# 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
summarized
paper authored Apr 4 to math-ph
edited Apr 6

## 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): Email me at this address if my review is selected or commented on: 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$\varnothing$owThen 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.