Mass and spin are fundamental characteristics of particle. Those quantities are eigenvalues of the Casimir operators of the Poincaré group. My book then writes that $$ p^\mu p_\mu = m_0^2, $$ where $m_0$ is mass of idle and mass $m=\gamma m_0$ is mass of moving (relativistic mass).
If we boost the first equation, we have $$ ({\Lambda_{\nu }^{\mu }}p_{\mu })({\Lambda_{\mu }^{\nu }}p^{\mu })=\gamma^2m_{0}^2=(\Lambda_{\nu }^{\mu }\Lambda_{\mu }^{\nu })p_{\mu }p^{\mu }=1\cdot p_{\mu }p^{\mu } =m_{0}^2, $$ and this is a contradiction! One other author says that exist only mass of idle, and no sense that we speak about mass of moving. Why we hadn't speak about mass of moving?
P.S. Casimir operators are scalar operators, but and $m_0$ is scalar, but it is change as which quantity (scalar, tensor or vector)? This transform as $m=m_0\times gamma$ if we has relativistic mass, but this concept I think that is not valid, it is interpretation.
