It is shown that the Schr\"odinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation velocity. For a system of interacting particles, a fully nonrelativistic nonlinear system of integro-differential equations is proposed. In the case where the size of the system of particles is of the same order as the Compton wavelength associated with particles, certain essential differences are shown to exist as compared with traditional consequences of the nonrelativistic Schr\"odinger equation.It is shown that the Schr\"odinger nonrelativistic equation of a system of interacting particles is not a rigorously nonrelativistic equation since it is based on the implicit assumption of finiteness of the interaction propagation velocity. For a system of interacting particles, a fully nonrelativistic nonlinear system of integro-differential equations is proposed. In the case where the size of the system of particles is of the same order as the Compton wavelength associated with particles, certain essential differences are shown to exist as compared with traditional consequences of the nonrelativistic Schr\"odinger equation.

arXiv:quant-ph/0002012Physical Review ADec 8, 19993 citations

Nonrelativistic particles with spin

Springer eBooksApr 6, 20080 citations

Quantum theory of nonrelativistic particles interacting with gravity

Charis Anastopoulos

We investigate the effects of the gravitational field on the quantum dynamics of nonrelativistic particles. We consider $N$ nonrelativistic particles, interacting with the linearized gravitational field. Using the Feynman-Vernon influence functional technique, we trace out the graviton field to obtain a master equation for the system of particles to first order in $G$ . The effective interaction between the particles as well as the self-interaction is in general non-Markovian. We show that the gravitational self-interaction cannot be held responsible for decoherence of microscopic particles due to the fast vanishing of the diffusion function. For macroscopic particles though, it leads to diagonalization to the energy eigenstate basis, a desirable feature in gravity-induced collapse models. We finally comment on possible applications.We investigate the effects of the gravitational field on the quantum dynamics of nonrelativistic particles. We consider $N$ nonrelativistic particles, interacting with the linearized gravitational field. Using the Feynman-Vernon influence functional technique, we trace out the graviton field to obtain a master equation for the system of particles to first order in $G$. The effective interaction between the particles as well as the self-interaction is in general non-Markovian. We show that the gravitational self-interaction cannot be held responsible for decoherence of microscopic particles due to the fast vanishing of the diffusion function. For macroscopic particles though, it leads to diagonalization to the energy eigenstate basis, a desirable feature in gravity-induced collapse models. We finally comment on possible applications.

arXiv:gr-qc/9511004Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsJul 15, 199637 citations

Nonrelativistic Elementary Particles

Springer eBooksJan 1, 20020 citations

We investigate the effects of the gravitational field on the quantum dynamics of nonrelativistic particles. We consider

N

nonrelativistic particles, interacting with the linearized gravitational field. Using the Feynman-Vernon influence functional technique, we trace out the graviton field to obtain a master equation for the system of particles to first order in

G

. The effective interaction between the particles as well as the self-interaction is in general non-Markovian. We show that the gravitational self-interaction cannot be held responsible for decoherence of microscopic particles due to the fast vanishing of the diffusion function. For macroscopic particles though, it leads to diagonalization to the energy eigenstate basis, a desirable feature in gravity-induced collapse models. We finally comment on possible applications.