A functional directional derivative in infinite dimensional spaces and its application to \(\overline{\partial}\)-equations

DOI10.1016/j.jmaa.2018.04.001zbMath1391.81216OpenAlexW2795370448MaRDI QIDQ1748302

Yuta Aihara

Publication date: 9 May 2018

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2018.04.001

zbMATH Keywords

Fock space\(\overline{\partial}\)-equationfunctional directional derivative

Mathematics Subject Classification ID

Many-body theory; quantum Hall effect (81V70) Commutation relations and statistics as related to quantum mechanics (general) (81S05) Operator algebra methods applied to problems in quantum theory (81R15) Derivatives of functions in infinite-dimensional spaces (46G05) Infinite-dimensional manifolds (46T05)

Cites Work

• A general class of infinite dimensional Dirac operators and path integral representation of their index
• Path integral representation of the index of Kähler-Dirac operators on an infinite dimensional manifold
• Semi-classical asymptotic expansions up to any finite orders of the partition function of an abstract Bose field model
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