On higher-dimensional loop algebras, pseudodifferential operators and Fock space realizations
Abstract
We discuss a previously discovered [hep-th/9401027] extension of the infinite-dimensional Lie algebras Map(M,g) which generalizes the Kac-Moody algebras in 1+1 dimensions and the Mickelsson-Faddeev algebras in 3+1 dimensions to manifolds M of general dimensions. Furthermore, we review the method of regularizing current algebras in higher dimensions using pseudodifferential operator (PSDO) symbol calculus. In particular, we discuss the issue of Lie algebra cohomology of PSDOs and its relation to the Schwinger terms arising in the quantization process. Finally, we apply this regularization method to the algebra of the above reference with partial success, and discuss the remaining obstacles to the construction of a Fock space representation.
Keywords
Cite
@article{arxiv.hep-th/9612167,
title = {On higher-dimensional loop algebras, pseudodifferential operators and Fock space realizations},
author = {Anders Westerberg},
journal= {arXiv preprint arXiv:hep-th/9612167},
year = {2010}
}
Comments
6 pages, LaTeX, requires espcrc2.sty and amsfonts.sty. Contribution to the proceedings of the 30th Int. Symposium Ahrenshoop on the theory of elementary particles, Buckow, Germany, August 27-31, 1996