearities seen in this…