Witten Laplacian on pinned path group and its expected semiclassical behavior

Shigeki Aida

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


A right invariant Riemannian metric is defined on a pinned path group over a compact Lie group G. The energy function of the path is a Morse function and the critical points are geodesics. We calculate the eigenvalues of the Hessian at the critical points when G = SU(n). On the other hand, there exists a pinned Brownian motion measure νλ with a variance parameter 1/λ on the pinned path group and we can define a Hodge-Kodaira-Witten type operator □λ on L2λ)-space of p-forms on the pinned path group. By using the explicit expression of eigenvalues of the Hessian of the energy function, we discuss the asymptotic behavior of the botton of the spectrum of □λ as λ → ∞ by a formal semiclassical analysis.

Original languageEnglish
Pages (from-to)103-114
Number of pages12
JournalInfinite Dimensional Analysis, Quantum Probability and Related Topics
Issue numberSUPPL. 1
Publication statusPublished - 2003 Sep


  • Morse function
  • Pinned path group
  • Semiclassical analysis
  • Witten Laplacian

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Mathematical Physics
  • Applied Mathematics


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