Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  A 'Fock'-type construction on a $C^*$-algebra

+ 6 like - 0 dislike
746 views

In very rough terms, let $A$ be a complex unital $C^*$-algebra. Assume it nuclear for convenience, but it doesn't matter much. Consider the 'Fock'-type $C^*$-algebra (don't know a better name for it) $$ \mathbb{C}\bigoplus A\bigoplus A\otimes A\bigoplus\ldots $$ This can be thought of as the $C^*$-algebra of continuous sections in the 'power bundle' $n\mapsto A^{\otimes n}$ vanishing at infinity. It can be made unital by considering the 1-point compactification etc. etc. If $A$ is simple, this should be the Dauns-Hofmann representation of the resulting algebra, I think. This is a graded $C^*$-algebra, but I am not sure what that gives.

The corresponding construction for von Neumann algebras is a bit easier and is related to the Fock representations in QFT.

Question: Has this thing been studied in the literature and does it have a proper name?

Thank you.

This post imported from StackExchange MathOverflow at 2018-01-20 17:45 (UTC), posted by SE-user Bedovlat
asked Jan 6, 2018 in Theoretical Physics by Bedovlat (30 points) [ no revision ]
retagged Jan 20, 2018
I've never seen this in the literature.

This post imported from StackExchange MathOverflow at 2018-01-20 17:45 (UTC), posted by SE-user Nik Weaver
Well, right, I would rather reformulate it as follows; the infinite convex linear combination of powers of a fixed faithful state on $A$ is a faithful state on the above algebra. But I don't see this as a subrepresentation of the universal representation, since, for instance, $A\otimes A$ is not the image of a representation of $A$. There is in general no surjective homomorphism $A\to A\otimes A$.

This post imported from StackExchange MathOverflow at 2018-01-20 17:45 (UTC), posted by SE-user Bedovlat
Wow, comment disappeared? Now my comment looks weird :-/

This post imported from StackExchange MathOverflow at 2018-01-20 17:45 (UTC), posted by SE-user Bedovlat

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysicsOver$\varnothing$low
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...