Semiclassical trace formulas in terms of phase space path integrals

Details Semiclassical trace formulas in terms of phase space path integrals Semiclassical trace formulas in terms of phase space path integrals

2000-05-06

arxiv.org/abs/nlin/0005011v2

Ann. Phys. 288 (2001) 277-324

Nonlinear Sciences

Chaotic Dynamics

59pages 8figures, typos corrected

Scientific paper

10.1006/aphy.2001.6115

Semiclassical trace formulas are examined using phase space path integrals. Our main concern in this paper is the Maslov index of the periodic orbit, which seems not 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.

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