=?ISO-8859-1?Q?M-theory,_strings,_and_outr=E9_things?= [Archive]

Brian J Flanagan

Aug9-04, 12:55 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>A few new books to recommend:\n\n\'The Future of Theoretical Physics & Cosmology,\' a collection in honor\nof Hawking\'s 60th birthday, featuring contributions from the "A list"\nof contemporary physicists. (Cambridge)\n\n\'The Global Approach to QFT,\' by Bryce DeWitt, a handsome book with a\nthoroughly modern approach and a pleasant pedagogical style. (Oxford)\n\nAlso ...\n\nfrom "SUPERMEMBRANES AND M(ATRIX) THEORY"\n\nHermann Nicolai and Robert Helling\nMax Planck Institut fur Gravitationsphysik\nAlbert-Einstein-Institut\n\nhep-th/9809103\n\n"Despite the recent excitement, however, we do not think that M(atrix)\ntheory and the d = 11 supermembrane in their present incarnation are\nalready the final answer in the search for M-Theory, even though they\nprobably are important pieces of the puzzle. There are still too many\ningredients missing that we would expect the final theory to possess.\n[...] there should exist some huge and so far completely hidden\nsymmetries generalizing not only the duality symmetries of extended\nsupergravity and string theory, but also the principles underlying\ngeneral relativity."\n\nThe dualities referred to in the foregoing are akin to those found in\nprojective geometry. Bearing in mind the manifest symmetries of the\nsecondary properties of observation (viz., color, sound, and the\nlike), which are only "hidden" in plain view, it is intriguing to\nconsider the correspondence between the manifold of color vectors and\nthe axioms of vector geometry, as noted by Weyl: "Thus the colors with\ntheir various qualities and intensities fulfill the axioms of vector\ngeometry if addition is interpreted as mixing; consequently,\nprojective geometry applies to the color qualities."\n\nGiven the above considerations, another of Weyl\'s remarks might strike\none as quite prescient: "Epistemologically it is not without interest\nthat in addition to ordinary space there exists quite another domain\nof intuitively given entities, namely the colors, which forms a\ncontinuum capable of geometric treatment."\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>A few new books to recommend:

'The Future of Theoretical Physics & Cosmology,' a collection in honor
of Hawking's 60th birthday, featuring contributions from the "A list"
of contemporary physicists. (Cambridge)

'The Global Approach to QFT,' by Bryce DeWitt, a handsome book with a
thoroughly modern approach and a pleasant pedagogical style. (Oxford)

Also ...

from "SUPERMEMBRANES AND M(ATRIX) THEORY"

Hermann Nicolai and Robert Helling
Max Planck Institut fur Gravitationsphysik
Albert-Einstein-Institut

http://www.arxiv.org/abs/hep-th/9809103

"Despite the recent excitement, however, we do not think that M(atrix)
theory and the d = 11 supermembrane in their present incarnation are
already the final answer in the search for M-Theory, even though they
probably are important pieces of the puzzle. There are still too many
ingredients missing that we would expect the final theory to possess.
[...] there should exist some huge and so far completely hidden
symmetries generalizing not only the duality symmetries of extended
supergravity and string theory, but also the principles underlying
general relativity."

The dualities referred to in the foregoing are akin to those found in
projective geometry. Bearing in mind the manifest symmetries of the
secondary properties of observation (viz., color, sound, and the
like), which are only "hidden" in plain view, it is intriguing to
consider the correspondence between the manifold of color vectors and
the axioms of vector geometry, as noted by Weyl: "Thus the colors with
their various qualities and intensities fulfill the axioms of vector
geometry if addition is interpreted as mixing; consequently,
projective geometry applies to the color qualities."

Given the above considerations, another of Weyl's remarks might strike
one as quite prescient: "Epistemologically it is not without interest
that in addition to ordinary space there exists quite another domain
of intuitively given entities, namely the colors, which forms a
continuum capable of geometric treatment."

