@article{oai:u-ryukyu.repo.nii.ac.jp:02005317,
 author = {Matsumoto, Shuichi and 松本, 修一},
 journal = {Ryukyu mathematical journal},
 month = {Dec},
 note = {When we quantize a system consisting of a single particle, the proper time τ and the rest mass m are usually dealt with as parameters. In the present article, however, we introduce a new quantization rule by which these quantities are regarded as operators in addition to the position and the momentum. Applying this new rule to a scalar particle and to a particle with spin 1/2, we analyze the time evolution of the operator τ. In the former case, the evolution of the proper time perfectly matches several well-established classical formulae. In the case of the particle with spin 1/2, our new rule implies that an oscillation appears in the time evolution of the operator τ. This oscillation is similar to Zitterbewegung which is well-known in the ordinary Dirac theory. We formulate one physical effect of this oscillation by considering the interaction with a gravitational field, and estimate how small it is., 紀要論文},
 pages = {37--51},
 title = {Proper time as an operator},
 volume = {12},
 year = {1999}
}