Studies on a trajectory-based approach to relativistic quantum-particle dynamics

Anastasios Kyprianidis

Paulina Corona-Ugalde, Eduardo Martín-Martínez, Christopher M. Wilson +1 more

We propose a generalization of the superconducting circuit simulation of the dynamical Casimir effect where we consider relativistically moving boundary conditions following different trajectories. We study the feasibility of the setup used in the past to simulate the dynamical Casimir effect to reproduce richer relativistic trajectories differing from purely sinusoidal ones. We show how different relativistic oscillatory trajectories of the boundaries of the same period and similar shape produce a rather different spectrum of particles characteristic of their respective motions.

Jan Rzewuski

K. Kowalski

Abstract The Bohmian trajectories for a free spinless relativistic particle that is initially in a coherent state are studied in the Hamiltonian dynamics based on the Salpeter equation as an alternative to the Klein–Gordon Equation. The guidance equation is introduced utilizing the probability density and relativistic probability current obtained from the Salpeter equation.

Bill Poirier, Hung-Ming Tsai

Abstract 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)].