𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Algebraic quantization

✍ Scribed by R. Berger


Publisher
Springer
Year
1989
Tongue
English
Weight
384 KB
Volume
17
Category
Article
ISSN
0377-9017

No coin nor oath required. For personal study only.

✦ Synopsis


The different correspondences (or orderings) used in quantum mechanics and the associated deformations, are both seen from an algebraic viewpoint. The deformations which are compatible with the diagonal map (the 'A0-deformations' ) are introduced and connected to the formal groups. A very straighforward example of a A0-deformatlon (the 'multiplicative deformation') appears m the normal quantization of the harmonic oscillator.


πŸ“œ SIMILAR VOLUMES


q-Schur Algebras as Quotients of Quantiz
✍ R.M. Green πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 266 KB

We study the properties of the surjective homomorphism, defined by Beilinson, Lusztig, and MacPherson, from the quantized enveloping algebra of gl to the n Ε½ . q-Schur algebra, S n, r . In particular, we find an expression for the preimage of q Ε½ . an arbitrary element of S n, r under this map and a

Symmetric Pairs for Quantized Enveloping
✍ Gail Letzter πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 290 KB

Let ΞΈ be an involution of a semisimple Lie algebra g, let g ΞΈ denote the fixed Lie subalgebra, and assume the Cartan subalgebra of g has been chosen in a suitable way. We construct a quantum analog of U g ΞΈ which can be characterized as the unique subalgebra of the quantized enveloping algebra of g

Deformation Quantization of Polynomial P
✍ Michael Penkava; Pol Vanhaecke πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 205 KB

This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We compute an explicit third order deformation quantization of A and show that it comes from a quantized enveloping algebra. We show that this deformation extends to a fourth order deformatio