• 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 , 22,728 comments
1,470 users with positive rep
818 active unimported users
More ...

  Normal ordering in curved spacetime

+ 7 like - 0 dislike

In the flat spacetime, one can perform normal-ordering to set the energy of the vacuum state to zero. I read in some places that this procedure cannot be consistently performed in the curved spacetimes. I have not found any explanation of this fact in the literature. Why is this a case?

This post imported from StackExchange Physics at 2014-06-25 21:03 (UCT), posted by SE-user Newman
asked Jun 23, 2014 in Theoretical Physics by Newman (75 points) [ no revision ]

1 Answer

+ 7 like - 0 dislike

The normal ordering procedure is nothing but the a recurrent machinery to remove vacuum expectation values by means of the so-called Wick's theorem procedure. There, the vacuum state is the unique Poincaré invariant one, the Minkowski vacuum. In curved spacetime there is no such an invariant state. Therefore the normal ordering product must be defined referring to some other fixed states. These states (their two-point functions) should have a short distance behaviour similar to the one of Minkowski vacuum state. Technically they must be Hadamard states. Unfortunately there is no canonical (functorial) way to associate Hadamard states with (globally hyperbolic) spacetimes. This fact prevents one for defining a true generally covariant normal ordering procedure. A way out consists of removing not the expectation value of a state, but the "expectation value" of a local functional defined in terms of the local geometry only (the Hadamard parametrix). This procedure, in view of the fact that the functional is not a (weak) bi-solution of the field equations, has nonetheless annoying shortcomings, in particular the appearance of anomalies (the trace anomaly first of all). This machinery has been developed by various authors in the last 15 years (including myself). For a recent overview see the PhD thesis http://arxiv.org/abs/arXiv:1008.1776 (I was one of the advisors, together with K. Fredenhagen and R.M. Wald).

This post imported from StackExchange Physics at 2014-06-25 21:03 (UCT), posted by SE-user V. Moretti
answered Jun 23, 2014 by Valter Moretti (2,085 points) [ revision history ]
edited Jun 26, 2014 by Valter Moretti

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