1996/12/16 by Anders Westerberg
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Fock space #Lie algebra #Mathematics #Nonlinear Waves and Solitons #Operator algebra #Physics #Pseudodifferential operators #Pure mathematics #Quantum mechanics #hep-th
paper · pdf · doi:10.1016/s0920-5632(97)00336-8
published in Nuclear Physics B - Proceedings Supplements 56(3), 275-280 (Elsevier BV) · 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
arxiv created 1996/12/16 · openalex publication_date 1997/07/01 · arxiv updated 2010/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.