2007/01/31 by N. Obadia, M. Milgrom, Mordehai Milgrom · 1 citation
Mathematics · Physics and Astronomy · #Classical mechanics #Computer science #Cosmology and Gravitation Theories #Exponential function #Feynman diagram #Mathematical analysis #Mathematical physics #Mathematics #Minkowski space #Noncommutative and Quantum Gravity Theories #Physics #Proper time #Quantum Electrodynamics and Casimir Effect #Quantum mechanics #Regularization (linguistics) #Scalar (mathematics) #Scalar field #Statistical physics #Unruh effect #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.75.065006
published as Phys.Rev.D75:065006,2007 · 17 pages, 9 figures, one paragraph added, version accepted in Phys.Rev.D
arxiv created 2007/03/04 · openalex publication_date 2007/03/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the Feynman prescription that is explicitly causal, and we compare it to other expressions used in the literature. We then use this expression to study, analytically and numerically, the time dependence of the response function in various nonstationarity situations. We show that, generically, the response function decreases like a power in the detector's level spacing, E, for high E. It is only for stationary worldlines that the response function decays faster than any power law, in keeping with the known exponential behavior for some stationary cases. Under some conditions the (time-dependent) response function for a nonstationary worldline is well approximated by the value of the response function for a stationary worldline having the same instantaneous acceleration, torsion, and hypertorsion. While we cannot offer general conditions for this to apply, we discuss special cases; in particular, the low-energy limit for linear space trajectories.