From: "Foundations of Physics"
To: ilja.schmelzer@gmail.com
Date: 25 Sep 2008 03:44:59 -0400
Subject: Major Revisions requested FOOP438
Message-ID:
[...]
Dear Schmelzer,
We have received the reports (see below) from our reviewers on your manuscript,
"Geometric and condensed matter interpretation of SM fermions and gauge fields", which you submitted to Foundations of Physics.
Based on the advice received, the editors have decided that your manuscript could be reconsidered for publication should you be prepared to incorporate major revisions. In case you decide to prepare a revised manuscript, you are asked to carefully consider the reviewer comments which are attached, and submit a list of responses to the comments.
Please find attached the reviewer comments for your perusal.
[...]
With kind regards,
Gerard 't Hooft
Chief Editor
---
COMMENTS FOR THE AUTHOR:
Reviewer #2: This paper offers a novel approach to understanding the field content
and gauge interactions of
the Standard Model. It embeds the usual electroweak doublet in a three
dimensional Kaehler-Dirac field. These Kaehler-Dirac fields carry additional
indices corresponding to generation number and a combined color/lepton
number (rather similar at first sight to Patti-Salam models) and can be
mapped into the parameters of a affine transformation. The author argues that
the natural action of translations and rotations associated with this
affine structure restricts the possible gauge groups to essentially SU(3)xU(1).
This part seems clear to the referee.
The author then argues that
electroweak gauge invariance is then an emergent symmetry associated with
deformations of the affine parameters. I don't think this section is very clear.
It seems that this requires a commuting interpretation of fermions which seems
a very drastic departure from conventional wisdom. I realize the author
tries to address this in the later sections of his paper but I am
personally unconvinced. In addition there seems to be
no strong argument for the
appearance of an SU(2) gauge field in the long wavelength limit.
Overall this paper outlines a quite radical approach to understanding
the Standard Model and most probably will not turn out to be correct (the
author would need to show how Lorentz invariance is recovered, how mass
terms arise and how the electroweak breaking occurs for it to be taken
very seriously). Nevertheless off-the-beaten track approaches like this
one can be important and the paper brings up a number of nice ideas. If the
author can strengthen and clarify the sections of the paper concerned with
the generation of the electroweak SU(2) I think it would be suitable for
publication.
That said there seem to be a couple of references missing concerned with
models using Kaehler-Dirac fields to provide models for beyond standard
models physics -- I am thinking of the the paper by Banks et al
Phys.Lett.B117:413,1982 and also
concerning the absence of fermion doubling in lattice transcriptions of the
Kaehler-Dirac equation (J. Rabin, Nucl.Phys.B201:315,1982).
These should be added.
Reviewer #3: The author discusses an attempt to reformulate the standard model (SM)
in terms of condensed matter physics.
It starts from the observation that the number of SM fermion doublets is
equal to the dimension of the three-dimensional affine transformation group
Aff(3). Here, right-handed neutrinos are assumed to exist so that neutrinos form
usual Dirac particles.
The three-dimensional space is latticized, and the fermions are expressed
as staggered fermions on ${\bf Z}^3$. A $U(3)$ gauge symmetry, which contains
the $SU(3)$ strong interaction, is incorporated by introducing corresponding
Wilson's lattice gauge field.
He explains that phonon-like d.o.f. corresponding to lattice deformations
play a role of $U(2)L \times U(1)$ gauge fields.
The $U(2)_L$ contains the $SU(2)_L$ weak interaction, and the $U(1)$, linearly
combined with the central $U(1)$ of $U(3)$, is regarded as electromagnetic $U(1)$.
As he wrote, the derivation of $U(2)_L \times U(1)$ gauge fields from lattice deformations
should be clarified, and the Higgs sector is not considered here.
In appendix A, he discusses that general relativity has a condensed matter interpretation.
Four-dimensional metric is expressed in terms of fields of density, velocity and stress tensor,
and the continuity and Euler equations correspond to the harmonic gauge condition for the
metric.
Although the idea seems somewhat interesting, I think that a number of arguments need to be
refined before the publication.
In particular, it is not clear why the chiral structure of $U(2)_L$ arises under
the assumption that right-handed neutrinos exist.
In order to realize SM, the right-handed neutrinos have to be eventually decoupled.
There should be some argument how to realize the decoupling.