Quantum field theory measurements for relativistic particles

TL;DR

This paper develops a relativistic measurement theory for quantum fields, addressing the limitations of non-relativistic models by incorporating spin, polarization, and internal degrees of freedom, with applications to various quantum field measurements.

Contribution

It introduces a relativistic measurement framework using Quantum Temporal Probabilities, extending measurement models to include spin, polarization, and internal structures of particles.

Findings

Probabilities for time-of-arrival including spin/polarization

Generalized photodetection formulas beyond Glauber's theory

Derivation of particle oscillation formula and its limitations

Abstract

The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential relativistic principles of locality, causality, and Lorentz covariance, and are therefore inadequate for quantum field theoretic settings. While most existing work focuses on scalar fields, realistic particles possess spin, polarization, and internal degrees of freedom that introduce new conceptual and operational challenges. To this end, we employ the Quantum Temporal Probabilities (QTP) framework for relativistic measurements to describe electromagnetic, Dirac, and internally structured scalar fields. Our results include probabilities for the time-of-arrival that take spin/polarization into account, generalized photodetection formulas beyond Glauber's theory, an unambiguous derivation of the particle oscillation formula together with its limitations, and a first-principles analysis of relativistic qudits.