Evolution of confined quantum scalar fields in curved spacetime. Part I
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Regular Article - Theoretical Physics
Evolution of confined quantum scalar fields in curved spacetime. Part I Spacetimes without boundaries or with static boundaries in a synchronous gauge Luis C. Barbado1,2,a , Ana L. Báez-Camargo1,b , Ivette Fuentes1,3,c 1
Quantenoptik, Quantennanophysik und Quanteninformation, Fakultät für Physik, Universität Wien, Boltzmanngasse 5, 1090 Wien, Austria Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Boltzmanngasse 3, 1090 Wien, Austria 3 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK
2
Received: 12 March 2020 / Accepted: 18 August 2020 © The Author(s) 2020
Abstract We develop a method for computing the Bogoliubov transformation experienced by a confined quantum scalar field in a globally hyperbolic spacetime, due to the changes in the geometry and/or the confining boundaries. The method constructs a basis of modes of the field associated to each Cauchy hypersurface, by means of an eigenvalue problem posed in the hypersurface. The Bogoliubov transformation between bases associated to different times can be computed through a differential equation, which coefficients have simple expressions in terms of the solutions to the eigenvalue problem. This transformation can be interpreted physically when it connects two regions of the spacetime where the metric is static. Conceptually, the method is a generalisation of Parker’s early work on cosmological particle creation. It proves especially useful in the regime of small perturbations, where it allows one to easily make quantitative predictions on the amplitude of the resonances of the field, providing an important tool in the growing research area of confined quantum fields in table-top experiments. We give examples within the perturbative regime (gravitational waves) and the nonperturbative regime (cosmological particle creation). This is the first of two articles introducing the method, dedicated to spacetimes without boundaries or which boundaries remain static in some synchronous gauge.
1 Introduction Quantum field theory in curved spacetime is the theory that studies the evolution of quantum fields which propagate in a classical general relativistic background geometry. To this a e-mail:
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date, the theory has been able to yield many quantitative theoretical predictions for physically relevant problems within its scope, such as cosmological particle creation [1,2], the Unruh effect [3] or Hawking radiation [4]. The success in the study of those concrete well-known problems can be related to the use of different mathematical techniques and simplifications, adapted to the specific problem and which yield the computations tractable. For instance, in the study of phenomena such as Hawking radiation or the Unruh effect, the presence of horizons (or “would-be horizons” [5,6]) al
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