Physically sound Hamiltonian formulati on of the dynamical Casimir effect

Journal Article · Sat Sep 15 04:00:00 EDT 2007 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.76.065001· OSTI ID:21032269

Haro, Jaume ^[1]; Elizalde, Emilio ^[2]

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1. Departament de Matematica Aplicada I, Universitat Politecnica de Catalunya, Diagonal 647, 08028 Barcelona (Spain)
2. Instituto de Ciencias del Espacio (CSIC) and Institut d'Estudis Espacials de Catalunya (IEEC/CSIC), Universitat Autonoma de Barcelona, Torre C5-Parell-2a planta, 08193 Bellaterra, Barcelona (Spain)

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.

• OSTI ID: 21032269
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 6 Vol. 76; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ACCELERATION
CASIMIR EFFECT
ENERGY CONSERVATION
HAMILTONIANS
OSCILLATIONS
QUANTUM ELECTRODYNAMICS
SCALAR FIELDS
SOUND WAVES