We study the survival probability of moving relativistic unstable particles with definite momentum $\vec{p} \neq 0$ . The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo\-nen\-tial form of the survival probability, should occur much earlier than it follows from the classical standard approach resolving itself into replacing time $t$ by $t/γ$ (where $γ$ is the relativistic Lorentz factor) in the formula for the survival probability and that the survival probabilities should tend to zero as $t\rightarrow \infty$ much slower than one would expect using classical time dilation relation. Here we show also that for some physically admissible models of unstable states the computed decay curves of the moving particles have fluctuating form at relatively short times including times of order of the lifetime.We study the survival probability of moving relativistic unstable particles with definite momentum $\vec{p} \neq 0$. The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo\-nen\-tial form of the survival probability, should occur much earlier than it follows from the classical standard approach resolving itself into replacing time $t$ by $t/γ$ (where $γ$ is the relativistic Lorentz factor) in the formula for the survival probability and that the survival probabilities should tend to zero as $t\rightarrow \infty$ much slower than one would expect using classical time dilation relation. Here we show also that for some physically admissible models of unstable states the computed decay curves of the moving particles have fluctuating form at relatively short times including times of order of the lifetime.

arXiv:1506.05076Acta Physica Polonica BJan 1, 20176 citations

On classical and quantum relativistic dynamics

F. Reuse

Foundations of PhysicsDec 1, 197918 citations

Remarks on Relativistic Quantum Mechanics

K. V. Roberts

Physical ReviewJan 1, 19512 citations

Quasi-relativistic description of a quantum particle moving through one-dimensional piecewise constant potentials

Luis Grave de Peralta

Using a novel quasi-relativistic wave equation, which can give precise results up to energies ~mc2, exact quantum mechanical solutions are found which corresponds to a particle with mass moving through one-dimensional piecewise constant potentials. As expected, at low particle’s speeds, the found solutions coincide with the solutions of the same problems calculated using the Schrödinger equation; however, as it should be, both solutions have a significative difference at quasi-relativistic speeds. Then, it is argued that the quasi-relativistic wave equation provides a simpler description than a fully relativistic theory or the perturbation approach for a quantum particle moving at quasi-relativistic energies through piecewise constant potentials.Using a novel quasi-relativistic wave equation, which can give precise results up to energies ~mc2, exact quantum mechanical solutions are found which corresponds to a particle with mass moving through one-dimensional piecewise constant potentials. As expected, at low particle’s speeds, the found solutions coincide with the solutions of the same problems calculated using the Schrödinger equation; however, as it should be, both solutions have a significative difference at quasi-relativistic speeds. Then, it is argued that the quasi-relativistic wave equation provides a simpler description than a fully relativistic theory or the perturbation approach for a quantum particle moving at quasi-relativistic energies through piecewise constant potentials.

Results in PhysicsAug 18, 202013 citations

Relativistic effect of entanglement in fermion-fermion scattering

Jinbo Fan, Xinfei Li

We study the properties of entanglement entropy among scattering particles as observed from different inertial moving frames, based on an exemplary QED process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. By the explicit calculation of the Wigner rotation, the entanglement entropy of scattering particles is found to be Lorentz invariant. We also study the behavior of the entanglement between spin degrees of freedom for scattering particles in moving frames. This quantity, being found to change with different inertial reference frames, does not exhibit as a Lorentz invariant.We study the properties of entanglement entropy among scattering particles as observed from different inertial moving frames, based on an exemplary QED process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. By the explicit calculation of the Wigner rotation, the entanglement entropy of scattering particles is found to be Lorentz invariant. We also study the behavior of the entanglement between spin degrees of freedom for scattering particles in moving frames. This quantity, being found to change with different inertial reference frames, does not exhibit as a Lorentz invariant.

arXiv:1712.06237Physical review. D/Physical review. D.Jan 23, 201840 citations

A Note on Relativistic Quantum Mechanics

Hartland S. Snyder

Physical ReviewMar 1, 19480 citations

We study the survival probability of moving relativistic unstable particles with definite momentum

\vec{p} \neq 0

. The amplitude of the survival probability of these particles is calculated using its integral representation. We found decay curves of such particles for the quantum mechanical models considered. These model studies show that late time deviations of the survival probability of these particles from the exponential form of the decay law, that is the transition times region between exponential and non-expo\-nen\-tial form of the survival probability, should occur much earlier than it follows from the classical standard approach resolving itself into replacing time

t

t/γ

(where

γ

is the relativistic Lorentz factor) in the formula for the survival probability and that the survival probabilities should tend to zero as

t\rightarrow \infty

much slower than one would expect using classical time dilation relation. Here we show also that for some physically admissible models of unstable states the computed decay curves of the moving particles have fluctuating form at relatively short times including times of order of the lifetime.