Minimal electromagnetic coupling schemes. II. Relativistic and nonrelativistic Maxwell groups

Abstract

Minimal electromagnetic coupling schemes entering into Klein–Gordon or Schrödinger equations are studied in connection with symmetries outside the symmetry groups of the corresponding free equations. The Schrader construction of the so-called (relativistic) Maxwell group is reviewed through group extensions of kinematical groups associated with (constant and uniform) electromagnetic fields. The construction of the Galilean (nonrelativistic) Maxwell group is given.

Gauge theory of the Maxwell-Weyl group

“…Motivation behind this kind of extension is that symmetries of empty Minkowski space-time is described by Poincare algebra if such a space-time filled with some background field must lead to modification of the Poincare algebra. The extension of the Poincare algebra by six additional abelian generators is called the Maxwell algebra [3][4][5][6][7][8]. Addition of new generators to the Poincare algebra leads naturally to extended space-time geometry.…”

Kappa-deformations: historical developments and recent results

“…In Sect.5 I shall describe briefly two recent applications of κ-deformations: the introduction of quantum-covariant κ-deformed phase space as an example of quantum space with Hopf algebroid structure [44,45] and the insertion of κ-deformation into the Yang-Baxter (YB) sigma model defined on (5) coset space, which leads to the κ-deformation of D=10 GS superstring target space geometry [46].…”

“…The presence of a constant relativistic EM background (F µν = ∂ µ A ν − ∂ ν A µ ; µ, ν = 0, 1, 2, 3) leads to the deformation of Poincaré algebra into Maxwell algebra [3]- [5], with noncommutative fourmomenta generators P µ [P µ , P ν ] = 0 (Poincaré algebra)…”

Geometric model of topological insulators from the Maxwell algebra

“…The corresponding geometric action on the gapped boundary, where the gap is induced by an external electromagnetic field, is implemented by gauging the Maxwell algebra [44][45][46][47]. This represents a noncentral extension of the Poincaré algebra.…”