تقرير
Erlangen Programme at Large: An Overview
| العنوان: | Erlangen Programme at Large: An Overview |
|---|---|
| المؤلفون: | Kisil, Vladimir V. |
| سنة النشر: | 2011 |
| المجموعة: | Mathematics Mathematical Physics Quantum Physics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, Mathematical Physics, Mathematics - Functional Analysis, Mathematics - Representation Theory, Quantum Physics, 30G35, 22E46, 30F45, 32F45, 43A85, 30G30, 42C40, 46H30, 47A13, 81R30, 81R60 |
| الوصف: | This is an overview of Erlangen Programme at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the group SL(2,R). Starting from the conformal geometry we develop analytic functions and apply these to functional calculus. Finally we link this to quantum mechanics and conclude by a list of open problems. Keywords: Special linear group, Hardy space, Clifford algebra, elliptic, parabolic, hyperbolic, complex numbers, dual numbers, double numbers, split-complex numbers, Cauchy-Riemann-Dirac operator, M\"obius transformations, functional calculus, spectrum, quantum mechanics, non-commutative geometry Comment: 77 pages, AMS-LaTeX, 12 figures (29 EPS graphic files); v2: section on QM was extended |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1007/978-3-0348-0417-2_1 |
| URL الوصول: | http://arxiv.org/abs/1106.1686 |
| رقم الأكسشن: | edsarx.1106.1686 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1007/978-3-0348-0417-2_1 |
|---|