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 nice overview (and maybe derivation) of the Poincaré transformations of the Vector Spherical Harmonics

+ 3 like - 0 dislike
597 views

With $Y_{lm}(\vartheta,\varphi)$ being the Spherical Harmonics and $z_l^{(j)}(r)$ being the Spherical Bessel functions ($j=1$), Neumann functions ($j=2$) or Hankel functions ($j=3,4$) defining $$\psi_{lm}^{(j)}(r,\vartheta,\varphi)=z_l^{(j)}(r)Y_{lm}(\vartheta,\varphi),$$ what are representations of the Poincaré transformations applied to the Vector Spherical Harmonics

$$\vec L_{lm}^{(j)} = \vec\nabla \psi_{lm}^{(j)},\\ \vec M_{lm}^{(j)} = \vec\nabla\times\vec r \psi_{lm}^{(j)},\\ \vec N_{lm}^{(j)} = \vec\nabla\times\vec M_{lm}^{(j)}$$

? Does any publication cover all Poincaré-transformations, i.e. not only translations and rotations but also Lorentz boosts? I'd prefer one publication covering all transformations at once due to the different normalizations sometimes used.

This post has been migrated from (A51.SE)
asked Feb 28, 2012 in Theoretical Physics by Tobias Kienzler (260 points) [ no revision ]
retagged Mar 18, 2014 by dimension10
disclaimer: I also asked this at [MathOverflow](http://mathoverflow.net/questions/89955/a-nice-overview-and-maybe-derivation-of-the-poincare-transformations-of-the-vec)

This post has been migrated from (A51.SE)

1 Answer

+ 1 like - 0 dislike

The problem with Poincaré group is in the fact that it is not compact. That's why this question is non-trivial. Though, properly formulated search gives few papers on this topic. Try to find the answer in this paper http://arxiv.org/abs/math-ph/0507056 . The paper itself may be not that interesting, but there is a nice introduction with a number of useful references.

This post has been migrated from (A51.SE)
answered Feb 28, 2012 by Nestoklon (340 points) [ no revision ]

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$\hbar$ysicsOve$\varnothing$flow
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
...