Issues in Quantum-Geometric Propagation

TL;DR

This paper explores relativistic quantum-geometric mechanics on phase space, demonstrating that propagators in flat spacetime are Lorentz-equivalent to Minkowski results, with implications for quantum fields in curved spacetimes.

Contribution

It generalizes quantum-geometric scalar field propagation to curved spacetimes and shows Lorentz invariance of propagators in flat spacetime within this formalism.

Findings

Propagator in flat spacetime is Lorentz-equivalent to Minkowski propagator.

Lorentz boosts act as Bogolubov transformations in this framework.

Explicit demonstration in a Milne universe confirms theoretical results.

Abstract

A discussion of relativistic quantum-geometric mechanics on phase space and its generalisation to the propagation of free, massive, quantum-geometric scalar fields on curved spacetimes is given. It is shown that in an arbitrary coordinate system and frame of reference in a flat spacetime, the resulting propagator is necessarily the same as derived in the standard Minkowski coordinates up to a Lorentz boost acting on the momentum content of the field, which is therefore seen to play the role of Bogolubov transformations in this formalism. These results are explicitly demonstrated in the context of a Milne universe.