• 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
5,064 questions , 2,215 unanswered
5,347 answers , 22,734 comments
1,470 users with positive rep
818 active unimported users
More ...

  Full form of the Pauli-Fierz action

+ 4 like - 0 dislike

In Deser's paper on the fully interacting version of the Pauli Fierz theory, he does a rather simple method of treating the Pauli Fierz equation without going with infinite sums, just by treating the metric and the connection separately, hiding the infinite sum in the dynamics linking the (inverse) metric to the connection. But in this paper, he writes the Hilbert action as

\begin{equation} S = \int d^4x\ g^{\mu\nu} R_{\mu\nu} \end{equation}

which I suppose will derive something of the form

\begin{equation} S = \int d^4x\ (\eta^{\mu\nu} + h^{\mu\nu}) R_{\mu\nu} (\Gamma) \end{equation}

But his definition of the Hilbert action lacks the determinant of the metric to fix the integral volume in curved space, which according to Feynman's lecture in gravitation does intervene in the action, of the form

\begin{equation} \sqrt{-g} = 1 + h^\beta_\beta + \mathcal{O}(h^2) \end{equation}

But while he does offer some perturbative expansion of the Hilbert action in terms of the spin 2 field of the Pauli Fierz theory, he does not really give its full expression as an infinite sum.

Is Deser's action correct? I have seen this document implying that the determinant might be absorbed in the field we use for $g^{\mu\nu}$ (as it is just slides it's rather sparse on details), but even then that would not work in general since we would still need it for the matter term of the Lagrangian. Also what is actually the infinite sum formulation? I have yet to see it actually written down properly and not cut off rather quickly.

This post imported from StackExchange Physics at 2015-11-02 20:31 (UTC), posted by SE-user Slereah
asked Nov 1, 2015 in Theoretical Physics by Slereah (540 points) [ no revision ]

1 Answer

+ 3 like - 0 dislike

There has been some substantial increase in the knowledge of massive gravity (and the non-linear completion) in the past few (maybe less than 10) years. Its worth checking out this paper on arxiv; written by Claudia de Rham who was one of the discoverers of the new non-linear massive gravity.

answered Nov 18, 2015 by jpoffline (30 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:
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