Brian J Flanagan

Aug10-04, 11:41 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Previous contributors wrote:\n\n> > The dualities referred to in the foregoing are akin to those found in\n> > projective geometry. Bearing in mind the manifest symmetries of the\n> > secondary properties of observation (viz., color, sound, and the\n> > like), which are only "hidden" in plain view, it is intriguing to\n> > consider the correspondence between the manifold of color vectors and\n> > the axioms of vector geometry, as noted by Weyl: "Thus the colors with\n> > their various qualities and intensities fulfill the axioms of vector\n> > geometry if addition is interpreted as mixing; consequently,\n> > projective geometry applies to the color qualities."\n>\n> So I if I am getting this right, you are saying, as long as there is\n> some correspondance to projective geometry (has it been found?) that M\n> Theory will be of value?\n\nI\'m not sure I understand your question. There is a direct\ncorrespondence via Calabi-Yau:\n\n"Actually, it is known in the mathematical literature, that all\nCalabi-Yau spaces can be defined as (intersection of) hypersurfaces in\nweighted projective spaces."\n\nhttp://fisica.usac.edu.gt/public/curccaf_proc/quevedo1/node6.html\n\nSee also:\n\nhttp://www.th.physik.uni-bonn.de/th/Supplements/cy.html\n\nhttp://www.sciencesbookreview.com/Calabi_Yau_Manifolds_A_Bestiary_for_Physicists_981 021927X.html\n\nIt is interesting to note in this connection that the manifold of\ncolors appears to fiber over the 4D spacetime manifold *as observed.*\nI place a special emphasis here because one typically encounters\nstatements in the literature to the effect that the observed universe\nis 4D -- but that is manifestly not the case: Without the manifold of\ncolors, 4D spacetime would be quite literally invisible to us. 4D is\nthus an abstraction of the world as given to us in everyday\nobservation. (Notice that, should this interpretation stand up to\ninspection -- sorry, I can\'t help myself -- it would remove the\noutstanding objection to string/M-theory, viz., its failure to make\ncontact with observation.)\n\nWell, but perhaps this is all out in left field? Maybe so, but at\nleast I\'m in good company:\n\n"... so few and far between are the occasions for forming notions\nwhose specialisations make up a continuous manifoldness, that the only\nsimple notions whose specialisations form a multiply extended\nmanifoldness are the positions of perceived objects and colours. More\nfrequent occasions for the creation and development of these notions\noccur first in the higher mathematic.\n\nDefinite portions of a manifoldness, distinguished by a mark or a\nboundary, are called Quanta ..." (Riemann)\n\nhttp://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/WKCGeom.html\n\n"The characteristic of an n-dimensional manifold is that each of the\nelements composing it (in our examples, single points, conditions of a\ngas, colours, tones) may be specified by the giving of n quantities,\nthe "co-ordinates," which are continuous functions within the\nmanifold." (Weyl, \'Space-time-matter\')\n\n\nThere is also, of course, Cartan\'s projective geometric approach to\nrelativity:\n\nhttp://encyclopedia.thefreedictionary.com/Elie%20Cartan\n\n(I\'ve just now cracked a rather advanced text on \'Geometric\nQuantization in Action,\' by Hurt, who notes at the outset that\n"everything is found in Cartan.")\n\nA. Magnon and A. Ashtekar, Translation from French of Elie Cartan\'s\nwork, "Sur les Varietes a Connexion Affine et la Relativite Generale"*\nwith a Commentary and Foreword by A. Trautman.\n\nhttp://cgpg.gravity.psu.edu/people/Ashtekar/publications.html\n\n\n* \'On the Varieties of Affine Connections and General Relativity\'\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Previous contributors wrote:

> > The dualities referred to in the foregoing are akin to those found in
> > projective geometry. Bearing in mind the manifest symmetries of the
> > secondary properties of observation (viz., color, sound, and the
> > like), which are only "hidden" in plain view, it is intriguing to
> > consider the correspondence between the manifold of color vectors and
> > the axioms of vector geometry, as noted by Weyl: "Thus the colors with
> > their various qualities and intensities fulfill the axioms of vector
> > geometry if addition is interpreted as mixing; consequently,
> > projective geometry applies to the color qualities."
>
> So I if I am getting this right, you are saying, as long as there is
> some correspondance to projective geometry (has it been found?) that M
> Theory will be of value?

