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

Journal Article · Thu Jun 15 04:00:00 EDT 1995 · Physical Review, D

DOI:https://doi.org/10.1103/PhysRevD.51.6917· OSTI ID:55214

de Vega, H J ^[1]; Larsen, A L; Sanchez, N ^[2]

---

1. Laboratoire de Physique Theorique et Hautes Energies, Universite de Paris VI et VII, Tour 16, 1er etage, 4, Place Jussieu, 75252 Paris cedex 05 (France)
2. Observatoire de Paris, DEMIRM, Observatoire de Paris et Ecole Normale Superieure, 61, Avenue de l`Observatoire, 75014 Paris (France)

We compute the {ital 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 {ital P}=({gamma}{minus}1){ital E}, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient {gamma} depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is {ital m}= {radical}{ital C} /({pi}{ital H}{alpha}{prime}), {ital C} being the Casimir operator, {ital C}={minus}{ital L}{sub {mu}{nu}}{ital L}{sup {mu}{nu}}, of the O(3,1)-dS [O(2,2)-AdS] group, and {ital H} is the Hubble constant. We find {alpha}{prime}{ital m}{sub dS}{sup 2}{approx}4{ital n}{minus}5{ital H}{sup 2}{alpha}{prime}{ital n}{sup 2} ({ital n}{element_of}{ital N}{sub 0}), and a {ital finite} number of states {ital N}{sub dS}{approx}0.34/({ital H}{sup 2}{alpha}{prime}) in de Sitter spacetime; {ital m}{sub AdS}{sup 2}{approx}{ital H}{sup 2}{ital n}{sup 2} (large {ital n}{element_of}{ital N}{sub 0}) and {ital N}{sub AdS}={infinity} in anti--de Sitter spacetime. The level spacing grows with {ital 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 {ital exact} (circular) strings and the canonical quantization of generic string perturbations around the string center of mass qualitatively agree.

• OSTI ID: 55214
• Journal Information: Physical Review, D, Journal Name: Physical Review, D Journal Issue: 12 Vol. 51; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CASIMIR OPERATORS
CENTER-OF-MASS SYSTEM
ENERGY
EQUATIONS OF STATE
MASS
MINKOWSKI SPACE
QUANTIZATION
SEMICLASSICAL APPROXIMATION
SPACE-TIME
STRING MODELS
THREE-DIMENSIONAL CALCULATIONS