Beginning Asymptotic Analysis of Twisted Products

Pedro de M. Rios and Eldar Straume
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Pedro de M. Rios: Universidade de São Paulo, Departamento de Matemática, ICMC
Eldar Straume: Norwegian University of Science and Technology, Department of Mathematical Sciences

Chapter Chapter 8 in Symbol Correspondences for Spin Systems, 2014, pp 135-157 from Springer

Abstract: Abstract As we saw in the previous chapter, each symbol correspondence W c → j $$ {W}_{\overrightarrow{c}}^j $$ defines a c → $$ \overrightarrow{c} $$ twisted j-algebra on Poly $$_\mathbb{C}$$ (S 2) ≤ n. However, despite the fact that all c → $$ \overrightarrow{c} $$ -twisted j-algebras are isomorphic for each finite j, we shall see in this chapter that only a subclass of symbol correspondence sequences yield Poisson dynamics in the asymptotic limit of high spin numbers (j → ∞). This subclass realizes Rieffel’s “strict deformation quantization” of the 2-sphere in reverse order (from quantum to classical). But as we shall see, this subclass is far from being generic.

Keywords: Poisson Bracket; Asymptotic Limit; Characteristic Number; Poisson Algebra; Twisted Product (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-08198-4_8

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