Relativistic Tunneling Time

Quantum tunneling times is an old and fundamental problem; it has been debated for decades since it was first pointed out in 1931.the interest on this subject has grown up, not only for it's theoretical valuable, for example the physical meaning of superluminal tunneling; but also for it's connect with hi-tech, especially during the last twenty years, for the increaseing use of high-speed electronic devices (based on tunneling processes) as well as for the acknowledged importance of the tunnel effect in nuclear fission and fusion, more and more interest be taken on this problem. In this paper we firstly introduce the history of tunneling times in introduction, and the major debated questions in tunneling times (the validity of the various tunneling times, the relation between those tunneling times, and the physical meaning of superluminal transmission times). In the second part we examine in detail some existing definitions for the tunneling times, namely: the phase-time; the B'uttiker and Landauer times; the Larmor times; the complex (path-integral and Bohm) times; the dwell time; and give the using condition of the various tunneling times, the relation between those tunneling times, the Hartman effect of those times. In the third part we firstly introduce some previous works, we find only a few papers have discussed relativistic tunneling time, and the tunneling time has been also traditionally examined for stationary state which is inaccurate in certain condition(for example, the relativistic Larmor time). In order to avoid the weakness and discuss the relation between those tunneling times, we give the general forms of the dwell time and the Larmor time, and compare the relationship between two times; in nonrelativistic limit we reduced our calculation to the previous nonrelativistic papers. Finally, we calculate tunneling times of the square barrier which is most simple and representative, and analyze the superluminal tunneling (Hartman effect). In the last part we introduce our next works.The debates focused on the validity of the various tunneling times, the relation between those tunneling times, and the physical meaning of superluminal transmission times indicated by a number of experiments. One commonly cited reason for these debates is time enters in quantum theory as a parameter rather than an observable, in other words, a quantum-mechanical time operator is nonexistent, and there is no direct way to calculate tunneling times. Thus a series of approaches have been proposed to address this issue, but there have been no clear-cut solutions to this old and fundamental problem.