Abstract
AbstractFollowing Nag–Sullivan, we study the representation of the group $$\textrm{Diff}^+(S^1)$$
Diff
+
(
S
1
)
of diffeomorphisms of the circle on the Hilbert space of holomorphic functions. Conformal welding provides triangular decompositions for the corresponding symplectic transformations. We apply Berezin formalism and lift this decomposition to operators acting on the Fock space. This lift provides quantization of conformal welding, gives a new representative of the Bott–Virasoso cocycle class, and leads to a surprising identity for the Takhtajan–Teo energy functional on $$\textrm{Diff}^+(S^1)$$
Diff
+
(
S
1
)
.
Funder
Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
Simons Foundation
University of Dublin, Trinity College
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Nuclear and High Energy Physics,Statistical and Nonlinear Physics