2005/10/04 by Sergei Winitzki · 4 citations
Mathematics · Physics and Astronomy · #Adiabatic process #Ansatz #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Series (stratigraphy) #Statistical physics #WKB approximation #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.72.104011
published as Phys.Rev. D72 (2005) 104011 · 14 pages, RevTeX, 5 figures; minor changes, a clarification in Sec. II D
arxiv created 2005/10/04 · openalex publication_date 2005/11/17 · arxiv updated 2016/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Particle production by slow-changing gravitational fields is usually described using quantum field theory in curved spacetime. Calculations require a definition of the vacuum state, which can be given using the adiabatic (WKB) approximation. I investigate the best attainable precision of the resulting approximate definition of the particle number. The standard WKB ansatz yields a divergent asymptotic series in the adiabatic parameter. I derive a novel formula for the optimal number of terms in that series and demonstrate that the error of the optimally truncated WKB series is exponentially small. This precision is still insufficient to describe particle production from vacuum, which is typically also exponentially small. An adequately precise approximation can be found by improving the WKB ansatz through perturbation theory. I show quantitatively that the fundamentally unavoidable imprecision in the definition of particle number in a time-dependent background is equal to the particle production expected to occur during that epoch. The results are illustrated by analytic and numerical examples.