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
5,082 questions , 2,232 unanswered
5,353 answers , 22,786 comments
1,470 users with positive rep
820 active unimported users
More ...

  PT-Symmetric Quantum Electrodynamics

Originality
+ 3 - 0
Accuracy
+ 1 - 0
Score
2.32
799 views
Referee this paper: arXiv:hep-th/0501180v1 by Carl M. Bender, Ines Cavero-Pelaez, (show more)

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?)


This 2005 paper by C.M. Bender, I. Cavero-Pelaez, K.A. Milton and K.V. Shajesh considers the situation where the Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge e is taken to be imaginary.

''However, if one also specifies that the potential $A^μ$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. The resulting non-Hermitian theory of electrodynamics is the analog of a spinless quantum field theory in which a pseudoscalar field $ϕ$ has a cubic self-interaction of the form $iϕ^3$. The Hamiltonian for this cubic scalar field theory has a positive spectrum, and it has recently been demonstrated that the time evolution of this theory is unitary. The proof of unitarity requires the construction of a new operator called C, which is then used to define an inner product with respect to which the Hamiltonian is self-adjoint. In this paper the corresponding C operator for non-Hermitian quantum electrodynamics is constructed perturbatively. This construction demonstrates the unitarity of the theory. Non-Hermitian quantum electrodynamics is a particularly interesting quantum field theory model because it is asymptotically free.''

summarized by Arnold Neumaier
paper authored Jan 20, 2005 to quant-ph by  (no author on PO assigned yet) 
  • [ revision history ]
    edited Aug 27, 2014 by Arnold Neumaier

    From Abstract: "The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the unrenormalized electric charge $e$ is taken to be imaginary. However, if one also specifies that the potential $A_{\mu}$ in such a theory transforms as a pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric. ... 

    This construction demonstrates the unitarity of the theory. Non-Hermitian quantum electrodynamics is a particularly interesting quantum field theory model because it is asymptotically free."

    I think the paper is a great achievement. Indeed, if for some particular reason one wants to make a QED calculation with an imaginary charge (that is not forbidden by any human law), one can take advantage of this construction and be happy with the unitary evolution. The latter provides conservation of probability in the theory. The necessary C-operator $C$ can be constructed perturbatively. In addition, the theory is asymptotically free which is another thing to enjoy.

    The only thing I could not understand was whether the perturbative series in this theory became free from Dyson's argument of being asymptotical.

    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):
    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$\hbar$ysicsOverfl$\varnothing$w
    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
    ...