Semiclassical trace formulas in terms of phase space path integrals

Abstract

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.

59pages 8figures, typos corrected

References in corpus (1)

• Geometrical properties of Maslov indices in periodic-orbit theory

Cited by in corpus (12)

• Semiclassical theory of spin-orbit interactions using spin coherent states
• Path integration over closed loops and Gutzwiller's trace formula
• Semiclassical theory of spin-orbit interaction in the extended phase space
• The "Symplectic Camel Principle" and Semiclassical Mechanics
• On the canonically invariant calculation of Maslov indices
• Effect of pitchfork bifurcations on the spectral statistics of Hamiltonian systems
• Semiclassical spin coherent state method in the weak spin-orbit coupling limit
• Transcritical bifurcations in non-integrable Hamiltonian systems
• Semiclassical theory for spatial density oscillations in fermionic systems
• Anomalous shell effect in the transition from a circular to a triangular billiard
• The Maslov Indices of Hamiltonian Periodic Orbits
• Gutzwiller's Semiclassical Trace Formula and Maslov-Type Index Theory for Symplectic Paths