An explicit formula for the Berezin star product

A. Karabegov; A. Karabegov; A. Karabegov; A. Karabegov; A. Loi; A. Unterberger; B. Fedosov; C. Fefferman; C. Fefferman; C. Moreno; C. Moreno; D. Cvetković; E. Calabi; E. Ligocka; F. Bayen; F. Bayen; F.A. Berezin; F.A. Berezin; G. Tian; H. Omori; H. Omori; Hao Xu; L. Charles; L. Monvel; M. Bordemann; M. Bordemann; M. Cahen; M. Cahen; M. Cahen; M. De Wilde; M. Engliš; M. Engliš; M. Engliš; M. Engliš; M. Engliš; M. Engliš; M. Kontsevich; N. Nakazawa; X. Dai; X. Ma; X. Ma; Z. Lu

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An explicit formula for the Berezin star product

Authors: A. Karabegov
A. Karabegov
A. Karabegov
A. Karabegov
A. Loi
A. Unterberger
B. Fedosov
C. Fefferman
C. Fefferman
C. Moreno
C. Moreno
D. Cvetković
E. Calabi
E. Ligocka
F. Bayen
F. Bayen
F.A. Berezin
F.A. Berezin
G. Tian
H. Omori
H. Omori
Hao Xu
L. Charles
L. Monvel
M. Bordemann
M. Bordemann
M. Cahen
M. Cahen
M. Cahen
M. De Wilde
M. Engliš
M. Engliš
M. Engliš
M. Engliš
M. Engliš
M. Engliš
M. Kontsevich
N. Nakazawa
X. Dai
X. Ma
X. Ma
Z. Lu
Publication date: 22 April 2012
Publisher: 'Springer Science and Business Media LLC'
Doi

Abstract

We prove an explicit formula of the Berezin star product on Kaehler manifolds. The formula is expressed as a summation over certain strongly connected digraphs. The proof relies on a combinatorial interpretation of Englis' work on the asymptotic expansion of the Laplace integral.Comment: 19 pages, to appear in Lett. Math. Phy

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