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

M. Elbistan 1,2,3, N. Dimakis 4, K. Andrzejewski 5, P.A. Horvathy 1, P. Kosínski 2,3, P.M. Zhang 1


1 School of Physics and Astronomy, Sun Yat-sen University, China

2 Institut Denis Poisson, Tours University, France

3 Orléans University, UMR, 7013, France

4 Center for Theoretical Physics, College of Physical Science and Technology, Sichuan University, China

5 Department of Computer Science, Faculty of Physics and Applied Informatics, University of Lódź, Poland


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.


Published by

Elsevier - Annals of Physics