I'm not sure I understand your question. There is a direct
correspondence via Calabi-Yau:

"Actually, it is known in the mathematical literature, that all
Calabi-Yau spaces can be defined as (intersection of) hypersurfaces in
weighted projective spaces."

http://fisica.usac.edu.gt/public/curccaf_proc/quevedo1/node6.html

See also:

http://www.th.physik.uni-bonn.de/th/Supplements/cy.html

http://www.sciencesbookreview.com/Calabi_Yau_Manifolds_A_Bestiary_for_Physicists_981 021927X.html

It is interesting to note in this connection that the manifold of
colors appears to fiber over the 4D spacetime manifold *as observed.*
I place a special emphasis here because one typically encounters
statements in the literature to the effect that the observed universe
is 4D -- but that is manifestly not the case: Without the manifold of
colors, 4D spacetime would be quite literally invisible to us. 4D is
thus an abstraction of the world as given to us in everyday
observation. (Notice that, should this interpretation stand up to
inspection -- sorry, I can't help myself -- it would remove the
outstanding objection to string/M-theory, viz., its failure to make
contact with observation.)

Well, but perhaps this is all out in left field? Maybe so, but at
least I'm in good company:

"... so few and far between are the occasions for forming notions
whose specialisations make up a continuous manifoldness, that the only
simple notions whose specialisations form a multiply extended
manifoldness are the positions of perceived objects and colours. More
frequent occasions for the creation and development of these notions
occur first in the higher mathematic.

Definite portions of a manifoldness, distinguished by a mark or a
boundary, are called Quanta ..." (Riemann)

http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/WKCGeom.html

"The characteristic of an n-dimensional manifold is that each of the
elements composing it (in our examples, single points, conditions of a
gas, colours, tones) may be specified by the giving of n quantities,
the "co-ordinates," which are continuous functions within the
manifold." (Weyl, 'Space-time-matter')

There is also, of course, Cartan's projective geometric approach to
relativity:

http://encyclopedia.thefreedictionary.com/Elie%20Cartan

(I've just now cracked a rather advanced text on 'Geometric
Quantization in Action,' by Hurt, who notes at the outset that
"everything is found in Cartan.")

A. Magnon and A. Ashtekar, Translation from French of Elie Cartan's
work, "Sur les Varietes a Connexion Affine et la Relativite Generale"*
with a Commentary and Foreword by A. Trautman.

http://cgpg.gravity.psu.edu/people/Ashtekar/publications.html

* 'On the Varieties of Affine Connections and General Relativity'

Urs Schreiber

Aug12-04, 12:56 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Mon, 9 Aug 2004, Brian J Flanagan wrote:\n\n> from "SUPERMEMBRANES AND M(ATRIX) THEORY"\n>\n> Hermann Nicolai and Robert Helling\n> Max Planck Institut fur Gravitationsphysik\n> Albert-Einstein-Institut\n>\n> hep-th/9809103\n>\n> "Despite the recent excitement, however, we do not think that M(atrix)\n> theory and the d = 11 supermembrane in their present incarnation are\n> already the final answer in the search for M-Theory, even though they\n> probably are important pieces of the puzzle. There are still too many\n> ingredients missing that we would expect the final theory to possess.\n> [...] there should exist some huge and so far completely hidden\n> symmetries generalizing not only the duality symmetries of extended\n> supergravity and string theory, but also the principles underlying\n> general relativity."\n>\n> The dualities referred to in the foregoing are akin to those found in\n> projective geometry.\n\nDunno. But I am pretty sure that the "huge and so far completely hidden\nsymmetries" that Hermann Nicolai is alluding to are, at least by now,\nassumed by him to be those of exp(E10), roughly, where E10 is a hyperbolic\nKac-Moody algebra. There are some intriguing hints for this assumption.\nSearch the sps archive for "E10".\n\nLubos Motl has previously emphasized that he thinks it is not fruitful to\nsearch the "final theory" in terms of its symmetry group, the point being\nthat gauge groups seem to depend heavily on the perspective we have on a\ncertain theory, and that they may change, appear and disappear from other\npoints of view.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Mon, 9 Aug 2004, Brian J Flanagan wrote:

