Quantum phase shift and neutrino oscillations in a stationary, weak gravitational field

TL;DR

This paper introduces a novel method using Synge's world function to calculate gravitationally induced quantum phase shifts, specifically applied to neutrino oscillations in weak gravitational fields, avoiding geodesic calculations.

Contribution

The paper develops a new approach based on Synge's world function for calculating quantum phase shifts in stationary spacetimes, simplifying previous methods and applying it to neutrino oscillations.

Findings

Neutrino oscillations are insensitive to gravitomagnetic effects when spin is ignored.

Explicit calculations for spherical, homogeneous bodies are provided.

Comparison with Schwarzschild spacetime results confirms the method's validity.

Abstract

A new method based on Synge's world function is developed for determining within the WKB approximation the gravitationally induced quantum phase shift of a particle propagating in a stationary spacetime. This method avoids any calculation of geodesics. A detailed treatment is given for relativistic particles within the weak field, linear approximation of any metric theory. The method is applied to the calculation of the oscillation terms governing the interference of neutrinos considered as a superposition of two eigenstates having different masses. It is shown that the neutrino oscillations are not sensitive to the gravitomagnetic components of the metric as long as the spin contributions can be ignored. Explicit calculations are performed when the source of the field is a spherical, homogeneous body. A comparison is made with previous results obtained in Schwarzschild spacetime.