Conformal symmetries and integrals of the motion in pp waves with external electromagnetic fields

Abstract

The integrals of the motion associated with conformal Killing vectors of a curved space-time with an additional electromagnetic background are studied for massive particles. They involve a new term which might be non-local. The difficulty disappears for pp-waves, for which explicit, local conserved charges are found. Alternatively, the mass can be taken into account by "distorting" the conformal Killing vectors. The relation of these non-point symmetries to the charges is analysed both in the Lagrangian and Hamiltonian approaches, as well as in the framework of Eisenhart-Duval lift.

arXiv commentaffiliation corrected

References in corpus (21)

• Invariant Variation Problems
• Black holes and the double copy
• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Local scale invariance and strongly anisotropic equilibrium critical systems
• The Memory Effect for Plane Gravitational Waves
• Lie and Noether symmetries of geodesic equations and collineations
• Lie - point and variational symmetries in minisuperspace Einstein's gravity
• Screw-symmetric gravitational waves: a double copy of the vortex
• Exact classical and quantum dynamics in background electromagnetic fields
• Eisenhart lifts and symmetries of time-dependent systems
• Conformal symmetry classes for pp-wave spacetimes
• Embedding nonrelativistic physics inside a gravitational wave
• Optics in a nonlinear gravitational plane wave
• Superintegrable relativistic systems in spacetime-dependent background fields
• Memory effect, conformal symmetry and gravitational plane waves
• A generalized Noether theorem for scaling symmetry
• From polarized gravitational waves to analytically solvable electromagnetic beams
• Niederer's transformation, time-dependent oscillators and polarized gravitational waves
• "Kepler Harmonies" and conformal symmetries
• Revisiting the gauge principle: enforcing constants of motion as constraints
• Affine Symmetry, Geodesics, and Homogeneous Spacetimes

Cited by in corpus (13)

• Advances in QED with intense background fields
• Geodesic motion in Bogoslovsky-Finsler Spacetimes
• Schrödinger symmetry: a historical review
• Displacement within velocity effect in gravitational wave memory
• Particle motion in circularly polarized vacuum pp waves
• Gravitational Waves and Conformal Time Transformations
• Memory Effect and Carroll Symmetry: 50 years later
• Hidden symmetries from distortions of the conformal structure
• Various disguises of the Pais-Uhlenbeck oscillator
• Hidden Symmetries in Deformed Very Special Relativity
• Conformally related vacuum gravitational waves, and their symmetries
• Revisiting the dynamics of a charged spinning body in curved spacetime
• Generation of new symmetries from explicit symmetry breaking