Semiclassical trace formulas in terms of phase space path integrals

摘要

Semiclassical trace formulas are examined using phase space path integrals. Our main concern in tills paper is the Maslov index of the periodic orbit, which seems nor fully understood in previous works. We show that the calculation of the Maslov index is reduced to a classification of connections on a vector bundle over S-1 with structure group Sp(2n, R). We derive a formula for the index of the n-repetition, and show that a Bohr-Sommerfeld type quantization condition including quadratic fluctuation around the orbit is derived using this formula. (C) 2001 Academic Press. [References: 13]