> from "SUPERMEMBRANES AND M(ATRIX) THEORY"
>
> Hermann Nicolai and Robert Helling
> Max Planck Institut fur Gravitationsphysik
> Albert-Einstein-Institut
>
> http://www.arxiv.org/abs/hep-th/9809103
>
> "Despite the recent excitement, however, we do not think that M(atrix)
> theory and the d = 11 supermembrane in their present incarnation are
> already the final answer in the search for M-Theory, even though they
> probably are important pieces of the puzzle. There are still too many
> ingredients missing that we would expect the final theory to possess.
> [...] there should exist some huge and so far completely hidden
> symmetries generalizing not only the duality symmetries of extended
> supergravity and string theory, but also the principles underlying
> general relativity."
>
> The dualities referred to in the foregoing are akin to those found in
> projective geometry.

Dunno. But I am pretty sure that the "huge and so far completely hidden
symmetries" that Hermann Nicolai is alluding to are, at least by now,
assumed by him to be those of \exp(E10), roughly, where E10 is a hyperbolic
Kac-Moody algebra. There are some intriguing hints for this assumption.
Search the sps archive for "E10".

Lubos Motl has previously emphasized that he thinks it is not fruitful to
search the "final theory" in terms of its symmetry group, the point being
that gauge groups seem to depend heavily on the perspective we have on a
certain theory, and that they may change, appear and disappear from other
points of view.

Brian J Flanagan

Aug13-04, 07:36 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Urs Schreiber wrote in message:\n\n> Dunno. But I am pretty sure that the "huge and so far completely hidden\n> symmetries" that Hermann Nicolai is alluding to are, at least by now,\n> assumed by him to be those of exp(E10), roughly, where E10 is a hyperbolic\n> Kac-Moody algebra. There are some intriguing hints for this assumption.\n> Search the sps archive for "E10".\n\nNews to me.\n\n> Lubos Motl has previously emphasized that he thinks it is not fruitful to\n> search the "final theory" in terms of its symmetry group, the point being\n> that gauge groups seem to depend heavily on the perspective we have on a\n> certain theory, and that they may change, appear and disappear from other\n> points of view.\n\nI\'ve not heard of Motl, but Weinberg says it seems pretty clear that\nthe symmetry group of nature is the deepest thing we understand about\nnature today.\n\n[Moderator\'s note: Maybe you\'ve heard of Seiberg? Gauge symmetry is just a\nredundancy, as he emphasizes all the time, and his examples with Seiberg\ndualities, Seiberg-Witten works, both the N=2 supersymmetric ones as well\nas the noncommutative gauge theory ones, are examples how a single theory\ncan have several descriptions with different gauge symmetries. The\nemergence of enhanced symmetries; their Higgsing and confinement are\nalso commonplace in string theory which includes all field-theoretical\nphysics mentioned above. Weinberg is describing the situation in physics\nabout 30 years ago which does not really take the new developments into\naccount. Symmetries are powerful, but gauge symmetries are neither\nuniquely determined by physics, nor they determine physics uniquely. LM ]\n\nGauge theory has been wonderfully successful, and then, if one assigns -a\nto a photon of a given color, but 180 degrees out of phase with photon a\nof the same color, adding them together gives back darkness, or no light,\nand "no color." (And clearly, adding "no color" to a gives back a.) We\nthen have a natural inverse element for every color under addition. The\nother group properties are quite evident at a glance, as are the group\nproperties of the other secondary quantities. I\'m rather pleased to have\nfigured this out, as it seems to have escaped Schrodinger. Also, now that\nwe\'ve introduced the phase of the photons, we are on our way to doing\ngauge theory, which, as Yang notes, really ought to be called phase\ntheory, but there it is.\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Urs Schreiber wrote in message:

