Read e-book online A von Neumann algebra approach to quantum metrics. Quantum PDF

By Greg Kuperberg

ISBN-10: 0821853414

ISBN-13: 9780821853412

Quantity 215, quantity 1010 (first of five numbers).

Show description

Read or Download A von Neumann algebra approach to quantum metrics. Quantum relations PDF

Best science & mathematics books

Shmuel Weinberger's The topological classification of stratified spaces PDF

This booklet offers the idea for stratified areas, besides very important examples and purposes, that's analogous to the surgical procedure conception for manifolds. within the first expository account of this box, Weinberger offers topologists with a brand new means of the class concept of singular areas along with his unique effects.

New PDF release: Advice To A Young Scientist

To these drawn to a lifestyles in technological know-how, Sir Peter Medawar, Nobel laureate, deflates the myths of invincibility, superiority and genius; as a substitute, he demonstrates it's common feel and an inquiring brain which are necessary to the scientist's calling.

Download e-book for iPad: A Century of mathematics in America (History of Mathematics, by Peter L. Duren, Richard Askey, Uta C. Merzbach

###############################################################################################################################################################################################################################################################

Extra resources for A von Neumann algebra approach to quantum metrics. Quantum relations

Example text

5. Quantum tori We formulate a notion of translation invariant quantum pseudometrics on quantum tori. 7 of [35], it is then straightforward to deduce strong structural information about translation invariant quantum pseudometrics. Quantum tori are the simplest examples of noncommutative manifolds. They are related to the quantum plane, which plays the role of the phase space of a spinless one-dimensional particle. The classical version of such a system has phase space R2 , with the point (q, p) ∈ R2 representing a state with position q and momentum p, so that the position and momentum observables are just the coordinate functions on phase space.

5) which states that every such map can be expressed as an inflation followed by a restriction followed by an isomorphism. Since this expression is not unique, if we defined L(φ) in the concrete way indicated below then the definition would appear to be ambiguous. But the fact that this definition is equivalent to the intrinsic one given above means that there is actually no real ambiguity. 31. Let V and W be quantum pseudometrics on von Neumann algebras M ⊆ B(H) and N ⊆ B(K) and let φ : M → N be a unital weak* continu˜ be a Hilbert space, R a projection in B(K)⊗M ˜ , and ous ∗-homomorphism.

The quantum torus von Neumann algebra for the given value of mann algebra W ∗ (U , V ) generated by U and V . is the von Neu- 44 3. 38). If is an irrational multiple of π then W ∗ (U , V ) is a hyperfinite II1 factor. We will not need this fact. Conjugating U and V by the Fourier transform F : L2 (T2 ) → l2 (Z2 ) yields the operators ˆ f (x, y) U = eix f x, y − Vˆ f (x, y) = eiy f x + ,y 2 2 ˆ , Vˆ ) reducing to the algebra of bounded multiplication on L2 (T2 ), with W ∗ (U operators when = 0. However, for our purposes the l2 (Z2 ) picture is more convenient.

Download PDF sample

A von Neumann algebra approach to quantum metrics. Quantum relations by Greg Kuperberg


by Joseph
4.3

Rated 4.34 of 5 – based on 23 votes