Geometrical evaluation of the Maslov index

A geometrical method to calculate the Maslov index, which is an important part of the quantum phase, is proposed. This method is particularly useful for the recently proposed amplitude-free quasicorrelation function approach for the quantization of chaos [K. Hotta and K. Takatsuka, J. Phys. A 36, 4785 (2003)]. In this theory the Maslov index is involved with no need to calculate the amplitude factor, which is usually obtained through integration of the stability matrix. Since this matrix constitutes the major origin of difficulty in semiclassical quantization of chaos and since its integration is time consuming, the present method, which avoids the stability matrix, should assist in opening a gate for practical semiclassical quantization of chaos in a large molecular system.