What are physicists doing?
nsrivast: You say "physics textbooks don't give this system explicitly". They don't need to - they simply present the system that's most instructive to learn or is most interesting to their authors. As long as your formula or "system" is consistent with the accepted formulations of special relativity, you have no reason to worry.PS - Most physics communities are getting by with their own methods, and if you really think yours adds something you should write a textbook (or a paper).