|
University of the Ryukyus Repository >
Faculty of Science >
Bulletin >
Ryukyu mathematical journal >
Vol.12 (1999) >
| |
| Title | : | Proper time as an operator |
| Authors | : | Matsumoto, Shuichi |
| Authors alternative | : | 松本, 修一 |
| Issue Date | : | 30-Dec-1999 |
| Abstract | : | 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. |
| Type Local | : | 紀要論文 |
| ISSN | : | 1344-008X |
| Publisher | : | Department of Mathematical Sciences, Faculty of Science, University of the Ryukyus |
| URI | : | http://hdl.handle.net/20.500.12000/15167 |
| Citation | : | Ryukyu mathematical journal Vol.12 p.37 -51 |
| Appears in Collections | : | Vol.12 (1999)
|
Files in This Item:
| File |
Description |
Size | Format |
|---|
| Vol12p037.pdf | | 3964Kb | Adobe PDF | View/Open |
|
|
|
