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Semiclassical Trace Formulas in Terms of Phase Space Path Integrals

✍ Scribed by Ayumu Sugita

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
254 KB
Volume
288
Category
Article
ISSN
0003-4916

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✦ Synopsis

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.

📜 SIMILAR VOLUMES

Semiclassical approximation of path inte
Semiclassical approximation of path integrals on and near caustics in terms of catastrophes: G. Dangelmayr and W. Veit, Institute for Information Sciences, University of Tübingen, Tübingen, Germany
📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 84 KB

A semiclassical approximation of Feynman's path integral is derived which, in contradistinction to conventional formulae, remains finite in conjugate (focal) points and on caustics, exhibits the experimentally observed oscillatory behavior near these and reduces to familiar approximations far away.