피카르-렙셰츠 이론

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  1. Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly.[1]
  2. A robust possibility for treating the quantum tunneling of a spacetime geometry is through a complex path integral and Picard-Lefschetz theory.[2]
  3. In mathematics, Picard–Lefschetz theory studies the topology of a complex manifold by looking at the critical points of a holomorphic function on the manifold.[3]
  4. It was introduced by Émile Picard for complex surfaces in his book Picard & Simart (1897), and extended to higher dimensions by Solomon Lefschetz (1924).[3]
  5. The monodromy action of π 1 (P1 – {x 1 , ..., x n }, x) on H k (Y x ) is described as follows by the Picard–Lefschetz formula.[3]
  6. As for the P-L theory, I do not think there are any textbook-level treatments, "Applied Picard–Lefschetz theory" by V.Vassiliev is probably your best option.[4]
  7. We demonstrate that complex saddle points have a natural interpretation in terms of the Picard-Lefschetz theory.[5]
  8. Picard-Lefschetz gives a complementing picture from a path-integral perspective.[6]
  9. The author also shows how these versions of the Picard-Lefschetz theory are used in studying a variety of problems arising in many areas of mathematics and mathematical physics.[7]
  10. In this work, we first solve complex Morse flow equations for the simplest case of a bosonic harmonic oscillator to discuss localization in the context of Picard-Lefschetz theory.[8]
  11. Motivated by Picard-Lefschetz theory, we write down a general formula for the index of N = 4 quantum mechanics with background R -symmetry gauge fields.[8]
  12. Topics covered include: invariants of complex singularities, topological aspects of complex singularities, the Milnor fibration, vanishing cycles, monodromies, Picard-Lefschetz theory.[9]
  13. Moreover, from the mirror geometry for the del Pezzos arise certain Diophantine equations which classify all quivers related by Picard-Lefschetz.[10]
  14. N=2 susy is related to the Picard-Lefschetz theory much in the same way as N=1 susy is related to Morse theory.[11]

소스

  1. ↑ Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling
  2. ↑ Complex Quantum Tunneling, Picard-Lefschetz Theory, and the Decay of Black Holes
  3. ↑ 3.0 3.1 3.2 Picard–Lefschetz theory
  4. ↑ Reference for Picard-Lefschetz theory
  5. ↑ Toward Picard-Lefschetz Theory of Path Integrals and the Physics of Complex Saddles
  6. ↑ YTF 12
  7. ↑ Applied Picard-Lefschetz Theory: Buy Applied Picard-Lefschetz Theory by unknown at Low Price in India
  8. ↑ 8.0 8.1 More on homological supersymmetric quantum mechanics
  9. ↑ Course Catalogue
  10. ↑ Quiver theories, soliton spectra and Picard-Lefschetz transformations
  11. ↑ SINGULARITY-THEORY AND N=2 SUPERSYMMETRY

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