Deformation Quantization for Actions of rd - download pdf or read online

By Marc A. Rieffel

ISBN-10: 0821825755

ISBN-13: 9780821825754

This paintings describes a normal building of a deformation quantization for any Poisson bracket on a manifold which comes from an motion of $R^d$ on that manifold. those deformation quantizations are strict, within the feel that the deformed fabricated from any services is back a functionality and that there are corresponding involutions and operator norms. the various concepts concerned are tailored from the speculation of pseudo-differential operators. the development is proven to have many favorable houses. a few particular examples are defined, starting from simple ones resembling quantum disks, quantum tori, and quantum spheres, to elements of quantum teams.

Show description

Read or Download Deformation Quantization for Actions of rd PDF

Similar linear books

New PDF release: Applied Numerical Linear Algebra

Attractive! Very easily, that allows you to have an perception on linear algebraic systems, and why this and that occurs so and so, this can be the e-book. Topic-wise, it's nearly entire for a primary remedy. each one bankruptcy starts off with a gradual advent, construction instinct after which will get into the formal fabric.

New PDF release: Hilbert Spaces, Wavelets, Generalised Functions and Modern

This booklet offers a accomplished creation to fashionable quantum mechanics, emphasising the underlying Hilbert house concept and generalised functionality thought. all of the significant glossy strategies and techniques utilized in quantum mechanics are brought, similar to Berry part, coherent and squeezed states, quantum computing, solitons and quantum mechanics.

Download e-book for kindle: Linear Algebra, Geometry and Transformation by Bruce Solomon

"Starting with all of the average issues of a primary path in linear algebra, this article then introduces linear mappings, and the questions they increase, with the expectancy of resolving these questions during the e-book. finally, by means of supplying an emphasis on constructing computational and conceptual talents, scholars are increased from the computational arithmetic that regularly dominates their adventure sooner than the direction to the conceptual reasoning that regularly dominates on the conclusion"-- learn extra.

Extra info for Deformation Quantization for Actions of rd

Sample text

Let BA denote the completion of BA for its operator norm. We then form the space S(V,BA), equipped with the structure of a right BA -rigged space. As earlier, let r denote the action of V on we let F be the function in B(V,BA) defined by F(t) = rt(F). We equip B(V,BA) with the product xK, and let it act on S(V, BA) by this product. In particular, F can be viewed in this way as an operator on S(V,BA). The norm of F as an element of (BA)K is then, by definition, the norm of this operator (with respect to the BA -rigged structure).

9 to conclude that Aj is an essential ideal in Cj, so that Cj, and thus Bj, are contained in M(Aj). 17 there is a bounded approximate identity {e\} for the Frechet algebra D°°. 17, we see that it can be arranged to be an approximate identity for all of C°°. 13 it will then be an approximate identity for Cj, and so has the desired property with respect to Aj. But, of course, it is contained in Bj. • We continue by extending a to Aj. 5 that a gives an action of V as automorphisms of A°° for the product Xj, and that this action is strongly continuous for the Frechet topology.

Assume that J is invertible (and skew- symmetric), and let 6 = |det(J~ 1 )|. Let f G SA. Then Lf is a bounded operator on the A-rigged space SA, and in fact iii/ii<« 1 / 2 n/iii- Proof. For g G SA we have (Lfg)(x) = = 6 f(x + Ju)e(u • x)g[u) f(x + u)e(J~xu = 6 f f(u)e(J-Xu • x)g{J^u) • x)g(J-x{u - x)). For fixed u define an operator, Tu, on SA by (Tuh){x) = 61/2e{J~1u • x^J-^u - x)). Then this operator is "unitary" for the A-valued inner product, since for h, k G SA we have (Tuh,Tuk)A = 6 Je(J_1« • ar)fc(J _1 (u - x ) ) ' e ( J - 1 « • a:)A;(

Download PDF sample

Deformation Quantization for Actions of rd by Marc A. Rieffel


by Richard
4.4

Rated 4.13 of 5 – based on 11 votes