An Index Formula for Groups of Isometric Linear Canonical Transformations
Operator Algebras
2020-08-04 v1 K-Theory and Homology
Quantum Algebra
Abstract
We define a representation of the unitary group by metaplectic operators acting on and consider the operator algebra generated by the operators of the representation and pseudodifferential operators of Shubin class. Under suitable conditions, we prove the Fredholm property for elements in this algebra and obtain an index formula.
Cite
@article{arxiv.2008.00734,
title = {An Index Formula for Groups of Isometric Linear Canonical Transformations},
author = {Anton Savin and Elmar Schrohe},
journal= {arXiv preprint arXiv:2008.00734},
year = {2020}
}