Emergence of the wavefunction of a non-relativistic quantum particle from QFT

TL;DR

This paper derives the nonrelativistic electron wavefunction from the Dirac field within QED, showing how wave-packets and the Pauli equation arise in the $NR$ limit. It frames the wavefunction as the matrix element $ \psi_{k,s}(x)=\langle 0| \Psi(x) | k,s,\text{electron}\rangle$ and demonstrates how external fields and vacuum fluctuations generate corrections such as vacuum polarization and the anomalous magnetic moment via the vertex operator, e.g. the Pauli term $ \frac{g-2}{4m} e F_{\mu\nu} S^{\mu\nu}$. The approach provides a field-theoretic basis for the one-particle truncation and shows how the NR Schrödinger/Pauli dynamics emerge from the underlying fields, connecting NR QM with the Standard Model. This has implications for interpreting the wavefunction as a real physical object and for computing electron dynamics in weak fields within a unified QFT framework.

Abstract

The nonrelativistic wavefunction of a quantum state that contains all its information is derived directly from the effective quantum fields of the standard model of particle physics, which are the fundamental elements of reality of the universe unveiled to us so far. Consequently, the endless debate about the reality of a wavefunction can now be reasonably put to rest and nonrelativistic quantum mechanics can cogently be considered as a genuine theory.

Figures (1)

• Figure 1: Plot of Gaussian wave packet function of an electron portrayed in position space.