Semi-Classical Theory — Path Integrals
The “Old Quantum Theory” which is based on the Bohr-Sommerfeld quantization condition, provided a means of quantizing a classical mechanical system by quantizing the action variables associated with invariant tori. (For a historical discussion see [Born 1960].) However, it was recognized by Einstein, as early as 1917 [Einstein 1917], that this method could only be used for systems in which trajectories lie on invariant tori. The Bohr-Sommerfeld quantization condition could not be used to quantize chaotic systems and until recently no method existed by which to connect classically chaotic systems with their quantum counterpart.
KeywordsPeriodic Orbit Chaotic System Path Integral Trace Formula Conjugate Point
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