TY - JOUR
T1 - Trajectory-based conservation laws for massive spin-zero relativistic quantum particles in 1 + 1 spacetime
AU - Poirier, Bill
AU - Tsai, Hung Ming
N1 - Publisher Copyright:
© 2020 Institute of Physics Publishing. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/8/7
Y1 - 2020/8/7
N2 - We present novel aspects of a trajectory-based theory of massive spin-zero relativistic quantum particles. In this approach, the quantum trajectory ensemble is the fundamental entity. It satisfies its own action principle, leading to a dynamical partial differential equation (via the Euler-Lagrange procedure), as well as to conservation laws (via Noether's theorem). In this paper, we focus on the derivation of the latter. In addition to the usual expected energy and momentum conservation laws, there is also a third law that emerges, associated with the conditions needed to maintain global simultaneity. We also show that the nonrelativistic limits of these conservation laws match those of the earlier, nonrelativistic quantum trajectory theory [J. Chem. Phys. 136, 031102 (2012)].
AB - We present novel aspects of a trajectory-based theory of massive spin-zero relativistic quantum particles. In this approach, the quantum trajectory ensemble is the fundamental entity. It satisfies its own action principle, leading to a dynamical partial differential equation (via the Euler-Lagrange procedure), as well as to conservation laws (via Noether's theorem). In this paper, we focus on the derivation of the latter. In addition to the usual expected energy and momentum conservation laws, there is also a third law that emerges, associated with the conditions needed to maintain global simultaneity. We also show that the nonrelativistic limits of these conservation laws match those of the earlier, nonrelativistic quantum trajectory theory [J. Chem. Phys. 136, 031102 (2012)].
UR - http://www.scopus.com/inward/record.url?scp=85092023846&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/1612/1/012022
DO - 10.1088/1742-6596/1612/1/012022
M3 - Conference article
AN - SCOPUS:85092023846
VL - 1612
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
SN - 1742-6588
IS - 1
M1 - 012022
Y2 - 4 August 2019 through 9 August 2019
ER -