2005/08/05 by Shoju Kudaka, Kudaka, Shoju, Shuichi Matsumoto +1
Physics and Astronomy · #FOS: Physical sciences #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum and Classical Electrodynamics #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0508046
15 pages, no figure
arxiv created 2005/08/05 · openalex publication_date 2005/08/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We find a quantum mechanical formulation of proper time for spin 1/2 particles within the framework of the Dirac theory. It is shown that the rate of proper time can be represented by an operator called the ` ` tempo operator'', and that the proper time itself be given by the integral of the expectation value of the operator. The tempo operator has some terms involving the Pauli spin matrices, and the evolution of the proper time is influenced by the spin state via these terms. The relation between the tempo operator and the metric tensor is elucidated.