> Dunno. But I am pretty sure that the "huge and so far completely hidden
> symmetries" that Hermann Nicolai is alluding to are, at least by now,
> assumed by him to be those of \exp(E10), roughly, where E10 is a hyperbolic
> Kac-Moody algebra. There are some intriguing hints for this assumption.
> Search the sps archive for "E10".

News to me.

> Lubos Motl has previously emphasized that he thinks it is not fruitful to
> search the "final theory" in terms of its symmetry group, the point being
> that gauge groups seem to depend heavily on the perspective we have on a
> certain theory, and that they may change, appear and disappear from other
> points of view.

I've not heard of Motl, but Weinberg says it seems pretty clear that
the symmetry group of nature is the deepest thing we understand about
nature today.

[Moderator's note: Maybe you've heard of Seiberg? Gauge symmetry is just a
redundancy, as he emphasizes all the time, and his examples with Seiberg
dualities, Seiberg-Witten works, both the N=2 supersymmetric ones as well
as the noncommutative gauge theory ones, are examples how a single theory
can have several descriptions with different gauge symmetries. The
emergence of enhanced symmetries; their Higgsing and confinement are
also commonplace in string theory which includes all field-theoretical
physics mentioned above. Weinberg is describing the situation in physics
about 30 years ago which does not really take the new developments into
account. Symmetries are powerful, but gauge symmetries are neither
uniquely determined by physics, nor they determine physics uniquely. LM ]

Gauge theory has been wonderfully successful, and then, if one assigns -a
to a photon of a given color, but 180 degrees out of phase with photon a
of the same color, adding them together gives back darkness, or no light,
and "no color." (And clearly, adding "no color" to a gives back a.) We
then have a natural inverse element for every color under addition. The
other group properties are quite evident at a glance, as are the group
properties of the other secondary quantities. I'm rather pleased to have
figured this out, as it seems to have escaped Schrodinger. Also, now that
we've introduced the phase of the photons, we are on our way to doing
gauge theory, which, as Yang notes, really ought to be called phase
theory, but there it is.

A.J. Tolland

Aug13-04, 11:59 PM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Fri, 13 Aug 2004, Brian J Flanagan wrote:\n\n> [Moderator\'s note: Maybe you\'ve heard of Seiberg? Gauge symmetry is just a\n> redundancy, as he emphasizes all the time ... -LM ]\n\nIt\'s often difficult to write down a theory with explicit symmetry\nwithout also introducing a gauge symmetry... should we regard this as\nsimply an artifact of quantization?\n\n--A.J.\n\n[Moderator\'s note: In perturbative string theory it is easy to show that\na global continuous symmetry is always extended into a local, gauge\nsymmetry. Well, you multiply the current by a standard operator to obtain\na vertex operator for the gauge boson. Morally it is believed to be the\ncase nonperturbatively, too. At least as far as I know. A local symmetry\nmay resemble a global symmetry if the coupling of the corresponding\ngauge group goes to zero, but it\'s not always possible. Otherwise in\nfield theory I disagree with you; it is very easy to construct theories\nwith global symmetries which are not local. For example, the Standard\nModel with identical masses across the generations has a generational\nSU(3) which is not local. LM]\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Fri, 13 Aug 2004, Brian J Flanagan wrote:

> [Moderator's note: Maybe you've heard of Seiberg? Gauge symmetry is just a
> redundancy, as he emphasizes all the time ... -LM ]

It's often difficult to write down a theory with explicit symmetry
without also introducing a gauge symmetry... should we regard this as
simply an artifact of quantization?

--A.J.

