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

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

160 submissions , 132 unreviewed
4,169 questions , 1,545 unanswered
5,018 answers , 21,289 comments
1,470 users with positive rep
589 active unimported users
More ...

  Introduction to coherent quantization

Originality
+ 1 - 0
Accuracy
+ 1 - 0
Score
1.79
80 views
Referee this paper: arXiv:1804.01400 by Arnold Neumaier, Arash Ghaani Farashahi

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

(Is this your paper?)


Abstract:

This paper is the second in a series of papers on coherent spaces and 
their applications. It begins the study of coherent quantization - the 
way operators in a quantum space can be studied in terms of objects 
defined directly on the coherent space. The results may be viewed as a 
generalization of geometric quantization to the non-unitary case. 

Care has been taken to work with the weakest meaningful topology and 
to assume as little as possible about the spaces and groups involved. 
Unlike in geometric quantization, the groups are not assumed to be 
compact, locally compact, or finite-dimensional. This implies that the 
setting can be successfully applied to quantum field theory, where the 
groups involved satisfy none of these properties. 

The paper characterizes linear operators acting on the quantum space 
of a coherent space in terms of their coherent matrix elements. 
Coherent maps and associated symmetry groups for coherent spaces are 
introduced, and formulas are derived for the quantization of coherent 
maps. 

The importance of coherent maps for quantum mechanics is due to the 
fact that there is a quantization operator that associates 
homomorphically with every coherent map a linear operator from the 
quantum space into itself. This operator generalizes to general 
symmetry groups of coherent spaces the second quantization procedure 
for free classical fields. The latter is obtained by specialization 
to Klauder spaces, whose quantum spaces are the bosonic Fock spaces.
 A coordinate-free derivation is given of the basic properties of 
creation and annihilation operators in Fock spaces.

requested Apr 6 by Arnold Neumaier (13209 points)
summarized by Arnold Neumaier
paper authored Apr 4 to math-ph by Arnold Neumaier
  • [ revision history ]
    edited Apr 6 by Arnold Neumaier

    Your Review:

    Please use reviews only to (at least partly) review submissions. 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 review 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$\hbar$ysicsOverf$\varnothing$ow
    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).
    To avoid this verification in future, please log in or register.




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

    Your rights
    ...