Non-relativistic Quantum Field Theory of Verlinde's Emergent Entropic Gravity

M. C. ROCCA; A. PLASTINO

ANNALS OF PHYSICS (NEW YORK)

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2020 vol. 412 p. 168013 - 168025

0003-4916

Non relativistic quantum field theory propagators are indispensable tools in nuclear physics and condensed matter theory. Here we apply them to gravitation, that is, discuss a non relativistic quantum field theory for fermions and bosons in a Verlinde-information theory-scenario. In it, gravity becomes an emergent entropic force. In a first previous paper [Physica A {f 505} 190 (2018)], we have shown, via statistical mechanics, that emergent gravity can indeed be thought of as an entropic force at a {it classical} level. In two subsequent works [Physica A {f 518} 139 (2019); {f 518} 265 (2019)] we did the same at a {it quantum level}, for bosons and fermions. Further, thetwo additional papers [DOI: 10.13140/RG.2.2.17894.88641; Entropy {f 21} 682 (2019)] discussed the first quantization of EEG for bosons and fermions, by solving the corresponding Schr"{o}dinger equations.{it In the present effort} we deal with the pertinent Non-Relativistic (NR) Quantum Field Theory (QFT) corresponding to fermions and bosons´ EEG. With this purpose, we use the results previously obtained in the above mentioned papers together with the formulation of the NR QFT described in the classical text-book by Fetter and Walecka. Note that we are speaking of an NR QFT because we are using Verlinde´s gravitational potential (in relativistic QFT people do not use potentials)