Energy Vector and Time Vector in the Dirac Theory

A sign operator of energy, analogous to the helicity operator, but in the direction of what we call energy vector has been introduced. It is possible that there may be physical phenomena where energy vector should be considered. However, to write a wave function this energy vector needs a time vector. But, unlike the energy vector the time vector has no physical meaning yet. To make physical senses of the components of the time vector, the time dilation in special relativity has been studied and also the components of the time vector have been related to the tunneling times when an electron crosses a potential barrier. Physical results for quantum tunneling time will not be limited to this study.