Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0608031 · Journal of Physics A Mathematical and Theoretical

Relativistic free-motion time-of-arrival

Zhi-Yong Wang, Cai-Dong Xiong

Published Feb 6, 2007• 6 citations
arXivHTMLPDF

Abstract

Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in the previous literatures, the relativistic time-of-arrival operator possesses self-adjoint extensions because of the particle–antiparticle symmetry. The nonrelativistic limit of our theory is in agreement with the nonrelativistic time-of-arrival theory.

DOI
10.1088/1751-8113/40/8/014

Related papers

Relativistic free-motion time-of-arrival

Wang, Z Y, Xiong, C D

Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in previous literatures, the relativistic time-of-arrival operator possesses self-adjoint extensions because of the particle-antiparticle symmetry. The nonrelativistic limit of our theory is in agreement with the nonrelativistic time-of-arrival theory. By comparing the time-of-arrival operator with the Hamiltonian operator of a free Dirac particle, one can show a duality between position space and momentum space.

•Jan 17, 2007•5 citations

Relativistic free-motion time-of-arrival operator for massive spin-0 particles with positive energy

Philip Caesar Flores, Eric A. Galapon

A relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles was constructed by Razavi [Il Nuovo Cimento B 63, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the time-of-arrival problem that goes beyond Razavi's original results. This allows us to use time-of-arrival eigenfunctions that exhibit unitary arrival to construct time-of-arrival distributions. The expectation value is also calculated and shown that particles can arrive earlier or later than expected classically. Last, the constructed time-of-arrival distribution and expectation value are shown to be consistent with special relativity.

arXiv:2203.00898•Physical Review A•Jun 8, 2022•11 citations

Relativistic time of arrival and traversal time

A. Ruschhaupt

The time of arrival and the traversal time through a region of a free particle with spin 1/2 are computed by applying the relativistic extension of the event-enhanced quantum theory presented in a previous paper. There is a very good coincidence of the results of this formalism and the results obtained by using classical relativistic mechanics.

arXiv:quant-ph/0207014•Journal of Physics A Mathematical and General•Nov 19, 2002•22 citations

Comment on “Arrival time in quantum mechanics” and “Time of arrival in quantum mechanics”

Jerzy Kijowski

Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the ``time operator,'' which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.

Physical Review A•Jan 1, 1999•45 citations

Spin-dependent observable effect for free particles using the arrival time distribution

Md. Manirul Ali, A. S. Majumdar, Dipankar Home +1 more

The mean arrival time of free particles is computed using the quantum-mechanical probability current. This is uniquely determined in the nonrelativistic limit of Dirac equation, although the Schr\"odinger probability current has an inherent nonuniqueness. Since the Dirac probability current contains a spin-dependent term, an arrival time distribution based on the probability current shows an observable spin-dependent effect, even for free particles. This arises essentially from relativistic quantum dynamics, but persists even in the nonrelativistic regime.

arXiv:quant-ph/0306106•Physical Review A•Oct 9, 2003•22 citations

Arrival time in quantum field theory

Zhiyong Wang, Cai-Dong Xiong, Bing He

Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is based on a position-momentum dual formalism. Within the framework of field quantization, the total time-of-arrival is the sum of the single event-of-arrival contributions, and contains zero-point quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics.

arXiv:0711.2011•Physics Letters B•Jul 24, 2008•2 citations
Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in the previous literatures, the relativistic time-of-arrival operator possesses self-adjoint extensions because of the particle–antiparticle symmetry. The nonrelativistic limit of our theory is in agreement with the nonrelativistic time-of-arrival theory.
Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in previous literatures, the relativistic time-of-arrival operator possesses self-adjoint extensions because of the particle-antiparticle symmetry. The nonrelativistic limit of our theory is in agreement with the nonrelativistic time-of-arrival theory. By comparing the time-of-arrival operator with the Hamiltonian operator of a free Dirac particle, one can show a duality between position space and momentum space.
A relativistic version of the Aharonov-Bohm time-of-arrival operator for spin-0 particles was constructed by Razavi [Il Nuovo Cimento B 63, 271 (1969)]. We study the operator in detail by taking its rigged Hilbert space extension. It is shown that the rigged Hilbert space extension of the operator provides more insights into the time-of-arrival problem that goes beyond Razavi's original results. This allows us to use time-of-arrival eigenfunctions that exhibit unitary arrival to construct time-of-arrival distributions. The expectation value is also calculated and shown that particles can arrive earlier or later than expected classically. Last, the constructed time-of-arrival distribution and expectation value are shown to be consistent with special relativity.
The mean arrival time of free particles is computed using the quantum-mechanical probability current. This is uniquely determined in the nonrelativistic limit of Dirac equation, although the Schr\"odinger probability current has an inherent nonuniqueness. Since the Dirac probability current contains a spin-dependent term, an arrival time distribution based on the probability current shows an observable spin-dependent effect, even for free particles. This arises essentially from relativistic quantum dynamics, but persists even in the nonrelativistic regime.
Via the proper-time eigenstates (event states) instead of the proper-mass eigenstates (particle states), free-motion time-of-arrival theory for massive spin-1/2 particles is developed at the level of quantum field theory. The approach is based on a position-momentum dual formalism. Within the framework of field quantization, the total time-of-arrival is the sum of the single event-of-arrival contributions, and contains zero-point quantum fluctuations because the clocks under consideration follow the laws of quantum mechanics.