H2N2V1, France, Analysis, bibRecord, 000287

Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes

Identifieur interne : 000287 ( France/Analysis ); précédent : 000286; suivant : 000288

Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes

Auteurs : H. J. De Vega [France, Royaume-Uni] ; A. L. Larsen [France] ; N. Sánchez [France]

Source :

Physical Review D (Particles and Fields) [ 0556-2821 ] ; 1995-06-15.

RBID : Pascal:95-0291912

Descripteurs français

Pascal (Inist)
- Etude théorique, 1127, 1125M, Modèle corde, Calcul 3 dimensions, Espace temps, Equation état, Energie, Masse, Quantification, Approximation semiclassique, Opérateur Casimir, Système centre masse, Espace Minkowski.

English descriptors

KwdEn :
- Casimir operators, Center-of-mass system, Energy, Equations of state, Mass, Minkowski space, Quantization, Semiclassical approximation, Space-time, String models, Theoretical study, Three-dimensional calculations.

Abstract

We compute the exact equation of state of circular strings in the (2+1)-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting, and expanding) strings. The string equation of state has the perfect fluid form P = (γ-1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient γ depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is m = * root *C /(πHα′), C being the Casimir operator, C = -L_μνL^μν, of the O(3,1)-dS [O(2,2)-AdS] group, and H is the Hubble constant. We find α′m_dS²* roughly-equal *4n-5H²α′n² (n* is-an-element-of *N₀), and a finite number of states N_dS* roughly-equal *0.34/(H²α′) in de Sitter spacetime; m_AdS²* roughly-equal *H²n² (large n* is-an-element-of *N₀) and N_AdS = ∞ in anti-de Sitter spacetime. The level spacing grows with n in AdS spacetime, while it is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime. The massive states in dS spacetime decay through the tunnel effect and the semiclassical decay probability is computed. The semiclassical quantization of exact (circular) strings and the canonical quantization of generic string perturbations around the string center of mass qualitatively agree.

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<front><div type="abstract" xml:lang="en">We compute the exact equation of state of circular strings in the (2+1)-dimensional de Sitter (dS) and anti-de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting, and expanding) strings. The string equation of state has the perfect fluid form P = (γ-1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient γ depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is m = * root *C /(πHα′), C being the Casimir operator, C = -L<sub>μν</sub>
L<sup>μν</sup>
, of the O(3,1)-dS [O(2,2)-AdS] group, and H is the Hubble constant. We find α′m<sub>dS</sub>
<sup>2</sup>
* roughly-equal *4n-5H<sup>2</sup>
α′n<sup>2</sup>
 (n* is-an-element-of *N<sub>0</sub>
), and a finite number of states N<sub>dS</sub>
* roughly-equal *0.34/(H<sup>2</sup>
α′) in de Sitter spacetime; m<sub>AdS</sub>
<sup>2</sup>
* roughly-equal *H<sup>2</sup>
n<sup>2</sup>
 (large n* is-an-element-of *N<sub>0</sub>
) and N<sub>AdS</sub>
 = ∞ in anti-de Sitter spacetime. The level spacing grows with n in AdS spacetime, while it is approximately constant (although smaller than in Minkowski spacetime and slightly decreasing) in dS spacetime. The massive states in dS spacetime decay through the tunnel effect and the semiclassical decay probability is computed. The semiclassical quantization of exact (circular) strings and the canonical quantization of generic string perturbations around the string center of mass qualitatively agree.</div>
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Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes

Semiclassical quantization of circular strings in de Sitter and anti-de Sitter spacetimes

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Descripteurs français

English descriptors

Abstract

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