SEMICLASSICAL QUANTIZATION OF CIRCULAR STRINGS IN DE SITTER AND ANTI DE SITTER SPACETIMES

We compute the exact equation of state of circular strings in the (2+1) dimensional de Sitter (dS) and antide 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=(-1)E, with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient depending on the elliptic modulus. We semiclassically quantize the oscillating circular strings. The string mass is m= C /(H), C being the Casimir operator, C=-LL, of the O(3,1)-dS [O(2,2)-AdS] group, and H is the Hubble constant. We find mdS2 4n-5H2 n2 (n N0), and a finite number of states NdS 0.34/(H2) in de Sitter spacetime; mAdS2 H2n2 (large n N0) and NAdS= in antide 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. © 1995 The American Physical Society.