Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1993-12-14
Nucl.Phys. B427 (1994) 643-668
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, Latex file, figures available from the authors under request. LPTHE-PAR 93-56
Scientific paper
10.1016/0550-3213(94)90643-2
The exact general evolution of circular strings in $2+1$ dimensional de Sitter spacetime is described closely and completely in terms of elliptic functions. The evolution depends on a constant parameter $b$, related to the string energy, and falls into three classes depending on whether $b<1/4$ (oscillatory motion), $b=1/4$ (degenerated, hyperbolic motion) or $b>1/4$ (unbounded motion). The novel feature here is that one single world-sheet generically describes {\it infinitely many} (different and independent) strings. The world-sheet time $\tau$ is an infinite-valued function of the string physical time, each branch yields a different string. This has no analogue in flat spacetime. We compute the string energy $E$ as a function of the string proper size $S$, and analyze it for the expanding and oscillating strings. For expanding strings $(\dot{S}>0)$: $E\neq 0$ even at $S=0$, $E$ decreases for small $S$ and increases $\propto\hspace*{-1mm}S$ for large $S$. For an oscillating string $(0\leq S\leq S_{max})$, the average energy $
de Vega Hector J.
Larsen Arne. L.
Sánchez Nadia
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