[Moderator's note: In perturbative string theory it is easy to show that
a global continuous symmetry is always extended into a local, gauge
symmetry. Well, you multiply the current by a standard operator to obtain
a vertex operator for the gauge boson. Morally it is believed to be the
case nonperturbatively, too. At least as far as I know. A local symmetry
may resemble a global symmetry if the coupling of the corresponding
gauge group goes to zero, but it's not always possible. Otherwise in
field theory I disagree with you; it is very easy to construct theories
with global symmetries which are not local. For example, the Standard
Model with identical masses across the generations has a generational
SU(3) which is not local. LM]

Brian J Flanagan

Aug14-04, 12:05 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resizable=yes,status=no ,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Lubos Motl wrote:\n\n> Moderator\'s note: Maybe you\'ve heard of Seiberg? Gauge symmetry is just a\n> redundancy, as he emphasizes all the time, and his examples with Seiberg\n> dualities, Seiberg-Witten works, both the N=2 supersymmetric ones as well\n> as the noncommutative gauge theory ones, are examples how a single theory\n> can have several descriptions with different gauge symmetries. The\n> emergence of enhanced symmetries; their Higgsing and confinement are\n> also commonplace in string theory which includes all field-theoretical\n> physics mentioned above. Weinberg is describing the situation in physics\n> about 30 years ago which does not really take the new developments into\n> account. Symmetries are powerful, but gauge symmetries are neither\n> uniquely determined by physics, nor [do] they determine physics\n> uniquely. LM\n\nWell, what a learned soul! Your points are familiar, as is Seiberg --\nif mostly by reputation. I am inclined at present to pursue a simpler\nline, stressing familiar symmetries. Indeed, it is the very simplicity\nof these notions which suggests to me that they may hold some\ninterest. I hope you will continue to bring the rest of us up to\nspeed, as time permits.\n\nHere are some helpful links to related material, including what is\nsometimes called Seiberg-Witten gauge theory:\n\nwww.math.ist.utl.pt/~cfloren/NTyurinDoklad.pdf\nhttp://64.233.167.104/search?q=cache:Kg6JM8n0WT0J:www.math.ist.utl.pt/~cfloren/NTyurinDoklad.pdf+gauge+seiberg-witten&hl=en\nhttp://www.wordiq.com/definition/Gauge_theory\nhttp://arxiv.org/PS_cache/hep-th/pdf/9611/9611190.pdf\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>Lubos Motl wrote:

> Moderator's note: Maybe you've heard of Seiberg? Gauge symmetry is just a
> redundancy, as he emphasizes all the time, and his examples with Seiberg
> dualities, Seiberg-Witten works, both the N=2 supersymmetric ones as well
> as the noncommutative gauge theory ones, are examples how a single theory
> can have several descriptions with different gauge symmetries. The
> emergence of enhanced symmetries; their Higgsing and confinement are
> also commonplace in string theory which includes all field-theoretical
> physics mentioned above. Weinberg is describing the situation in physics
> about 30 years ago which does not really take the new developments into
> account. Symmetries are powerful, but gauge symmetries are neither
> uniquely determined by physics, nor [do] they determine physics
> uniquely. LM

Well, what a learned soul! Your points are familiar, as is Seiberg --
if mostly by reputation. I am inclined at present to pursue a simpler
line, stressing familiar symmetries. Indeed, it is the very simplicity
of these notions which suggests to me that they may hold some
interest. I hope you will continue to bring the rest of us up to
speed, as time permits.

Here are some helpful links to related material, including what is
sometimes called Seiberg-Witten gauge theory:

www.math.ist.utl.pt/~cfloren/NTyurinDoklad.pdf
http://64.233.167.104/search?q=cache:Kg6JM8n0WT0J:www.math.ist.utl.pt/~cfloren/NTyurinDoklad.pdf+gauge+seiberg-witten&hl=en
http://www.wordiq.com/definition/Gauge_theory
http://arxiv.org/PS_cache/hep-th/pdf/9611/9611190.pdf