A Single Particle Interpretation of Relativistic Quantum Mechanics

TL;DR

This paper proposes a novel single-particle interpretation of relativistic quantum mechanics in 1+1 dimensions, using a bi-Hamiltonian framework that accounts for observer-dependent wave functions and non-local observables.

Contribution

It introduces a bi-Hamiltonian formulation for relativistic particles, providing a consistent single-particle quantum interpretation that incorporates observer dependence and non-locality.

Findings

Observer-dependent wave functions in relativistic QM

Both Hamiltonians become Hermitian operators upon quantization

Consistent single-particle interpretation with non-local observables

Abstract

The relativistic free particle system in 1+1 dimensions is formulated as a ``bi-Hamiltonian system''. One Hamiltonian generates ordinary time translations, and another generates (essentially) boosts. Any observer, accelerated or not, sees evolution as the continuous unfolding of a canonical transformation which may be described using the two Hamiltonians. When the system is quantized both Hamiltonians become Hermitian operators in the standard positive definite inner product. Hence, each observer sees the evolution of the wave function as the continuous unfolding of a unitary transformation in the standard positive definite inner product. The result appears to be a consistent single particle interpretation of relativistic quantum mechanics. This interpretation has the feature that the wave function is observer dependent, and observables have non-local character, similar to what one might expect in quantum gravity.