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

Variational Neural-Network Ansatz for Continuum Quantum Field Theory

John M. Martyn, Khadijeh Najafi, Di Luo

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In nonrelativistic quantum field theories, the challenge is to parametrize and optimize over the infinitely many n-particle wave functions comprising the state's Fock-space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to nonrelativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parametrize all of the n-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In nonrelativistic quantum field theories, the challenge is to parametrize and optimize over the infinitely many n-particle wave functions comprising the state's Fock-space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to nonrelativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parametrize all of the n-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

arXiv:2212.00782Physical Review LettersAug 24, 202318 citations

Methods of Nonrelativistic Quantum Field Theory

K. W. Kehr

Springer eBooksJan 1, 19770 citations

QUANTUM THEORY OF NON-INTERACTING FIELDS

H. Muirhead

Elsevier eBooksJan 1, 19650 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.