Action-Angle Variables for Complex Projective Space and Semiclassical Exactness

We construct the action-angle variables of a classical integrable model defined on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase approximation. We show that the resulting expression for the propagator coincides with the exact propagator which was obtained by solving the time-dependent Schr\"odinger equation.Comment: 11 pages, Revtex 3.0, SNUTP-94-6

Positive Equation-of-state Parameter in the Accelerating Dilaton Cosmology

In a semiclassically quantized two-dimensional cosmological model, it can be shown that the parameter of the equation of state for the accelerating universe can be positive due to the negative energy density and the negative pressure, which is a little different from the conventional wisdom that the parameter is negative with the positivity of the energy density. Furthermore, we show that the full parameter composed of the classical and the quantum-mechanical contributions is positive and finite even though the partial state parameter from the quantum-mechanical contribution is not positive definite, which means that the state parameter is not perturbatively additive in this model.Comment: 9 pages, 4 figures; to appear in the Journal of Korean Physical Societ

Phase Space Structure of Non-Abelian Chern-Simons Particles

We investigate the classical phase space structure of $N$ $SU(n+1)$ non-Abelian Chern-Simons (NACS) particles by first constructing the product space of associated $SU(n+1)$ bundle with ${\bf CP}^n$ as the fiber. We calculate the Poisson bracket using the symplectic structure on the associated bundle and find that the minimal substitution in the presence of external gauge fields is equivalent to the modification of symplectic structure by the addition of field strength two form. Then, we take a direct product of the associated bundle by the space of all connections and choose a specific connection by the condition of vanishing momentum map corresponding to the gauge transformation, thus recovering the quantum mechanical model of NACS particles in Ref.\cite{lo1}.Comment: 18 pages, REVTEX 3.0, SNUTP-93-4