• 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.


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


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,054 questions , 2,207 unanswered
5,345 answers , 22,721 comments
1,470 users with positive rep
818 active unimported users
More ...

  Chern-Simons form and Rarita-Schwinger operator

+ 9 like - 0 dislike

The Rarita-Schwinger (RS) operator naturally generalizes the Dirac operator and in Physics it describes particles with spin-3/2.

I was wondering if there exists any reference concerning the calculation of the Atiyah-Patodi-Singer relative eta invariant for the RS operator on three-dimensional spin manifolds. My issue concerns the calculation of the Chern-Simons form in the case of RS fermions. This calculation in the case of the Dirac operator was derived, for instance, in the following reference


through the relative eta invariant.

1) Is there any similar result for the RS operator?

2) Can I derive the relative eta invariant/Chern-Simons form in 3D from the index theorem in 4D spin manifolds? In this case, the value of the topological index for the RS operator is well known. See, for instance


This post imported from StackExchange MathOverflow at 2016-05-07 13:25 (UTC), posted by SE-user Gian
asked May 3, 2016 in Theoretical Physics by Gian (65 points) [ no revision ]
retagged May 7, 2016
Could you recall what a relative $\eta$-invariant is?

This post imported from StackExchange MathOverflow at 2016-05-07 13:25 (UTC), posted by SE-user Sebastian Goette
The relative eta-invariant has been nicely explained by Paul Siegel in one of my previous questions: mathoverflow.net/questions/85104/…

This post imported from StackExchange MathOverflow at 2016-05-07 13:25 (UTC), posted by SE-user Gian
Ah, it's the $\rho$ or $\xi$ invariant.

This post imported from StackExchange MathOverflow at 2016-05-07 13:25 (UTC), posted by SE-user Sebastian Goette

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:
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