Relativistic quantum backflow

In this paper we discuss relativistic quantum backflow. The general theory of relativistic
 backflow is written down and it is shown that the backflow can be written as a function of
 a simple parameter epsilon which is defined in terms of fundamental constants and the 
 backflow period. Backflow eigenfunctions are determined numerically for a range of values 
 of epsilon and an explicit expression for the relativistic backflow eigenvalue in terms of the 
 non-relativistic backflow constant is presented. Then backflow eigenvectors are fitted with 
 some standard functions which lead to substantially higher backflow than has been found 
 previously with fitting procedures, for some values of epsilon. In analysing the non-relativistic 
 limit of the theory we show that this problem is one of those rare cases where the relativistic 
 theory is intrinsically more simple than the non-relativistic theory.