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Unruh detectors, Feynman diagrams, acceleration and decay

Wim Beenakker, David Venhoek

TL;DR

This work builds a two-stage framework to compute the decay rate of accelerated particles. First, it relates the transition rate of an accelerated Unruh–DeWitt detector to the corresponding stationary rate through a Fourier-transform of energy-gap–dependent two-point correlators along the detector’s trajectory, with the acceleration encoded in the function $\,\Delta_\tau(\kappa)$. Second, it proves an exact equivalence between the Unruh-detector decay rate and the standard QFT decay rate at leading order, by constructing a quantity $X$ that matches both pictures in the appropriate limits, thereby enabling a straightforward calculation via Feynman diagrams and phase-space integrals. The paper confirms this equivalence with a concrete example of $\phi_1 \to \phi_2\phi_3$ decay and analyzes acceleration effects numerically (and analytically in 1+1D), while outlining generalizations to spins and more complex final states; this provides a practical route to first-order accelerated-decay rates and insights into the energy exchange mechanisms induced by acceleration.

Abstract

We present a method for relating the transition rate of an accelerated Unruh-deWitt detector to the rate of the same detector when stationary in Minkowski space. Furthermore, we show that when using the detector as a model for decay, its transition rate can be related directly to the decay rate obtained from QFT. Combined this provides a straightforward method for calculating the decay rate of accelerated particles to first order in the coupling constants.

Unruh detectors, Feynman diagrams, acceleration and decay

TL;DR

This work builds a two-stage framework to compute the decay rate of accelerated particles. First, it relates the transition rate of an accelerated Unruh–DeWitt detector to the corresponding stationary rate through a Fourier-transform of energy-gap–dependent two-point correlators along the detector’s trajectory, with the acceleration encoded in the function . Second, it proves an exact equivalence between the Unruh-detector decay rate and the standard QFT decay rate at leading order, by constructing a quantity that matches both pictures in the appropriate limits, thereby enabling a straightforward calculation via Feynman diagrams and phase-space integrals. The paper confirms this equivalence with a concrete example of decay and analyzes acceleration effects numerically (and analytically in 1+1D), while outlining generalizations to spins and more complex final states; this provides a practical route to first-order accelerated-decay rates and insights into the energy exchange mechanisms induced by acceleration.

Abstract

We present a method for relating the transition rate of an accelerated Unruh-deWitt detector to the rate of the same detector when stationary in Minkowski space. Furthermore, we show that when using the detector as a model for decay, its transition rate can be related directly to the decay rate obtained from QFT. Combined this provides a straightforward method for calculating the decay rate of accelerated particles to first order in the coupling constants.
Paper Structure (16 sections, 38 equations, 2 figures)

This paper contains 16 sections, 38 equations, 2 figures.

Table of Contents

  1. Conventions
  2. Unruh detectors as model for decay
  3. Relations between accelerated and non-accelerated decay
  4. Decay processes in ordinary QFT
  5. Equivalence between the Unruh detector model and ordinary QFT
  6. Reduction to Unruh detector
  7. Reduction to QFT
  8. Example: Real scalar field decay $\phi_1 \rightarrow \phi_2\phi_3$
  9. Rate from the Unruh detector perspective
  10. Rate from the QFT perspective
  11. Impact of acceleration on the decay rate
  12. Generalizations
  13. Conclusions and outlook
  14. Properties of decay rates in $d$ dimensions
  15. Behaviour near $\Delta=\overline{\Sigma}_n$
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Decay rate relative to the non-accelerated case for a particle with $\Delta = 1.5m$, in 3+1 dimensions.
  • Figure 2: Decay rate relative to the non-accelerated case for a particle with $\Delta = 1.5m$, in 1+1 dimensions. Both the numerically integrated result (dotted line), as well as the direct evaluation of the closed analytical form (solid line) are shown.