Fermi transport of spinors and free QED states in curved spacetime

TL;DR

This paper provides a detailed geometric analysis of Fermi transport for spinors in curved spacetime, linking it to classical field theory and applying it to construct free electron states in a detector-dependent QED framework.

Contribution

It introduces a precise geometric description of Fermi transport for spinors using 2-spinor geometry and connects it to the transport of vectors, with applications to quantum electrodynamics in curved spacetime.

Findings

Characterization of all transports yielding Fermi transport of vectors.

Identification of a distinguished spinor transport related to vector transport.

Application to constructing free electron states in curved spacetime QED.

Abstract

Fermi transport of spinors can be precisely understood in terms of 2-spinor geometry. By using a partly original, previously developed treatment of 2-spinors and classical fields, we describe the family of all transports, along a given 1-dimensional timelike submanifold of spacetime, which yield the standard Fermi transport of vectors. Moreover we show that this family has a distinguished member, whose relation to the Fermi transport of vectors is similar to the relation between the spinor connection and spacetime connection. Various properties of the Fermi transport of spinors are discussed, and applied to the construction of free electron states for a detector-dependent QED formalism introduced in a previous paper.