Physically sound Hamiltonian formulation of the dynamical Casimir effect

Jaume Haro and Emilio Elizalde
Phys. Rev. D 76, 065001 – Published 4 September 2007

Abstract

Recently [J. Haro and E. Elizalde, Phys. Rev. Lett. 97, 130401 (2006)], a Hamiltonian formulation has been introduced in order to address some long-standing severe problems associated with the physical description of the dynamical Casimir effect at all times while the mirrors are moving. Here we present the complete calculation providing precise details, in particular, of the regularization procedure, which is decisive for the correct derivation of physically meaningful quantities. A basic difference when comparing with the results previously obtained by other authors is the fact that the motion force derived in our approach contains a reactive term—proportional to the mirrors’ acceleration. This is of the essence in order to obtain particles with a positive energy at all times during the oscillation of the mirrors—while always satisfying the energy conservation law. A careful analysis of the interrelations among the different results previously obtained in the literature is then carried out. For simplicity, the specific case of a neutral scalar field in one dimension, with one or two partially transmitting mirrors (a fundamental proviso for the regularization issue), is considered in more detail, but our general method is shown to be generalizable, without essential problems (Sec. II of this paper), to fields of any kind in two and higher dimensions.

  • Received 7 May 2007

DOI:https://doi.org/10.1103/PhysRevD.76.065001

©2007 American Physical Society

Authors & Affiliations

Jaume Haro1,* and Emilio Elizalde2,†

  • 1Departament de Matemàtica Aplicada I, Universitat Politècnica de Catalunya, Diagonal 647, 08028 Barcelona, Spain
  • 2Instituto de Ciencias del Espacio (CSIC) and Institut d’Estudis Espacials de Catalunya (IEEC/CSIC), Universitat Autònoma de Barcelona, Torre C5-Parell-2a planta, 08193 Bellaterra (Barcelona) Spain

  • *jaime.haro@upc.edu
  • elizalde@ieec.fcr.es; elizalde@math.mit.edu

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Issue

Vol. 76, Iss. 6 — 15 September 2007

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