Abstract
We consider particle production in $1+1$ dimensional thermal Anti-de Sitter space under the influence of a constant electric field. The vacuum-persistence amplitude is given by a non-relativistic tunnelling instanton once we interpret the system as being governed by an "equivalent" non-relativistic Schr\"odinger equation. Working in the WKB approximation, we calculate the tunnelling rate in anti de Sitter space at finite temperature and observe that the particle production rate is enhanced. Additionally, it is observed that there is a critical temperature beyond which the production rate is affected by the thermal environment. We claim this to be a new result for Anti-de Sitter space in the semi-classical approximation.
Highlights
In the “Consequences of Dirac’s theory of positrons” [1], Heisenberg and Euler suggested that quantum vacuum fluctuations can be uplifted to a “real” observable pair of particles if given an external electric field of sufficient strength
This is a new result in anti–de Sitter space in the semiclassical approximation, and the temperature has an effect on the particle production only beyond a certain critical value similar to what we had for flat spacetime
In this paper we considered the issue of charged pair production in thermal anti–de Sitter space
Summary
In the “Consequences of Dirac’s theory of positrons” [1], Heisenberg and Euler suggested that quantum vacuum fluctuations can be uplifted to a “real” observable pair of particles if given an external electric field of sufficient strength. Πm; ð1Þ qE a result in quantum electrodynamics first computed by Julian Schwinger [2] These produced pairs constitute a current that backreacts to destabilize the otherwise classically stable background electric field configuration. The production rate is given by the Euclidean action computed over the tunneling instanton, or equivalently, a Wentzel– Kramers–Brillouin (WKB) quantum tunnelling probability [11,12,13,14,15,16] to go across a barrier At zero temperature, this process is solely dictated by quantum tunneling and the energy extracted from the background electric field. Working in the WKB approximation, we calculate the tunneling rate in AdS space at finite temperature and observe that the particle production rate is enhanced similar to what is seen in thermal Minkowski background with a critical temperature beyond which the production rate is affected by the thermal environment.
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