1996/02/27 by R. Cosgrove, R. B. Cosgrove, Cosgrove, R.
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #gr-qc #quant-ph
paper · pdf · doi:10.48550/arxiv.gr-qc/9602051
13 pages, LaTeX, no figures
arxiv created 1996/02/27 · openalex publication_date 1996/02/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.