Non-relativistic quantum field theory of Verlinde’s emergent entropic gravity

Abstract

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 (Plastino and Rocca (2018)), we have shown, via statistical mechanics, that emergent gravity can indeed be thought of as an entropic force at a classical level. In two subsequent works (Plastino and Rocca etal (2019); Plastino and Rocca (2019)) we did the same at a quantum level, for bosons and fermions. Further, the two additional papers (Plastino and Rocca (2019)) discussed the first quantization of EEG for bosons and fermions, by solving the corresponding Schrödinger equations. 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).